Showing 1–50 of 70 results for author: Sinha, A

Hidden Ising models from the generalized Yang-Baxter equation

Authors: Akash Sinha, Somnath Maity, Pramod Padmanabhan, Vladimir Korepin

Abstract: We introduce a one dimensional spin $\frac{1}{2}$ Hamiltonian with multi-site interactions, but still local. The algebra of its Hamiltonian densities resembles that of the transverse field Ising model. Using this fact we show that its spectrum is free-fermionic but with a huge degeneracy for each level. The source of the degeneracy is a set of local conserved quantities that act like a classical b… ▽ More We introduce a one dimensional spin $\frac{1}{2}$ Hamiltonian with multi-site interactions, but still local. The algebra of its Hamiltonian densities resembles that of the transverse field Ising model. Using this fact we show that its spectrum is free-fermionic but with a huge degeneracy for each level. The source of the degeneracy is a set of local conserved quantities that act like a classical background field for the quantum system. The thermodynamics of this system is contrasted with the standard Ising model. At the gapless points in the energy spectrum, we show that this system can be derived from the quantum inverse scattering method adapted to a multi-site generalization of the Yang-Baxter equation as introduced by E. Rowell and Z. Wang. The $R$-matrix is constructed using generators of extraspecial 2-groups. This helps us extract all the conserved charges and lay the framework for a general mechanism to generate such multi-site interaction spin systems that are transverse field Ising models under the hood. A remark on how to obtain P. Fendley's free-fermion in disguise models in this formalism is also included. △ Less

Submitted 28 May, 2026; originally announced May 2026.

Comments: 19 pages + References + Appendices, 7 figures

Photon-energy-programmable subnanometric electron birth-site control

Authors: Hirofumi Yanagisawa, Abhisek Sinha, Ravi Kumar, Neill Lambert, Hirotaka Kitoh-Nishioka

Abstract: Optical control of electron-generation sites has broadly enabled ultrafast nanoscale imaging, spectroscopy, and functional control. Existing approaches achieve nanoscale site selectivity by shaping localised optical fields around nanostructures, thereby limiting independent site selectivity within the same local-field hotspot. Here, using a single-molecule electron emitter, we show that site selec… ▽ More Optical control of electron-generation sites has broadly enabled ultrafast nanoscale imaging, spectroscopy, and functional control. Existing approaches achieve nanoscale site selectivity by shaping localised optical fields around nanostructures, thereby limiting independent site selectivity within the same local-field hotspot. Here, using a single-molecule electron emitter, we show that site selectivity can instead be encoded in the electronic excitation pathway, enabling subnanometric control of electron birth sites within the same local-field hotspot. By tuning the photon energy, we selectively access molecular states of different spatial symmetry and reversibly switch the electron birth site between distinct locations in the same emitter, with the change read out directly in the far-field emission pattern. The switching depends on photon energy alone and is absent under variations in intensity or polarisation. Our results establish optical birth-site selectivity that is not dictated by the local-field distribution, opening a route to electron birth-site control through the electronic excitation pathway. △ Less

Submitted 27 May, 2026; originally announced May 2026.

Cosmological Correlators Using Tensor Networks

Authors: Ujjwal Basumatary, Aninda Sinha, Xinan Zhou

Abstract: We develop a nonperturbative tensor-network framework for computing cosmological correlators in de Sitter space and use it to test the proposal that suitably defined in-in correlators can be obtained from an in-out formalism by gluing the expanding and contracting Poincaré patches. Focusing on interacting $1+1$-dimensional $φ^4$ theory, we formulate finite-time lattice observables using Matrix Pro… ▽ More We develop a nonperturbative tensor-network framework for computing cosmological correlators in de Sitter space and use it to test the proposal that suitably defined in-in correlators can be obtained from an in-out formalism by gluing the expanding and contracting Poincaré patches. Focusing on interacting $1+1$-dimensional $φ^4$ theory, we formulate finite-time lattice observables using Matrix Product State (MPS) techniques and analyze the regulator subtleties associated with the singular behavior near the patching surface. Within this regulated framework, we find controlled nonperturbative evidence for the proposed relation between in-in and in-out correlators in several examples. We also find suggestive evidence that the perturbative obstructions present for sufficiently light fields can be softened nonperturbatively, albeit in a regime of substantially larger entanglement. A central outcome of our analysis is an entanglement-based picture of the computation: for in-in evolution the entanglement remains modest and can decrease toward late times, whereas in the patched in-out set-up it grows significantly after the gluing slice. Thus, although the in-out formalism is perturbatively economical, the in-in formulation is numerically more favorable. We briefly discuss how the same strategy extends to low-angular-momentum sectors in $3+1$ dimensions, and why regimes of rapid entanglement growth may eventually motivate quantum-computing implementations. △ Less

Submitted 19 June, 2026; v1 submitted 27 March, 2026; originally announced March 2026.

Comments: v2: 51 pages, 11 figures, clarifications added

Talking with a ghost: semi-virtual coupled levitated oscillators

Authors: Ronghao Yin, Yugang Ren, Deok Young Seo, Anoushka Sinha, Jonathan D. Pritchett, Qiongyuan Wu, James Millen

Abstract: Mesoscopic particles levitated by optical, electrical or magnetic fields act as mechanical oscillators with a range of surprising properties, such as tuneable oscillation frequencies, access to rotational motion, and remarkable quality factors. Coupled levitated particles display rich dynamics and non-reciprocal interactions, with applications in sensing and the exploration of non-equilibrium and… ▽ More Mesoscopic particles levitated by optical, electrical or magnetic fields act as mechanical oscillators with a range of surprising properties, such as tuneable oscillation frequencies, access to rotational motion, and remarkable quality factors. Coupled levitated particles display rich dynamics and non-reciprocal interactions, with applications in sensing and the exploration of non-equilibrium and quantum physics. In this work, we present a single levitated particle displaying coupled-oscillator dynamics by generating an interaction with a virtual or ``ghost'' particle. This ghost levitated particle is simulated on an analogue computer, and its properties can thus be dynamically varied. Our work represents a new angle on measurement-based bath engineering and physical simulation and, in the future, could lead to the generation of novel cooling mechanisms and complex physical simulation. △ Less

Submitted 27 January, 2026; v1 submitted 22 December, 2025; originally announced December 2025.

Comments: 16 pages, 7 figures, Comments are welcome!

Journal ref: Photonics 2026, 13(2), 117

Lectures on Quantum Field Theory on a Quantum Computer

Authors: Aninda Sinha, Ujjwal Basumatary

Abstract: The lecture notes cover the basics of quantum computing methods for quantum field theory applications. No detailed knowledge of either quantum computing or quantum field theory is assumed and we have attempted to keep the material at a pedagogical level. We review the anharmonic oscillator, using which we develop a hands-on treatment of certain interesting QFTs in $1+1D$: $φ^4$ theory, Ising field… ▽ More The lecture notes cover the basics of quantum computing methods for quantum field theory applications. No detailed knowledge of either quantum computing or quantum field theory is assumed and we have attempted to keep the material at a pedagogical level. We review the anharmonic oscillator, using which we develop a hands-on treatment of certain interesting QFTs in $1+1D$: $φ^4$ theory, Ising field theory, and the Schwinger model. We review quantum computing essentials as well as tensor network techniques. The latter form an essential part for quantum computing benchmarking. Some error modelling on QISKIT is also done in the hope of anticipating runs on NISQ devices. These lecture notes are the expanded version of a one semester course taught by AS during August-November 2025 at the Indian Institute of Science and TA-ed by UB. The programs written for this course are available in a GitHub repository. △ Less

Submitted 2 December, 2025; originally announced December 2025.

Comments: 195 pages, many figures. Comments welcome

Noninvertible Kramers-Wannier duality symmetries for the discrete-time quantum Ising chain

Authors: Akash Sinha, Pramod Padmanabhan, Vladimir Korepin

Abstract: Integrable trotterization} provides a method to evolve a continuous time integrable many-body system in discrete time, such that it retains its conserved quantities. Here we explicitly show that the first order trotterization of the critical {\it transverse field Ising model} is integrable. The discrete time conserved quantities are obtained from an inhomogeneous transfer matrix constructed using… ▽ More Integrable trotterization} provides a method to evolve a continuous time integrable many-body system in discrete time, such that it retains its conserved quantities. Here we explicitly show that the first order trotterization of the critical {\it transverse field Ising model} is integrable. The discrete time conserved quantities are obtained from an inhomogeneous transfer matrix constructed using the {\it quantum inverse scattering method}. The inhomogeneity parameter determines the discrete time step. We then focus on the non-invertible {\it Kramers-Wannier} duality-symmetry for the trotterized evolution. We find that the discretization of both space and time leads to a doubling of these duality operators. They account for discrete translations in both space and time. As an interesting application, we find that these operators also provide maps between trotterizations of different orders. This helps us extend our results beyond the trotterization scheme and investigate the Kramers-Wannier duality-symmetry for finite time Floquet evolution of the critical transverse field Ising chain. {Finally, we investigate how these non-invertible operators shape the phase diagram of the discrete-time evolution. This question is particularly interesting in the Floquet setting, which is known to host a richer phase structure than its undriven counterpart. We systematically construct the necessary operators which relate different phases away from criticality for both trotterized and Floquet evolutions. △ Less

Submitted 24 June, 2026; v1 submitted 5 November, 2025; originally announced November 2025.

