Showing 1–34 of 34 results for author: Ahmed, Z

Lattice Reconstruction and Orbital Hybridization Suppress Magnetism in TaCo$_2$Te$_2$

Authors: Ulysse Chazarin, Bharat C. Bathu, Zuned Ahmed, Marta Zonno, Chiara Bigi, Francois Bertran, Adolfo O. Fumega, Orlando J. Silveira, Shawulienu Kezilebieke

Abstract: Structural reconstruction in low-dimensional quantum materials can strongly modify electronic symmetry and magnetic stability through orbital hybridization. Here, we investigate the interplay between lattice reconstruction, electronic structure, and magnetic instability in the layered van der Waals compound TaCo$_2$Te$_2$ using scanning tunneling microscopy and spectroscopy (STM/STS), non-contact… ▽ More Structural reconstruction in low-dimensional quantum materials can strongly modify electronic symmetry and magnetic stability through orbital hybridization. Here, we investigate the interplay between lattice reconstruction, electronic structure, and magnetic instability in the layered van der Waals compound TaCo$_2$Te$_2$ using scanning tunneling microscopy and spectroscopy (STM/STS), non-contact atomic force microscopy (nc-AFM), angle-resolved photoemission spectroscopy (ARPES), and density functional theory (DFT). While nc-AFM resolves a distorted hexagonal Te surface lattice, STM/STS reveal a pronounced square-like electronic symmetry that does not directly follow the atomic structure. ARPES further shows a strongly anisotropic Fermi surface and reconstructed low-energy states. Spatially resolved spectroscopy and orbital-projected DFT demonstrate that the bias-dependent STM contrast does not arise from a simple reversal between occupied and unoccupied states, but from the energy-integrated local density of states dominated by electronic states exhibiting opposite spatial contrast at selected energies. DFT calculations further show that reconstruction suppresses the magnetic instability present in the undistorted structure, stabilizing a nonmagnetic ground state through enhanced orbital hybridization. These results establish TaCo$_2$Te$_2$ as a model system in which lattice reconstruction reorganizes electronic symmetry and suppresses magnetism, highlighting structural reconstruction as a route for controlling correlated and magnetic phases in low-dimensional quantum materials. △ Less

Submitted 25 June, 2026; originally announced June 2026.

Towards Atom-by-Atom Fabrication: Mechanosynthetic donation and abstraction

Authors: Brandon Blue, Mathieu Morin, Alex Inayeh, Rosemary Cranston, Cameron J. Mackie, Marc Savoie, Adam Bottomley, Christian J. Imperiale, Zehra Ahmed, Rafik Addou, Aly Asani, Eduardo Barrera-Ramirez, Jeremy Barton, Doreen Cheng, Megan Cowie, Chris Deimert, Tyler Enright, James Zhangming Fan, Robert A. Freitas Jr, Alan T. K. Godfrey, Ryan Groome, Si Yue Guo, Kareem A. Clarcia, Aru Hill, Taleana Huff , et al. (33 additional authors not shown)

Abstract: Enabled by inverted-mode scanning tunneling microscopy (IM-STM) and the use of functionalized molecular tools, we demonstrate positionally-controlled mechanosynthetic addition (donation) of carbon and subtraction (abstraction) of silicon atoms on a model build site: atomically clean and crystalline Si(100). The resulting structures represent the first demonstrations of an emerging ability to manip… ▽ More Enabled by inverted-mode scanning tunneling microscopy (IM-STM) and the use of functionalized molecular tools, we demonstrate positionally-controlled mechanosynthetic addition (donation) of carbon and subtraction (abstraction) of silicon atoms on a model build site: atomically clean and crystalline Si(100). The resulting structures represent the first demonstrations of an emerging ability to manipulate radical chemistry with positional control of specific atoms and moieties in 3D. Furthermore, by comparing the behavior of molecular tools designed for atomic donation versus abstraction, we highlight general principles governing molecular tool design for selective and reliable mechanosynthetic functionality. △ Less

Submitted 11 June, 2026; originally announced June 2026.

Comments: 17 pages, 5 figures. Supplementary Information is available upon request

A Matrix Quantum Kinetic Treatment of Impact Ionization in Avalanche Photodiodes

Authors: Sheikh Z. Ahmed, Shafat Shahnewaz, Samiran Ganguly, Joe C Campbell, Avik W. Ghosh

Abstract: Matrix based quantum kinetic simulations have been widely used for the predictive modeling of electronic devices. Inelastic scattering from phonons and electrons are typically treated as higher order processes in these treatments, captured using mean-field approximations. Carrier multiplication in Avalanche Photodiodes (APDs), however, relies entirely on strongly inelastic impact ionization, makin… ▽ More Matrix based quantum kinetic simulations have been widely used for the predictive modeling of electronic devices. Inelastic scattering from phonons and electrons are typically treated as higher order processes in these treatments, captured using mean-field approximations. Carrier multiplication in Avalanche Photodiodes (APDs), however, relies entirely on strongly inelastic impact ionization, making electron-electron scattering the dominant term requiring a rigorous, microscopic treatment. We go well beyond the conventional Born approximation for scattering to develop a matrix-based quantum kinetic theory for impact ionization, involving products of multiple Green's functions. Using a model semiconductor in a reverse-biased p-i-n configuration, we show how its calculated non-equilibrium charge distributions show multiplication at dead-space values consistent with energy-momentum conservation. Our matrix approach can be readily generalized to more sophisticated atomistic Hamiltonians, setting the stage for a fully predictive, `first principles' theory of APDs. △ Less

Submitted 26 August, 2025; v1 submitted 24 March, 2025; originally announced March 2025.