Comments: 8 pages + Refs + Appendices ; v2 12 pages + Refs + Appendices, Includes discussion of KW duality for Floquet evolution of the TFIM, close to the published version

Journal ref: Phys. Rev. B 113, 235141 (2026)

Finite temperature dopant-induced spin reorganization explored via tensor networks in the two-dimensional $t$-$J$ model

Authors: Yintai Zhang, Aritra Sinha, Marek M. Rams, Jacek Dziarmaga

Abstract: We study the two-dimensional $t$--$J$ model at finite temperature directly in the thermodynamic limit using purification represented by an infinite projected entangled-pair state (iPEPS). We reach temperatures down to $T/t=0.1$ and hole concentrations up to $1-n\simeq0.25$, and provide benchmark thermodynamic-limit results for the specific heat, uniform susceptibility, and charge compressibility.… ▽ More We study the two-dimensional $t$--$J$ model at finite temperature directly in the thermodynamic limit using purification represented by an infinite projected entangled-pair state (iPEPS). We reach temperatures down to $T/t=0.1$ and hole concentrations up to $1-n\simeq0.25$, and provide benchmark thermodynamic-limit results for the specific heat, uniform susceptibility, and charge compressibility. We identify a susceptibility maximum $T^\ast$ that tracks the buildup of short-range antiferromagnetism and a shallow compressibility enhancement upon cooling in the same doping window. To expose the underlying microscopic mechanism, we introduce dopant-conditioned multi-point correlators that quantify how holes reorganize nearby exchange: single holes weaken adjacent antiferromagnetic bonds, while nearest-neighbor hole pairs produce a cooperative response that reinforces antiferromagnetism on the parallel plaquette edge. Over the same parameter window, $d$-wave pairing correlations remain short-ranged. These results provide experiment-compatible thermodynamic-limit benchmarks and establish dopant-conditioned correlators as incisive probes of finite-temperature spin-texture reorganization in doped Mott insulators. △ Less

Submitted 11 February, 2026; v1 submitted 6 October, 2025; originally announced October 2025.

Comments: 15 pages, 14 figures

Report number: Phys. Rev. B 113, 085113

The Yang-Baxter integrability of the critical Ising chain

Authors: Akash Sinha, Tinu Justin, Pramod Padmanabhan, Vladimir Korepin

Abstract: We show that the one dimensional, critical transverse field Ising model is Yang-Baxter integrable. This is done by constructing commuting transfer matrices built out of a $R$-matrix satisfying the Yang-Baxter equation with additive spectral parameters. The $R$-matrix is non-local, as it is expressed in terms of Majorana fermions. It is also non-regular. Nevertheless, we show that the quantum inver… ▽ More We show that the one dimensional, critical transverse field Ising model is Yang-Baxter integrable. This is done by constructing commuting transfer matrices built out of a $R$-matrix satisfying the Yang-Baxter equation with additive spectral parameters. The $R$-matrix is non-local, as it is expressed in terms of Majorana fermions. It is also non-regular. Nevertheless, we show that the quantum inverse scattering method can still be suitably adapted. We then recursively obtain the conserved quantities [in the infinite volume] by the boost operator method. Remarkably, among the conserved charges we also find the Kramers-Wannier duality and other non-invertible symmetries for the periodic transverse field Ising model. △ Less

Submitted 10 October, 2025; v1 submitted 4 June, 2025; originally announced June 2025.

Comments: v3 closer to the published version 29 pages + appendices + references

Journal ref: J. Stat. Mech. (2025) 103102

Probing the Topological Anderson Transition in Quasiperiodic Photonic Lattices via Chiral Displacement and Wavelength Tuning

Authors: Abhinav Sinha, Trideb Shit, Avinash Tetarwal, Diptiman Sen, Sebabrata Mukherjee

Abstract: The interplay of topology and disorder in quantum dynamics has recently attracted significant attention across diverse platforms, including solid-state devices, ultracold atoms, and photonic systems. Here, we report on a topological Anderson transition caused by quasiperiodic modulation of the stronger intra-cell couplings in photonic Su-Schrieffer-Heeger lattices. As the quasiperiodic strength is… ▽ More The interplay of topology and disorder in quantum dynamics has recently attracted significant attention across diverse platforms, including solid-state devices, ultracold atoms, and photonic systems. Here, we report on a topological Anderson transition caused by quasiperiodic modulation of the stronger intra-cell couplings in photonic Su-Schrieffer-Heeger lattices. As the quasiperiodic strength is varied, the system exhibits a reentrant transition from a trivial phase to a topological phase and back to a trivial phase, accompanied by the closing and reopening of the band gap around zero energy. Unlike the traditional detection of photonic topological edge modes, we measure the mean chiral displacement from the transport of light in the bulk of the lattices. In our photonic lattices with a fixed length, the propagation dynamics is retrieved by varying the wavelength of light, which tunes the inter-waveguide couplings. △ Less

Submitted 8 July, 2025; v1 submitted 10 March, 2025; originally announced March 2025.

Comments: Comments are welcome. Accepted in Phys. Rev. A

Journal ref: Phys. Rev. A 112, 013512 (2025)

Certified Random Number Generation using Quantum Computers

Authors: Pingal Pratyush Nath, Aninda Sinha, Urbasi Sinha

Abstract: In recent decades, quantum technologies have made significant strides toward achieving quantum utility. However, practical applications are hindered by challenges related to scaling the number of qubits and the depth of circuits. In this paper, we investigate how current quantum computers can be leveraged for practical applications, particularly in generating secure random numbers certified by Qua… ▽ More In recent decades, quantum technologies have made significant strides toward achieving quantum utility. However, practical applications are hindered by challenges related to scaling the number of qubits and the depth of circuits. In this paper, we investigate how current quantum computers can be leveraged for practical applications, particularly in generating secure random numbers certified by Quantum Mechanics. While random numbers can be generated and certified in a device-independent manner through the violation of Bell's inequality, this method requires significant spatial separation to satisfy the no-signaling condition, making it impractical for implementation on a single quantum computer. Instead, we employ temporal correlations to generate randomness by violating the Leggett-Garg inequality, which relies on the No-Signaling in Time condition to certify randomness, thus overcoming spatial constraints. By applying this protocol to existing quantum computers, we demonstrate the feasibility of secure, semi-device-independent random number generation using low-depth circuits with single-qubit gates. △ Less

Submitted 5 February, 2025; originally announced February 2025.

Journal ref: Front. Quantum Sci. Technol. 4:1661544.(2025)

Observation of emergent scaling of spin-charge correlations at the onset of the pseudogap

Authors: Thomas Chalopin, Petar Bojović, Si Wang, Titus Franz, Aritra Sinha, Zhenjiu Wang, Dominik Bourgund, Johannes Obermeyer, Fabian Grusdt, Annabelle Bohrdt, Lode Pollet, Alexander Wietek, Antoine Georges, Timon Hilker, Immanuel Bloch

Abstract: In strongly correlated materials, interacting electrons are entangled and form collective quantum states, resulting in rich low-temperature phase diagrams. Notable examples include cuprate superconductors, in which superconductivity emerges at low doping out of an unusual "pseudogap" metallic state above the critical temperature. The Fermi-Hubbard model, describing a wide range of phenomena associ… ▽ More In strongly correlated materials, interacting electrons are entangled and form collective quantum states, resulting in rich low-temperature phase diagrams. Notable examples include cuprate superconductors, in which superconductivity emerges at low doping out of an unusual "pseudogap" metallic state above the critical temperature. The Fermi-Hubbard model, describing a wide range of phenomena associated with strong electron correlations, still offers major computational challenges despite its simple formulation. In this context, ultracold atoms quantum simulators have provided invaluable insights into the microscopic nature of correlated quantum states. Here, we use a quantum gas microscope Fermi-Hubbard simulator to explore a wide range of dopings and temperatures in a regime where a pseudogap is known to develop. By measuring multi-point correlation functions up to fifth order, we uncover a novel universal scaling behaviour in magnetic and higher-order spin-charge correlations characterised by a doping-dependent temperature scale. Accurate comparisons with determinant Quantum Monte Carlo and Minimally Entangled Typical Thermal States simulations confirm that this temperature scale is comparable to the pseudogap temperature T*. Our quantitative findings reveal a novel qualitative behaviour of magnetic properties and spin-charge correlations in an emergent pseudogap and pave the way towards the exploration of charge pairing and collective phenomena expected at lower temperatures. △ Less

Submitted 27 January, 2026; v1 submitted 23 December, 2024; originally announced December 2024.

Comments: 8 + 11 pages, 5 + 10 figures. Accepted version

Pseudo-Hermitian extensions of the harmonic and isotonic oscillators

Authors: Aritra Ghosh, Akash Sinha

Abstract: In this work, we describe certain pseudo-Hermitian extensions of the harmonic and isotonic oscillators, both of which are exactly-solvable models in quantum mechanics. By coupling the dynamics of a particle moving in a one-dimensional potential to an imaginary-valued gauge field, it is possible to obtain certain pseudo-Hermitian extensions of the original (Hermitian) problem. In particular, it is… ▽ More In this work, we describe certain pseudo-Hermitian extensions of the harmonic and isotonic oscillators, both of which are exactly-solvable models in quantum mechanics. By coupling the dynamics of a particle moving in a one-dimensional potential to an imaginary-valued gauge field, it is possible to obtain certain pseudo-Hermitian extensions of the original (Hermitian) problem. In particular, it is pointed out that the Swanson oscillator arises as such an extension of the quantum harmonic oscillator. For the pseudo-Hermitian extensions of the harmonic and isotonic oscillators, we explicitly solve for the wavefunctions in the position representation and also explore their intertwining relations. △ Less

Submitted 16 January, 2025; v1 submitted 2 August, 2024; originally announced August 2024.

Comments: Based on talk delivered at the Xth International Workshop on New Challenges in Quantum Mechanics: Graphene, Supersymmetry, and Mathematical Physics (2024); v2: Some errors corrected; v3: Final version

Journal ref: J. Phys.: Conf. Ser. 2986, 012004 (2025)

Unitary tetrahedron quantum gates

Authors: Vivek Kumar Singh, Akash Sinha, Pramod Padmanabhan, Vladimir Korepin

Abstract: Quantum simulations of many-body systems using 2-qubit Yang-Baxter gates offer a benchmark for quantum hardware. This can be extended to the higher dimensional case with $n$-qubit generalisations of Yang-Baxter gates called $n$-simplex operators. Such multi-qubit gates potentially lead to shallower and more efficient quantum circuits as well. Finding them amounts to identifying unitary solutions o… ▽ More Quantum simulations of many-body systems using 2-qubit Yang-Baxter gates offer a benchmark for quantum hardware. This can be extended to the higher dimensional case with $n$-qubit generalisations of Yang-Baxter gates called $n$-simplex operators. Such multi-qubit gates potentially lead to shallower and more efficient quantum circuits as well. Finding them amounts to identifying unitary solutions of the $n$-simplex equations, the building blocks of higher dimensional integrable systems. These are a set of highly non-linear and over determined system of equations making it notoriously hard to solve even when the local Hilbert spaces are spanned by qubits. We systematically overcome this for higher simplex operators constructed using two methods: from Clifford algebras and by lifting Yang-Baxter operators. The $n=3$ or the tetrahedron case is analyzed in detail. For the qubit case our methods produce 13 inequivalent families of unitary tetrahedron operators. 12 of these families are obtained by appending the 5 unitary families of 4 by 4 constant Yang-Baxter operators of Dye-Hietarinta, with a single qubit operator. As applications, universal sets of single, two and three qubit gates are realized using such unitary tetrahedron operators. The ideas presented in this work can be naturally extended to the higher simplex cases. △ Less

Submitted 25 July, 2024; v1 submitted 15 July, 2024; originally announced July 2024.

Comments: 34 pages of main text + 4 pages of appendices + 8 pages of references; v2 Fixed minor typos, updated Acknowledgments

Toffoli gates solve the tetrahedron equations

Authors: Akash Sinha, Pramod Padmanabhan, Vladimir Korepin

Abstract: The circuit model of quantum computation can be interpreted as a scattering process. In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation and are potentially less noisy. These are realized through Yang-Baxter or 2-simplex operators. A natural question is to extend this construction to higher qubit gates, like the Toffoli ga… ▽ More The circuit model of quantum computation can be interpreted as a scattering process. In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation and are potentially less noisy. These are realized through Yang-Baxter or 2-simplex operators. A natural question is to extend this construction to higher qubit gates, like the Toffoli gates, which also lead to universal quantum computation but with shallower circuits. We show that unitary families of such operators are constructed by the 3-dimensional generalizations of the Yang-Baxter operators known as tetrahedron or 3-simplex operators. The latter satisfy a spectral parameter-dependent tetrahedron equation. This construction goes through for $n$-Toffoli gates realized using $n$-simplex operators. △ Less

Submitted 26 May, 2024; originally announced May 2024.

Comments: 8 pages + References

YASTN: Yet another symmetric tensor networks; A Python library for abelian symmetric tensor network calculations

Authors: Marek M. Rams, Gabriela Wójtowicz, Aritra Sinha, Juraj Hasik

Abstract: We present an open-source tensor network Python library for quantum many-body simulations. At its core is an abelian-symmetric tensor, implemented as a sparse block structure managed by logical layer on top of dense multi-dimensional array backend. This serves as the basis for higher-level tensor networks algorithms, operating on matrix product states and projected entangled pair states, implement… ▽ More We present an open-source tensor network Python library for quantum many-body simulations. At its core is an abelian-symmetric tensor, implemented as a sparse block structure managed by logical layer on top of dense multi-dimensional array backend. This serves as the basis for higher-level tensor networks algorithms, operating on matrix product states and projected entangled pair states, implemented here. Using appropriate backend, such as PyTorch, gives direct access to automatic differentiation (AD) for cost-function gradient calculations and execution on GPUs or other supported accelerators. We show the library performance in simulations with infinite projected entangled-pair states, such as finding the ground states with AD, or simulating thermal states of the Hubbard model via imaginary time evolution. We quantify sources of performance gains in those challenging examples allowed by utilizing symmetries. △ Less

Submitted 20 May, 2024; originally announced May 2024.

Comments: 10 pages, 6 figures, source code at https://github.com/yastn/yastn

Journal ref: SciPost Phys. Codebases 52 (2025)

Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator

Authors: Akash Sinha, Aritra Ghosh, Bijan Bagchi

Abstract: Motivated by the structure of the Swanson oscillator which is a well-known example of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian, we propose a fermionic extension of such a scheme which incorporates two fermionic oscillators together with bilinear-coupling terms that do not conserve particle number. We determine the eigenvalues and eigenvectors… ▽ More Motivated by the structure of the Swanson oscillator which is a well-known example of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian, we propose a fermionic extension of such a scheme which incorporates two fermionic oscillators together with bilinear-coupling terms that do not conserve particle number. We determine the eigenvalues and eigenvectors, and expose the appearance of exceptional points where two of the eigenstates coalesce with the corresponding eigenvectors exhibiting self-orthogonality with respect to the bi-orthogonal inner product. The model admits a quantum phase transition - we discuss the two phases and also demonstrate that the ground-state entanglement entropy exhibits a discontinuous jump indicating the transition between the two phases. △ Less

Submitted 4 September, 2024; v1 submitted 30 January, 2024; originally announced January 2024.

Comments: v1: Comments are welcome; v2: This version contains some new calculations and corrects some errors from the older version; v3: Substantially revised and to appear in Physica Scripta

Nav-Q: Quantum Deep Reinforcement Learning for Collision-Free Navigation of Self-Driving Cars

Authors: Akash Sinha, Antonio Macaluso, Matthias Klusch

Abstract: The task of collision-free navigation (CFN) of self-driving cars is an NP-hard problem usually tackled using Deep Reinforcement Learning (DRL). While DRL methods have proven to be effective, their implementation requires substantial computing resources and extended training periods to develop a robust agent. On the other hand, quantum reinforcement learning has recently demonstrated faster converg… ▽ More The task of collision-free navigation (CFN) of self-driving cars is an NP-hard problem usually tackled using Deep Reinforcement Learning (DRL). While DRL methods have proven to be effective, their implementation requires substantial computing resources and extended training periods to develop a robust agent. On the other hand, quantum reinforcement learning has recently demonstrated faster convergence and improved stability in simple, non-real-world environments. In this work, we propose Nav-Q, the first quantum-supported DRL algorithm for CFN of self-driving cars, that leverages quantum computation for improving the training performance without the requirement for onboard quantum hardware. Nav-Q is based on the actor-critic approach, where the critic is implemented using a hybrid quantum-classical algorithm suitable for near-term quantum devices. We assess the performance of Nav-Q using the CARLA driving simulator, a de facto standard benchmark for evaluating state-of-the-art DRL methods. Our empirical evaluations showcase that Nav-Q surpasses its classical counterpart in terms of training stability and, in certain instances, with respect to the convergence rate. Furthermore, we assess Nav-Q in relation to effective dimension, unveiling that the incorporation of a quantum component results in a model with greater descriptive power compared to classical baselines. Finally, we evaluate the performance of Nav-Q using noisy quantum simulation, observing that the quantum noise deteriorates the training performances but enhances the exploratory tendencies of the agent during training. △ Less

Submitted 23 December, 2023; v1 submitted 20 November, 2023; originally announced November 2023.

Comments: 28 pages, 12 figures, 4 tables

Efficient Representation of Minimally Entangled Typical Thermal States in two dimensions via Projected Entangled Pair States

Authors: Aritra Sinha, Marek M. Rams, Jacek Dziarmaga

Abstract: The Minimally Entangled Typical Thermal States (METTS) are an ensemble of pure states, equivalent to the Gibbs thermal state, that can be efficiently represented by tensor networks. In this article, we use the Projected Entangled Pair States (PEPS) ansatz as to represent METTS on a two-dimensional (2D) lattice. While Matrix Product States (MPS) are less efficient for 2D systems due to their comple… ▽ More The Minimally Entangled Typical Thermal States (METTS) are an ensemble of pure states, equivalent to the Gibbs thermal state, that can be efficiently represented by tensor networks. In this article, we use the Projected Entangled Pair States (PEPS) ansatz as to represent METTS on a two-dimensional (2D) lattice. While Matrix Product States (MPS) are less efficient for 2D systems due to their complexity growing exponentially with the lattice size, PEPS provide a more tractable approach. To substantiate the prowess of PEPS in modeling METTS (dubbed as PEPS-METTS), we benchmark it against the purification method for the 2D quantum Ising model at its critical temperature. Our analysis reveals that PEPS-METTS achieves accurate long-range correlations with significantly lower bond dimensions. We further corroborate this finding in the 2D Fermi Hubbard model at half-filling. At a technical level, we introduce an efficient \textit{zipper} method to obtain PEPS boundary matrix product states needed to compute expectation values. The imaginary time evolution is performed with the neighbourhood tensor update. △ Less

Submitted 23 January, 2024; v1 submitted 12 October, 2023; originally announced October 2023.

Comments: 14 pages, 14 figures

Journal ref: Phys. Rev. B 109, 045136 (January 2024)

Demonstration of a Hardware-Independent Toolkit for Automated Quantum Subcircuit Synthesis

Authors: Elena R. Henderson, Jessie M. Henderson, Aviraj Sinha, Eric C. Larson, Mitchell A. Thornton

Abstract: The quantum computer has become contemporary reality, with the first two-qubit machine of mere decades ago transforming into cloud-accessible devices with tens, hundreds, or -- in a few cases -- even thousands of qubits. While such hardware is noisy and still relatively small, the increasing number of operable qubits raises another challenge: how to develop the now-sizeable quantum circuits execut… ▽ More The quantum computer has become contemporary reality, with the first two-qubit machine of mere decades ago transforming into cloud-accessible devices with tens, hundreds, or -- in a few cases -- even thousands of qubits. While such hardware is noisy and still relatively small, the increasing number of operable qubits raises another challenge: how to develop the now-sizeable quantum circuits executable on these machines. Preparing circuits manually for specifications of any meaningful size is at best tedious and at worst impossible, creating a need for automation. This article describes an automated quantum-software toolkit for synthesis, compilation, and optimization, which transforms classically-specified, irreversible functions into both technology-independent and technology-dependent quantum circuits. We also describe and analyze the toolkit's application to three situations -- quantum read-only memories, quantum random number generators, and quantum oracles -- and illustrate the toolkit's start-to-finish features, from the input of classical functions to the output of technology-dependent quantum circuits. Furthermore, we illustrate how the toolkit enables research beyond circuit synthesis, including comparison of synthesis and optimization methods and deeper understanding of even well-studied quantum algorithms. As quantum hardware continues to develop, such quantum circuit toolkits will play a critical role in realizing its potential. △ Less

Submitted 8 February, 2024; v1 submitted 2 September, 2023; originally announced September 2023.

Comments: 48 pages, 23 figures, 20 tables

Disorder-free localisation in continuous-time quantum walks : Role of symmetries

Authors: A. P. Balachandran, Anjali Kundalpady, Pramod Padmanabhan, Akash Sinha

Abstract: We investigate the phenomenon of disorder-free localisation in quantum systems with global permutation symmetry. We use permutation group theory to systematically construct permutation symmetric many-fermion Hamiltonians and interpret them as generators of continuous-time quantum walks. When the number of fermions is very large we find that all the canonical basis states localise at all times, wit… ▽ More We investigate the phenomenon of disorder-free localisation in quantum systems with global permutation symmetry. We use permutation group theory to systematically construct permutation symmetric many-fermion Hamiltonians and interpret them as generators of continuous-time quantum walks. When the number of fermions is very large we find that all the canonical basis states localise at all times, without the introduction of any disorder coefficients. This time-independent localisation is not the result of any emergent disorder distinguishing it from existing mechanisms for disorder-free localisation. Next we establish the conditions under which the localisation is preserved. We find that interactions that preserve and break the global permutation symmetry sustains localisation. Furthermore the basis states of systems with reduced permutation symmetry, localise even for a small number of fermions when the symmetry-reducing parameters are tuned accordingly. We show that similar localisation also occurs for a permutation symmetric Heisenberg spin chain and permutation symmetric bosonic systems, implying that the localisation is independent of the superselected symmetry. Finally we make connections of the Hamiltonians studied here to the adjacency matrices of graphs and use this to propose a prescription for disorder-free localisation in continuous-time quantum walk systems. Many of the models proposed here feature all-to-all connectivity and can be potentially realised on superconducting quantum circuits, trapped ion systems and ultracold atoms. △ Less

Submitted 1 January, 2024; v1 submitted 4 July, 2023; originally announced July 2023.

Comments: v3 - 45 pages, 5 figures, published version, includes stability analysis, Author list in alphabetical order

Journal ref: Phys. Rev. A 109, 012205 (2024)

Dyck Paths and Topological Quantum Computation

Authors: Vivek Kumar Singh, Akash Sinha, Pramod Padmanabhan, Indrajit Jana

Abstract: The fusion basis of Fibonacci anyons supports unitary braid representations that can be utilized for universal quantum computation. We show a mapping between the fusion basis of three Fibonacci anyons, $\{|1\rangle, |τ\rangle\}$, and the two length 4 Dyck paths via an isomorphism between the two dimensional braid group representations on the fusion basis and the braid group representation built on… ▽ More The fusion basis of Fibonacci anyons supports unitary braid representations that can be utilized for universal quantum computation. We show a mapping between the fusion basis of three Fibonacci anyons, $\{|1\rangle, |τ\rangle\}$, and the two length 4 Dyck paths via an isomorphism between the two dimensional braid group representations on the fusion basis and the braid group representation built on the standard $(2,2)$ Young diagrams using the Jones construction. This correspondence helps us construct the fusion basis of the Fibonacci anyons using Dyck paths as the number of standard $(N,N)$ Young tableaux is the Catalan number, $C_N$ . We then use the local Fredkin moves to construct a spin chain that contains precisely those Dyck paths that correspond to the Fibonacci fusion basis, as a degenerate set. We show that the system is gapped and examine its stability to random noise thereby establishing its usefulness as a platform for topological quantum computation. Finally, we show braidwords in this rotated space that efficiently enable the execution of any desired single-qubit operation, achieving the desired level of precision($\sim 10^{-3}$). △ Less

Submitted 28 June, 2023; originally announced June 2023.

Comments: 30 pages, 20 figures

Dynamical symmetries of the anisotropic oscillator

Authors: Akash Sinha, Aritra Ghosh, Bijan Bagchi

Abstract: It is well known that the Hamiltonian of an $n$-dimensional isotropic oscillator admits an $SU(n)$ symmetry, making the system maximally superintegrable. However, the dynamical symmetries of the anisotropic oscillator are much more subtle. We introduce a novel set of canonical transformations that map an $n$-dimensional anisotropic oscillator to the corresponding isotropic problem. Consequently, t… ▽ More It is well known that the Hamiltonian of an $n$-dimensional isotropic oscillator admits an $SU(n)$ symmetry, making the system maximally superintegrable. However, the dynamical symmetries of the anisotropic oscillator are much more subtle. We introduce a novel set of canonical transformations that map an $n$-dimensional anisotropic oscillator to the corresponding isotropic problem. Consequently, the anisotropic oscillator is found to possess the same number of conserved quantities as the isotropic oscillator, making it maximally superintegrable too (commensurate case). The first integrals are explicitly calculated in the case of a two-dimensional anisotropic oscillator and remarkably, they admit closed-form expressions. △ Less

Submitted 27 January, 2026; v1 submitted 27 April, 2023; originally announced April 2023.

Comments: v1: Preliminary version, comments are welcome; v2: Includes post-publication corrections of typos and minor errors, as well as clarifying remarks in the Appendix

Journal ref: Phys. Scr. 98, 095253 (2023) [Corrigendum: Phys. Scr. 101, 149501 (2026)]

A Programmable True Random Number Generator Using Commercial Quantum Computers

Authors: Aviraj Sinha, Elena R. Henderson, Jessie M. Henderson, Eric C. Larson, Mitchell A. Thornton

Abstract: Random number generators (RNG) are essential elements in many cryptographic systems. True random number generators (TRNG) rely upon sources of randomness from natural processes such as those arising from quantum mechanics phenomena. We demonstrate that a quantum computer can serve as a high-quality, weakly random source for a generalized user-defined probability mass function (PMF). Specifically,… ▽ More Random number generators (RNG) are essential elements in many cryptographic systems. True random number generators (TRNG) rely upon sources of randomness from natural processes such as those arising from quantum mechanics phenomena. We demonstrate that a quantum computer can serve as a high-quality, weakly random source for a generalized user-defined probability mass function (PMF). Specifically, QC measurement implements the process of variate sampling according to a user-specified PMF resulting in a word comprised of electronic bits that can then be processed by an extractor function to address inaccuracies due to non-ideal quantum gate operations and other system biases. We introduce an automated and flexible method for implementing a TRNG as a programmed quantum circuit that executes on commercially-available, gate-model quantum computers. The user specifies the desired word size as the number of qubits and a definition of the desired PMF. Based upon the user specification of the PMF, our compilation tool automatically synthesizes the desired TRNG as a structural OpenQASM file containing native gate operations that are optimized to reduce the circuit's quantum depth. The resulting TRNG provides multiple bits of randomness for each execution/measurement cycle; thus, the number of random bits produced in each execution is limited only by the size of the QC. We provide experimental results to illustrate the viability of this approach. △ Less

Submitted 7 April, 2023; originally announced April 2023.

Comments: 15 pages, 7 figures, SPIE Defense + Commercial Sensing: Quantum Information Science, Sensing, and Computation XV

Automated Quantum Oracle Synthesis with a Minimal Number of Qubits

Authors: Jessie M. Henderson, Elena R. Henderson, Aviraj Sinha, Mitchell A. Thornton, D. Michael Miller

Abstract: Several prominent quantum computing algorithms--including Grover's search algorithm and Shor's algorithm for finding the prime factorization of an integer--employ subcircuits termed 'oracles' that embed a specific instance of a mathematical function into a corresponding bijective function that is then realized as a quantum circuit representation. Designing oracles, and particularly, designing them… ▽ More Several prominent quantum computing algorithms--including Grover's search algorithm and Shor's algorithm for finding the prime factorization of an integer--employ subcircuits termed 'oracles' that embed a specific instance of a mathematical function into a corresponding bijective function that is then realized as a quantum circuit representation. Designing oracles, and particularly, designing them to be optimized for a particular use case, can be a non-trivial task. For example, the challenge of implementing quantum circuits in the current era of NISQ-based quantum computers generally dictates that they should be designed with a minimal number of qubits, as larger qubit counts increase the likelihood that computations will fail due to one or more of the qubits decohering. However, some quantum circuits require that function domain values be preserved, which can preclude using the minimal number of qubits in the oracle circuit. Thus, quantum oracles must be designed with a particular application in mind. In this work, we present two methods for automatic quantum oracle synthesis. One of these methods uses a minimal number of qubits, while the other preserves the function domain values while also minimizing the overall required number of qubits. For each method, we describe known quantum circuit use cases, and illustrate implementation using an automated quantum compilation and optimization tool to synthesize oracles for a set of benchmark functions; we can then compare the methods with metrics including required qubit count and quantum circuit complexity. △ Less

Submitted 7 April, 2023; originally announced April 2023.

Comments: 18 pages, 10 figures, SPIE Defense + Commercial Sensing: Quantum Information Science, Sensing, and Computation XV

Bell inequalities in 2-2 scattering

Authors: Aninda Sinha, Ahmadullah Zahed

Abstract: We consider Bell inequalities in 2-2 scattering of photons, gravitons, fermions and pions. We choose measurement settings that give maximum Bell violation for maximally entangled states and calculate the relevant Bell inequalities for these processes. For photon scattering at low energies, QED exhibits Bell violation for all scattering angles except for a small transverse region. This leads to a f… ▽ More We consider Bell inequalities in 2-2 scattering of photons, gravitons, fermions and pions. We choose measurement settings that give maximum Bell violation for maximally entangled states and calculate the relevant Bell inequalities for these processes. For photon scattering at low energies, QED exhibits Bell violation for all scattering angles except for a small transverse region. This leads to a fine-tuning problem. Incorporating a light axion/axion-like particle (ALP) removes the fine-tuning problem and constrains the axion-coupling--axion-mass parameters. Allowing for graviton exchange and demanding Bell violation in photon scattering, we find that the Weak Gravity Conjecture is satisfied. Quantum gravity effect on axion coupling is discussed. For 2-2 graviton scattering, we find that CEMZ bounds allow for at most small Bell violations. Restriction on the Weinberg angle is found by demanding Bell violation in Bhabha scattering. We use recent S-matrix bootstrap data for pions and photons to study the Bell parameter in the space of allowed S-matrices. In the photon case, we study the Bell parameters as a function of energy and find support for the EFT observations. We discuss Bell parameter for pion S-matrices, which are qutrits. For pions, we find that there is a minimization of a suitable Bell parameter for S-matrices which exhibit Regge behaviour. △ Less

Submitted 6 July, 2023; v1 submitted 20 December, 2022; originally announced December 2022.

Comments: v3, 21 pages, 12 figures, version to appear in PRD

Automated Quantum Memory Compilation with Improved Dynamic Range

Authors: Aviraj Sinha, Elena R. Henderson, Jessie M. Henderson, Mitchell A. Thornton

Abstract: Emerging quantum algorithms that process data require that classical input data be represented as a quantum state. These data-processing algorithms often follow the gate model of quantum computing--which requires qubits to be initialized to a basis state, typically $\lvert 0 \rangle$--and thus often employ state generation circuits to transform the initialized basis state to a data-representation… ▽ More Emerging quantum algorithms that process data require that classical input data be represented as a quantum state. These data-processing algorithms often follow the gate model of quantum computing--which requires qubits to be initialized to a basis state, typically $\lvert 0 \rangle$--and thus often employ state generation circuits to transform the initialized basis state to a data-representation state. There are many ways to encode classical data in a qubit, and the oft-applied approach of basis encoding does not allow optimization to the extent that other variants do. In this work, we thus consider automatic synthesis of addressable, quantum read-only memory (QROM) circuits, which act as data-encoding state-generation circuits. We investigate three data encoding approaches, one of which we introduce to provide improved dynamic range and precision. We present experimental results that compare these encoding methods for QROM synthesis to better understand the implications of and applications for each. △ Less

Submitted 17 November, 2022; originally announced November 2022.

Comments: 14 pages, 9 figures, and 13 tables

Finite temperature tensor network study of the Hubbard model on an infinite square lattice

Authors: Aritra Sinha, Marek M. Rams, Piotr Czarnik, Jacek Dziarmaga

Abstract: The Hubbard model is a longstanding problem in the theory of strongly correlated electrons and a very active one in the experiments with ultracold fermionic atoms. Motivated by current and prospective quantum simulations, we apply a two-dimensional tensor network, an infinite projected entangled pair state, evolved in imaginary time by the neighborhood tensor update algorithm working directly in t… ▽ More The Hubbard model is a longstanding problem in the theory of strongly correlated electrons and a very active one in the experiments with ultracold fermionic atoms. Motivated by current and prospective quantum simulations, we apply a two-dimensional tensor network, an infinite projected entangled pair state, evolved in imaginary time by the neighborhood tensor update algorithm working directly in the thermodynamic limit. With U(1)xU(1) symmetry and the bond dimensions up to 29, we generate thermal states down to the temperature of 0.17 times the hopping rate. We obtain results for spin and charge correlators, unaffected by boundary effects. The spin correlators, measurable in prospective ultracold atoms experiments attempting to approach the thermodynamic limit, provide evidence of disruption of the antiferromagnetic background with mobile holes in a slightly doped Hubbard model. The charge correlators reveal the presence of hole-doublon pairs near half filling and signatures of hole-hole repulsion on doping. We also obtain specific heat in the slightly doped regime. △ Less

Submitted 29 October, 2022; v1 submitted 19 July, 2022; originally announced September 2022.

Comments: 18 pages; minor changes; accepted in PRB

Report number: LA-UR-22-26026

Journal ref: Phys. Rev. B 106, 195105 (2022)

qLEET: Visualizing Loss Landscapes, Expressibility, Entangling Power and Training Trajectories for Parameterized Quantum Circuits

Authors: Utkarsh Azad, Animesh Sinha

Abstract: We present qLEET, an open-source Python package for studying parameterized quantum circuits (PQCs), which are widely used in various variational quantum algorithms (VQAs) and quantum machine learning (QML) algorithms. qLEET enables the computation of properties such as expressibility and entangling power of a PQC by studying its entanglement spectrum and the distribution of parameterized states pr… ▽ More We present qLEET, an open-source Python package for studying parameterized quantum circuits (PQCs), which are widely used in various variational quantum algorithms (VQAs) and quantum machine learning (QML) algorithms. qLEET enables the computation of properties such as expressibility and entangling power of a PQC by studying its entanglement spectrum and the distribution of parameterized states produced by it. Furthermore, it allows users to visualize the training trajectories of PQCs along with high-dimensional loss landscapes generated by them for different objective functions. It supports quantum circuits and noise models built using popular quantum computing libraries such as Qiskit, Cirq, and Pyquil. In our work, we demonstrate how qLEET provides opportunities to design and improve hybrid quantum-classical algorithms by utilizing intuitive insights from the ansatz capability and structure of the loss landscape. △ Less

Submitted 26 June, 2023; v1 submitted 4 May, 2022; originally announced May 2022.

Comments: 11 pages, 8 figures (Main Text) and 8 pages, 6 figures (Supplementary)

Journal ref: Quantum Inf Process 22, 256 (2023)

Fast and Secure Routing Algorithms for Quantum Key Distribution Networks

Authors: Shahbaz Akhtar, Krishnakumar G, Vishnu B, Abhishek Sinha

Abstract: We consider the problem of secure packet routing at the maximum achievable rate in Quantum Key Distribution (QKD) networks. Assume that a QKD protocol generates symmetric private key pairs for secure communication over each link in a network. The quantum key generation process is modeled using a stochastic counting process. Packets are first encrypted with the quantum keys available for each hop a… ▽ More We consider the problem of secure packet routing at the maximum achievable rate in Quantum Key Distribution (QKD) networks. Assume that a QKD protocol generates symmetric private key pairs for secure communication over each link in a network. The quantum key generation process is modeled using a stochastic counting process. Packets are first encrypted with the quantum keys available for each hop and then transmitted on a point-to-point basis over the links. A fundamental problem in this setting is the design of a secure and capacity-achieving routing policy that takes into account the time-varying availability of the encryption keys and finite link capacities. In this paper, we propose a new secure throughput-optimal policy called Tandem Queue Decomposition (TQD). The TQD policy is derived by combining the QKD process with the Universal Max Weight routing policy, proposed earlier by Sinha and Modiano. We show that the TQD policy solves the problem of secure and efficient packet routing for a broad class of traffic, including unicast, broadcast, multicast, and anycast. The proposed decomposition reduces the problem to the generalized network flow problem without the key availability constraints over a transformed network. The proof of the throughput-optimality of the TQD policy uses the Lyapunov stability theory for analyzing the interdependent packet queueing process and the key-storage dynamics. Finally, we demonstrate the competitiveness of the TQD policy over the existing algorithms by numerically comparing them on a simulator that we build on top of the state-of-the-art OMNeT++ network simulator platform. △ Less

Submitted 27 May, 2022; v1 submitted 16 September, 2021; originally announced September 2021.

Qubit Routing using Graph Neural Network aided Monte Carlo Tree Search

Authors: Animesh Sinha, Utkarsh Azad, Harjinder Singh

Abstract: Near-term quantum hardware can support two-qubit operations only on the qubits that can interact with each other. Therefore, to execute an arbitrary quantum circuit on the hardware, compilers have to first perform the task of qubit routing, i.e., to transform the quantum circuit either by inserting additional SWAP gates or by reversing existing CNOT gates to satisfy the connectivity constraints of… ▽ More Near-term quantum hardware can support two-qubit operations only on the qubits that can interact with each other. Therefore, to execute an arbitrary quantum circuit on the hardware, compilers have to first perform the task of qubit routing, i.e., to transform the quantum circuit either by inserting additional SWAP gates or by reversing existing CNOT gates to satisfy the connectivity constraints of the target topology. We propose a procedure for qubit routing that is architecture agnostic and that outperforms other available routing implementations on various circuit benchmarks. The depth of the transformed quantum circuits is minimised by utilizing the Monte Carlo tree search to perform qubit routing, aided by a Graph neural network that evaluates the value function and action probabilities for each state. △ Less

Submitted 12 March, 2022; v1 submitted 1 April, 2021; originally announced April 2021.

Comments: 10 pages, 7 figures; Accepted in 36th AAAI Conference on Artificial Intelligence 2022

Non-adiabatic dynamics across a first order quantum phase transition: Quantized bubble nucleation

Authors: Aritra Sinha, Titas Chanda, Jacek Dziarmaga

Abstract: Metastability is a quintessential feature of first order quantum phase transitions, which is lost either by dynamical instability or by nucleating bubbles of a true vacuum through quantum tunneling. By considering a drive across the first order quantum phase transition in the quantum Ising chain in the presence of both transverse and longitudinal fields, we reveal multiple regions in the parameter… ▽ More Metastability is a quintessential feature of first order quantum phase transitions, which is lost either by dynamical instability or by nucleating bubbles of a true vacuum through quantum tunneling. By considering a drive across the first order quantum phase transition in the quantum Ising chain in the presence of both transverse and longitudinal fields, we reveal multiple regions in the parameter space where the initial metastable state loses its metastability in successive stages. The mechanism responsible is found to be semi-degenerate resonant tunnelings to states with specific bubble sizes. We show that such dynamics of quantized bubble nucleations can be understood in terms of Landau-Zener transitions, which provide quantitative predictions of nucleation probabilities for different bubble sizes. △ Less

Submitted 9 June, 2021; v1 submitted 4 March, 2021; originally announced March 2021.

Comments: 7+4 pages, 5+3 figures. Close to published version

Journal ref: Phys. Rev. B 103, L220302 (2021)

Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions

Authors: Aritra Sinha, Debasis Sadhukhan, Marek M. Rams, Jacek Dziarmaga

Abstract: Driving a homogeneous system across a quantum phase transition in a quench-time $τ_Q$ generates excitations on wavelengths longer than the Kibble-Zurek (KZ) length $\hatξ\proptoτ_Q^{ν/(1+zν)}$ within the KZ time window $\hat t\proptoτ_Q^{zν/(1+zν)}$, where $z$ and $ν$ are the critical exponents. Quenches designed with local time-dependent inhomogeneity can introduce a gap in the spectrum. For a va… ▽ More Driving a homogeneous system across a quantum phase transition in a quench-time $τ_Q$ generates excitations on wavelengths longer than the Kibble-Zurek (KZ) length $\hatξ\proptoτ_Q^{ν/(1+zν)}$ within the KZ time window $\hat t\proptoτ_Q^{zν/(1+zν)}$, where $z$ and $ν$ are the critical exponents. Quenches designed with local time-dependent inhomogeneity can introduce a gap in the spectrum. For a variety of setups with short-range interactions, they have been shown to suppress excitations if the spatial velocity of the inhomogenous front is below the characteristic KZ velocity $\hat v \propto \hatξ/\hat t$. Ising-like models with long-range interactions can have no sonic horizon, spreading information instantaneously across the system. Usually, this should imply that inhomogenous transitions will render the dynamics adiabatic regardless of the front velocity. However, we show that we get an adiabatic transition with no defects only when the inhomogeneous front moves slower than a characteristic crossover velocity $\tilde v \propto θ^{(z-1)ν/(1+ν)}$, where $θ$ is the slope of the inhomogeneous front at the critical point. The existence of this crossover velocity and adiabaticity of the model is a consequence of the energy gap in the quasiparticle spectrum that is opened by the inhomogeneity. This effect can be employed for efficient adiabatic quantum state preparation in systems with long-range interactions. △ Less

Submitted 16 December, 2020; v1 submitted 12 October, 2020; originally announced October 2020.

Comments: 12 pages, 10 figures (closed to published version)

Journal ref: Phys. Rev. B 102, 214203 (2020)

Relative entropy in scattering and the S-matrix bootstrap

Authors: Anjishnu Bose, Parthiv Haldar, Aninda Sinha, Pritish Sinha, Shaswat S Tiwari

Abstract: We consider entanglement measures in 2-2 scattering in quantum field theories, focusing on relative entropy which distinguishes two different density matrices. Relative entropy is investigated in several cases which include $φ^4$ theory, chiral perturbation theory ($χPT$) describing pion scattering and dilaton scattering in type II superstring theory. We derive a high energy bound on the relative… ▽ More We consider entanglement measures in 2-2 scattering in quantum field theories, focusing on relative entropy which distinguishes two different density matrices. Relative entropy is investigated in several cases which include $φ^4$ theory, chiral perturbation theory ($χPT$) describing pion scattering and dilaton scattering in type II superstring theory. We derive a high energy bound on the relative entropy using known bounds on the elastic differential cross-sections in massive QFTs. In $χPT$, relative entropy close to threshold has simple expressions in terms of ratios of scattering lengths. Definite sign properties are found for the relative entropy which are over and above the usual positivity of relative entropy in certain cases. We then turn to the recent numerical investigations of the S-matrix bootstrap in the context of pion scattering. By imposing these sign constraints and the $ρ$ resonance, we find restrictions on the allowed S-matrices. By performing hypothesis testing using relative entropy, we isolate two sets of S-matrices living on the boundary which give scattering lengths comparable to experiments but one of which is far from the 1-loop $χPT$ Adler zeros. We perform a preliminary analysis to constrain the allowed space further, using ideas involving positivity inside the extended Mandelstam region, and elastic unitarity. △ Less

Submitted 3 December, 2020; v1 submitted 22 June, 2020; originally announced June 2020.

Comments: v5: 83 pages, 21 figures. Typo fixed, reference updates

Journal ref: SciPost Phys. 9, 081 (2020)

Sonic horizons and causality in the phase transition dynamics

Authors: Debasis Sadhukhan, Aritra Sinha, Anna Francuz, Justyna Stefaniak, Marek M. Rams, Jacek Dziarmaga, Wojciech H. Zurek

Abstract: A system gradually driven through a symmetry-breaking phase transition is subject to the Kibble-Zurek mechanism (KZM). As a consequence of the critical slowing down, its state cannot follow local equilibrium, and its evolution becomes non-adiabatic near the critical point. In the simplest approximation, that stage can be regarded as "impulse" where the state of the system remains unchanged. It lea… ▽ More A system gradually driven through a symmetry-breaking phase transition is subject to the Kibble-Zurek mechanism (KZM). As a consequence of the critical slowing down, its state cannot follow local equilibrium, and its evolution becomes non-adiabatic near the critical point. In the simplest approximation, that stage can be regarded as "impulse" where the state of the system remains unchanged. It leads to the correct KZM scaling laws. However, such "freeze-out" might suggest that the coherence length of the nascent order parameter remains unchanged as the critical region is traversed. By contrast, the original causality-based discussion emphasized the role of the {\it sonic horizon}: domains of the broken symmetry phase can expand with a velocity limited by the speed of the relevant sound. This effect was demonstrated in the quantum Ising chain where the dynamical exponent $z=1$ and quasiparticles excited by the transition have a fixed speed of sound. To elucidate the role of the sonic horizon, in this paper we study two systems with $z>1$ where the speed of sound is no longer fixed, and the fastest excited quasiparticles set the size of the sonic horizon. Their effective speed decays with the increasing transition time. In the extreme case, the dynamical exponent $z$ can diverge such as in the Griffiths region of the random Ising chain where localization of excited quasiparticles freezes the growth of the correlation range when the critical region is traversed. Of particular interest is an example with $z<1$ -- the long-range extended Ising chain, where there is no upper limit to the velocity of excited quasiparticles with small momenta. Initially, the power-law tail of the correlation function grows adiabatically, but in the non-adiabatic stage it lags behind the adiabatic evolution -- in accord with a generalized Lieb-Robinson bound. △ Less

Submitted 15 April, 2020; v1 submitted 5 December, 2019; originally announced December 2019.

Comments: minor corrections, accepted in PRB

Report number: LA-UR-19-30546

Journal ref: Phys. Rev. B 101, 144429 (2020)

Renormalized Circuit Complexity

Authors: Arpan Bhattacharyya, Pratik Nandy, Aninda Sinha

Abstract: We propose a modification to Nielsen's circuit complexity for Hamiltonian simulation using the Suzuki-Trotter (ST) method, which provides a network like structure for the quantum circuit. This leads to an optimized gate counting linear in the geodesic distance and spatial volume, unlike in the original proposal. The optimized ST iteration order is correlated with the error tolerance and plays the… ▽ More We propose a modification to Nielsen's circuit complexity for Hamiltonian simulation using the Suzuki-Trotter (ST) method, which provides a network like structure for the quantum circuit. This leads to an optimized gate counting linear in the geodesic distance and spatial volume, unlike in the original proposal. The optimized ST iteration order is correlated with the error tolerance and plays the role of an anti-de Sitter (AdS) radial coordinate. The density of gates is shown to be monotonic with the tolerance and a holographic interpretation using path-integral optimization is given. △ Less

Submitted 20 February, 2020; v1 submitted 18 July, 2019; originally announced July 2019.

Comments: 12 pages, 2 figures, v3: to appear in Physical Review Letters

Report number: YITP-19-63

Journal ref: Phys. Rev. Lett. 124, 101602 (2020)

Kibble-Zurek mechanism with a single particle: dynamics of the localization-delocalization transition in the Aubry-André model

Authors: Aritra Sinha, Marek M. Rams, Jacek Dziarmaga

Abstract: The Aubry-André 1D lattice model describes a particle hopping in a pseudo-random potential. Depending on its strength $λ$, all eigenstates are either localized ($λ>1$) or delocalized ($λ<1$). Near the transition, the localization length diverges like $ξ\sim(λ-1)^{-ν}$ with $ν=1$. We show that when the particle is initially prepared in a localized ground state and the potential strength is slowly r… ▽ More The Aubry-André 1D lattice model describes a particle hopping in a pseudo-random potential. Depending on its strength $λ$, all eigenstates are either localized ($λ>1$) or delocalized ($λ<1$). Near the transition, the localization length diverges like $ξ\sim(λ-1)^{-ν}$ with $ν=1$. We show that when the particle is initially prepared in a localized ground state and the potential strength is slowly ramped down across the transition, then -- in analogy with the Kibble-Zurek mechanism -- it enters the delocalized phase having finite localization length $\hatξ\simτ_Q^{ν/(1+zν)}$. Here $τ_Q$ is ramp/quench time and $z$ is a dynamical exponent. At $λ=1$ we determine $z\simeq2.37$ from the power law scaling of energy gap with lattice size $L$. Even though for infinite $L$ the model is gapless, we show that the gap relevant for excitation during the ramp remains finite. Close to the critical point it scales like $ξ^{-z}$ with the value of $z$ determined by the finite size scaling. It is the gap between the ground state and the lowest of those excited states that overlap with the ground state enough to be accessible for excitation. We propose an experiment with a non-interacting BEC to test our prediction. Our hypothesis is further supported by considering a generalized version of Aubry-André model possessing an energy-dependent mobility edge. △ Less

Submitted 21 March, 2019; v1 submitted 13 November, 2018; originally announced November 2018.

Comments: 7 pages, 9 figures; close to the published version; new section on generalized Aubry-André model

Journal ref: Phys. Rev. B 99, 094203 (2019)

Circuit complexity in interacting QFTs and RG flows

Authors: Arpan Bhattacharyya, Arvind Shekar, Aninda Sinha

Abstract: We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the $φ^4$ theory. We work out the circuit complexity for evolving from a nearly Gaussian unentangled reference state to the entangled ground state of the theory. Our approach uses Nielsen's geometric method, which translates into working out the geodesic equation arising from a certain cost func… ▽ More We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the $φ^4$ theory. We work out the circuit complexity for evolving from a nearly Gaussian unentangled reference state to the entangled ground state of the theory. Our approach uses Nielsen's geometric method, which translates into working out the geodesic equation arising from a certain cost functional. We present a general method, making use of integral transforms, to do the required lattice sums analytically and give explicit expressions for the $d=2,3$ cases. Our method enables a study of circuit complexity in the epsilon expansion for the Wilson-Fisher fixed point. We find that with increasing dimensionality the circuit depth increases in the presence of the $φ^4$ interaction eventually causing the perturbative calculation to breakdown. We discuss how circuit complexity relates with the renormalization group. △ Less

Submitted 18 October, 2018; v1 submitted 9 August, 2018; originally announced August 2018.

Comments: 50 pages, 2 figures; references updated; version to appear in JHEP

Report number: YITP-18-89

Journal ref: JHEP 1810 (2018) 140

Dissipative nonlinear waves in a gravitating quantum fluid

Authors: Biswajit Sahu, Anjana Sinha, R. Roychoudhury

Abstract: Nonlinear wave propagation is studied analytically in a dissipative, self-gravitating Bose Einstein condensate, in the framework of Gross-Pitaevskii model. The linear dispersion relation shows that the effect of dissipation is to suppress dynamical instabilities that destabilize the system. The small amplitude analysis using reductive perturbation technique is found to yield a modified form of KdV… ▽ More Nonlinear wave propagation is studied analytically in a dissipative, self-gravitating Bose Einstein condensate, in the framework of Gross-Pitaevskii model. The linear dispersion relation shows that the effect of dissipation is to suppress dynamical instabilities that destabilize the system. The small amplitude analysis using reductive perturbation technique is found to yield a modified form of KdV equation. The soliton energy, amplitude and velocity are found to decay with time, whereas the soliton width increases, such that the soliton exists for a finite time only △ Less

Submitted 23 March, 2017; originally announced March 2017.

Comments: 7 pages, 5 figures

On the superposition principle in interference experiments

Authors: Aninda Sinha, Aravind H. Vijay, Urbasi Sinha

Abstract: The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the pr… ▽ More The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the principle. We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. The analytic handle would be useful for comparing theory with future experiments. It is applicable both to physics based on classical wave equations as well as the non-relativistic Schrodinger equation. △ Less

Submitted 22 April, 2015; v1 submitted 6 December, 2014; originally announced December 2014.

Comments: 8 pages, 4 figures, To appear in Scientific Reports (Nature)

Journal ref: Scientific Reports 5 Article Number: 10304, 2015

Nonlinear constraints on gravity from entanglement

Authors: Shamik Banerjee, Apratim Kaviraj, Aninda Sinha

Abstract: Using the positivity of relative entropy arising from the Ryu-Takayanagi formula for spherical entangling surfaces, we obtain constraints at the nonlinear level for the gravitational dual. We calculate the Green's function necessary to compute the first order correction to the entangling surface and use this to find the relative entropy for non-constant stress tensors in a derivative expansion. We… ▽ More Using the positivity of relative entropy arising from the Ryu-Takayanagi formula for spherical entangling surfaces, we obtain constraints at the nonlinear level for the gravitational dual. We calculate the Green's function necessary to compute the first order correction to the entangling surface and use this to find the relative entropy for non-constant stress tensors in a derivative expansion. We show that the Einstein value satisfies the positivity condition while the multi-dimensional parameter space away from it gets constrained. △ Less

Submitted 5 February, 2015; v1 submitted 15 May, 2014; originally announced May 2014.

Comments: 31 pages, 4 figures, to appear in CQG

Report number: IPMU14-0119

Journal ref: Class. Quantum Grav. 32 (2015) 065006

Constraining gravity using entanglement in AdS/CFT

Authors: Shamik Banerjee, Arpan Bhattacharyya, Apratim Kaviraj, Kallol Sen, Aninda Sinha

Abstract: We investigate constraints imposed by entanglement on gravity in the context of holography. First, by demanding that relative entropy is positive and using the Ryu-Takayanagi entropy functional, we find certain constraints at a nonlinear level for the dual gravity. Second, by considering Gauss-Bonnet gravity, we show that for a class of small perturbations around the vacuum state, the positivity o… ▽ More We investigate constraints imposed by entanglement on gravity in the context of holography. First, by demanding that relative entropy is positive and using the Ryu-Takayanagi entropy functional, we find certain constraints at a nonlinear level for the dual gravity. Second, by considering Gauss-Bonnet gravity, we show that for a class of small perturbations around the vacuum state, the positivity of the two point function of the field theory stress tensor guarantees the positivity of the relative entropy. Further, if we impose that the entangling surface closes off smoothly in the bulk interior, we find restrictions on the coupling constant in Gauss-Bonnet gravity. We also give an example of an anisotropic excited state in an unstable phase with broken conformal invariance which leads to a negative relative entropy. △ Less

Submitted 9 July, 2014; v1 submitted 20 January, 2014; originally announced January 2014.

Comments: 36 pages, 3 figures, v4: fig 1 modified

Journal ref: JHEP 1405 (2014) 029

Non-classical paths in interference experiments

Authors: Rahul Sawant, Joseph Samuel, Aninda Sinha, Supurna Sinha, Urbasi Sinha

Abstract: In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well known text books in quantum mechanics implicitly an… ▽ More In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well known text books in quantum mechanics implicitly and/or explicitly use this assumption which is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from non-classical paths in quantum interference experiments which provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these non-classical paths is hard. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence. △ Less

Submitted 9 August, 2014; v1 submitted 8 August, 2013; originally announced August 2013.

Comments: v2: 5 pages + 3 pages supplementary, title changed, version to appear in Physical Review Letters

Journal ref: Phys. Rev. Lett. 113, 120406 (2014)

Spectral Singularity in confined PT symmetric optical potential

Authors: Anjana Sinha, R. Roychoudhury

Abstract: We present an analytical study for the scattering amplitudes (Reflection $|R|$ and Transmission $|T|$), of the periodic ${\cal{PT}}$ symmetric optical potential $ V(x) = \displaystyle W_0 \left( \cos ^2 x + i V_0 \sin 2x \right) $ confined within the region $0 \leq x \leq L$, embedded in a homogeneous medium having uniform potential $W_0$. The confining length $L$ is considered to be some integral… ▽ More We present an analytical study for the scattering amplitudes (Reflection $|R|$ and Transmission $|T|$), of the periodic ${\cal{PT}}$ symmetric optical potential $ V(x) = \displaystyle W_0 \left( \cos ^2 x + i V_0 \sin 2x \right) $ confined within the region $0 \leq x \leq L$, embedded in a homogeneous medium having uniform potential $W_0$. The confining length $L$ is considered to be some integral multiple of the period $ π$. We give some new and interesting results. Scattering is observed to be normal ($|T| ^2 \leq 1, \ |R|^2 \leq 1$) for $V_0 \leq 0.5 $, when the above potential can be mapped to a Hermitian potential by a similarity transformation. Beyond this point ($ V_0 > 0.5 $) scattering is found to be anomalous ($|T| ^2, \ |R|^2 $ not necessarily $ \leq 1 $). Additionally, in this parameter regime of $V_0$, one observes infinite number of spectral singularities $E_{SS}$ at different values of $V_0$. Furthermore, for $L= 2 n π$, the transition point $V_0 = 0.5$ shows unidirectional invisibility with zero reflection when the beam is incident from the absorptive side ($Im [V(x)] < 0$) but finite reflection when the beam is incident from the emissive side ($Im [V(x)] > 0$), transmission being identically unity in both cases. Finally, the scattering coefficients $|R|^2$ and $|T|^2 $ always obey the generalized unitarity relation : $ ||T|^2 - 1| = \sqrt{|R_R|^2 |R_L|^2}$, where subscripts $R$ and $L$ stand for right and left incidence respectively. △ Less

Submitted 13 November, 2013; v1 submitted 7 July, 2013; originally announced July 2013.

Comments: 13 pages, 7 figures

Journal ref: Journal of Mathematical Physics vol. 54 (2013)

Scattering in a varying mass PT symmetric double heterojunction

Authors: Anjana Sinha, R. Roychoudhury

Abstract: We observe that the reflection and transmission coefficients of a particle within a double, PT symmetric heterojunction with spatially varying mass, show interesting features, depending on the degree of non Hermiticity, although there is no spontaneous breakdown of PT symmetry. The potential profile in the intermediate layer is considered such that it has a non vanishing imaginary part near the he… ▽ More We observe that the reflection and transmission coefficients of a particle within a double, PT symmetric heterojunction with spatially varying mass, show interesting features, depending on the degree of non Hermiticity, although there is no spontaneous breakdown of PT symmetry. The potential profile in the intermediate layer is considered such that it has a non vanishing imaginary part near the heterojunctions. Exact analytical solutions for the wave function are obtained, and the reflection and transmission coefficients are plotted as a function of energy, for both left as well as right incidence. As expected, the spatial dependence on mass changes the nature of the scattering solutions within the heterojunctions, and the space-time (PT) symmetry is responsible for the left-right asymmetry in the reflection and transmission coefficients. However, the non vanishing imaginary component of the potential near the heterojunctions gives new and interesting results. △ Less

Submitted 10 June, 2013; originally announced June 2013.

Comments: 7 pages, 8 figures

Journal ref: EPL vol. 103, (2013) 50007

Entanglement entropy from surface terms in general relativity

Authors: Arpan Bhattacharyya, Aninda Sinha

Abstract: Entanglement entropy in local quantum field theories is typically ultraviolet divergent due to short distance effects in the neighbourhood of the entangling region. In the context of gauge/gravity duality, we show that surface terms in general relativity are able to capture this entanglement entropy. In particular, we demonstrate that for 1+1 dimensional CFTs at finite temperature whose gravity du… ▽ More Entanglement entropy in local quantum field theories is typically ultraviolet divergent due to short distance effects in the neighbourhood of the entangling region. In the context of gauge/gravity duality, we show that surface terms in general relativity are able to capture this entanglement entropy. In particular, we demonstrate that for 1+1 dimensional CFTs at finite temperature whose gravity dual is the BTZ black hole, the Gibbons-Hawking-York term precisely reproduces the entanglement entropy which can be computed independently in the field theory. △ Less

Submitted 10 September, 2013; v1 submitted 15 May, 2013; originally announced May 2013.

Comments: 6 pages 1 fig. Essay awarded honourable mention in the Gravity Research Foundation 2013 Awards for Essays on Gravitation. v2: to appear in IJMPD spl. issue

Journal ref: IJMPD 22, 12 (2013) 1342020

Entanglement entropy from the holographic stress tensor

Authors: Arpan Bhattacharyya, Aninda Sinha

Abstract: We consider entanglement entropy in the context of gauge/gravity duality for conformal field theories in even dimensions. The holographic prescription due to Ryu and Takayanagi (RT) leads to an equation describing how the entangling surface extends into the bulk geometry. We show that setting to zero the time-time component of the Brown-York stress tensor evaluated on the co-dimension one entangli… ▽ More We consider entanglement entropy in the context of gauge/gravity duality for conformal field theories in even dimensions. The holographic prescription due to Ryu and Takayanagi (RT) leads to an equation describing how the entangling surface extends into the bulk geometry. We show that setting to zero the time-time component of the Brown-York stress tensor evaluated on the co-dimension one entangling surface, leads to the same equation. By considering a spherical entangling surface as an example, we observe that Euclidean action methods in AdS/CFT will lead to the RT area functional arising as a counterterm needed to regularize the stress tensor. We present arguments leading to a justification for the minimal area prescription. △ Less

Submitted 15 October, 2013; v1 submitted 7 March, 2013; originally announced March 2013.

Comments: 10 pages. v3: many changes. Observation that the RT area functional arises as a counterterm to regularize the stress tensor added. Discussion on Euclidean methods for computing EE added. v4: version to appear in CQG

Journal ref: Class. Quantum Grav. 30 (2013) 235032

The effect of environmental coupling on tunneling of quasiparticles in Josephson junctions

Authors: Mohammad H. Ansari, Frank K. Wilhelm, Urbasi Sinha, Aninda Sinha

Abstract: We study quasiparticle tunneling in Josephson tunnel junctions embedded in an electromagnetic environment. We identify tunneling processes that transfer electrical charge and couple to the environment in a way similar to that of normal electrons, and processes that mix electrons and holes and are thus creating charge superpositions. The latter are sensitive to the phase difference between the supe… ▽ More We study quasiparticle tunneling in Josephson tunnel junctions embedded in an electromagnetic environment. We identify tunneling processes that transfer electrical charge and couple to the environment in a way similar to that of normal electrons, and processes that mix electrons and holes and are thus creating charge superpositions. The latter are sensitive to the phase difference between the superconductor and are thus limited by phase diffusion even at zero temperature. We show that the environmental coupling is suppressed in many environments, thus leading to lower quasiparticle decay rates and thus better superconductor qubit coherence than previously expected. Our approach is nonperturbative in the environmental coupling strength. △ Less

Submitted 7 November, 2013; v1 submitted 20 November, 2012; originally announced November 2012.

Comments: 13 pages, 2 figures

Journal ref: Supercond. Sci. Technol. 26 (2013) 125013

Classical Trajectories of the Continuum States of the ${\cal{PT}}$ symmetric Scarf II potential

Authors: Anjana Sinha

Abstract: We apply the factorization technique developed by Kuru et. al. [Ann. Phys. {\bf 323} (2008) 413] to obtain the exact analytical classical trajectories and momenta of the continuum states of the non Hermitian but ${\cal{PT}}$ symmetric Scarf II potential. In particular, we observe that the strange behaviour of the quantum version at the spectral singularity has an interesting classical analogue. We apply the factorization technique developed by Kuru et. al. [Ann. Phys. {\bf 323} (2008) 413] to obtain the exact analytical classical trajectories and momenta of the continuum states of the non Hermitian but ${\cal{PT}}$ symmetric Scarf II potential. In particular, we observe that the strange behaviour of the quantum version at the spectral singularity has an interesting classical analogue. △ Less

Submitted 29 June, 2012; originally announced June 2012.

Comments: 7 pages, 8 figures

Journal ref: Eur. Phys. Lett. vol. 98 (2012) 60005

Scattering states of a particle, with position-dependent mass, in a ${\cal{PT}}$ symmetric heterojunction

Authors: Anjana Sinha

Abstract: The study of a particle with position-dependent effective mass (pdem), within a double heterojunction is extended into the complex domain --- when the region within the heterojunctions is described by a non Hermitian ${\cal{PT}}$ symmetric potential. After obtaining the exact analytical solutions, the reflection and transmission coefficients are calculated, and plotted as a function of the energy.… ▽ More The study of a particle with position-dependent effective mass (pdem), within a double heterojunction is extended into the complex domain --- when the region within the heterojunctions is described by a non Hermitian ${\cal{PT}}$ symmetric potential. After obtaining the exact analytical solutions, the reflection and transmission coefficients are calculated, and plotted as a function of the energy. It is observed that at least two of the characteristic features of non Hermitian ${\cal{PT}}$ symmetric systems --- viz., left / right asymmetry and anomalous behaviour at spectral singularity, are preserved even in the presence of pdem. The possibility of charge conservation is also discussed. △ Less

Submitted 11 April, 2012; originally announced April 2012.

Comments: 12 pages, including 6 figures; Journal of Physics A : Math. Theor. (2012)

Journal ref: J. Phys. A: Math. Theor. 45 (2012) 185305

Scattering states of a particle, with position-dependent mass, in a double heterojunction

Authors: Anjana Sinha

Abstract: In this work we obtain the exact analytical scattering solutions of a particle (electron or hole) in a semiconductor double heterojunction - potential well / barrier - where the effective mass of the particle varies with position inside the heterojunctions. It is observed that the spatial dependence of mass within the well / barrier introduces a nonlinear component in the plane wave solutions of t… ▽ More In this work we obtain the exact analytical scattering solutions of a particle (electron or hole) in a semiconductor double heterojunction - potential well / barrier - where the effective mass of the particle varies with position inside the heterojunctions. It is observed that the spatial dependence of mass within the well / barrier introduces a nonlinear component in the plane wave solutions of the continuum states. Additionally, the transmission coefficient is found to increase with increasing energy, finally approaching unity, whereas the reflection coefficient follows the reverse trend and goes to zero. △ Less

Submitted 17 November, 2011; originally announced November 2011.

Comments: 7 pages, 6 figures

Journal ref: Eur. Phys. Lett., vol. 96 (2011) 20008