Quantum degeneracy and spin entanglement in ideal quantum gases

Authors: Fatma Zouari Ahmed, Mohammed Tayeb Meftah, Tommaso Roscilde

Abstract: Quantum degeneracy is the central many-body feature of ideal quantum gases stemming from quantum mechanics. In this work we address its relationship to the most fundamental form of non-classicality in many-body system, i.e. many-body entanglement. We aim at establishing a quantitative link between quantum degeneracy and entanglement in spinful ideal gases, using entanglement witness criteria based… ▽ More Quantum degeneracy is the central many-body feature of ideal quantum gases stemming from quantum mechanics. In this work we address its relationship to the most fundamental form of non-classicality in many-body system, i.e. many-body entanglement. We aim at establishing a quantitative link between quantum degeneracy and entanglement in spinful ideal gases, using entanglement witness criteria based on the variance of the collective spin of the spin ensemble. We show that spin-1/2 ideal Bose gases do not possess entanglement which can be revealed from such entanglement criteria. On the contrary, ideal spin-1/2 Fermi gases exhibit spin entanglement revealed by the collective-spin variances upon entering quantum degeneracy, due to the formation of highly non-local spin singlets. We map out the regime of detectable spin entanglement for Fermi gases in free space as well as in a parabolic trap, and probe the robustness of spin entanglement to thermal effects and spin imbalance. Spin entanglement in degenerate Fermi gases is amenable to experimental observation using state-of-the-art spin detection techniques in ultracold atoms. △ Less

Submitted 27 January, 2024; originally announced January 2024.

Comments: 7 pages, 3 figures

Dipole-dipole correlations in the nematic phases of symmetric cyanobiphenyl dimers and their binary mixtures with 5CB

Authors: Evangelia E. Zavvou, Efthymia Ramou, Ziauddin Ahmed, Chris Welch, Georg H. Mehl, Alexandros G. Vanakaras, Panagiota K. Karahaliou

Abstract: We report on the temperature dependence of birefringence and of the static dielectric permittivity tensor in a series of binary mixtures between the symmetric, bent-shaped, 1",9"-bis(4-cyanobiphenyl-4'-yl) nonane (CB9CB) dimer and the monomeric nematogen 5CB. In the studied composition range the mixtures exhibit two nematic phases with distinct birefringence and dielectric features. Birefringence… ▽ More We report on the temperature dependence of birefringence and of the static dielectric permittivity tensor in a series of binary mixtures between the symmetric, bent-shaped, 1",9"-bis(4-cyanobiphenyl-4'-yl) nonane (CB9CB) dimer and the monomeric nematogen 5CB. In the studied composition range the mixtures exhibit two nematic phases with distinct birefringence and dielectric features. Birefringence measurements are used to estimate the temperature dependence of the tilt between the axis defining the nanoscale helical modulation of the low temperature nematic phase with the (local) direction of the maximal alignment of the cyanobiphenyl units. Planar as well as magnetically and/or electrically aligned samples are used to measure the perpendicular and parallel components of the dielectric permittivity in both nematic phases. A self-consistent molecular field theory that takes into account flexibility and symmetry of the constituent mesogens is introduced for the calculation of order parameters and intra-molecular orientational dipolar correlations of the flexible dimers as a function of temperature/concentration. Utilising the tilt angle, as calculated from the birefringence measurements, and the predictions of the molecular theory, dielectric permittivity is modelled in the framework of the anisotropic version of the Kirkwood-Frohlich theory. Using the inter-molecular Kirkwood correlation factors as adjustable parameters, excellent agreement between theory and permittivity measurements across the whole temperature range and composition of the mixtures is obtained. The importance of the orientational, intra- and inter-molecular, dipolar correlations, their relative impact on the static dielectric properties, as well as their connection with the local structure of the nematic phases of bent-shaped bimesogens, is discussed. △ Less

Submitted 1 November, 2023; originally announced November 2023.

Comments: 20 pages, 7 figures and 4 pages supporting information with 5 figures

Journal ref: Soft Matter, 2023, 19, 9224-9238

A large deformation model for quasi-static to high strain rate response of a rate-stiffening soft polymer

Authors: Aditya Konale, Zahra Ahmed, Piyush Wanchoo, Vikas Srivastava

Abstract: Polyborosiloxane (PBS) is an important rate-stiffening soft polymer with dynamic, reversible crosslinks used in applications ranging from self-healing sensing and actuation to body and structural protection. Its highly rate-dependent response, especially for impact-mitigating structures, is important. However, the large strain response of PBS has not been characterized over quasi-static to high st… ▽ More Polyborosiloxane (PBS) is an important rate-stiffening soft polymer with dynamic, reversible crosslinks used in applications ranging from self-healing sensing and actuation to body and structural protection. Its highly rate-dependent response, especially for impact-mitigating structures, is important. However, the large strain response of PBS has not been characterized over quasi-static to high strain rates. Currently, there are no constitutive models that can predict the strongly rate-dependent large-deformation elastic-viscoplastic response of PBS. To address this gap, we have developed a microstructural physics motivated constitutive model for PBS and similar soft polymers and polymer gels with dynamic crosslinks to predict their large strain, non-linear loading-unloading, and significantly rate-dependent response. We have conducted compression experiments on PBS up to true strains of $\sim$125$\%$ over a wide strain rate range of 10$^{-3}$ s$^{-1}$ to 10$^{3}$ s$^{-1}$. The model reasonably accurately captures the response of PBS over six decades of strain rates. We propose boron-oxygen coordinate-bond dynamic crosslinks with macroscopic relaxation timescale $τ\approx 3$ s and temporary entanglement lockups at high strain rates acting as crosslinks with $τ\approx 0.0005$ s as the two types of crosslink mechanisms in PBS. We have outlined a numerical update procedure to evaluate the convolution-like time integrals arising from dynamic crosslink kinetics. Experiments involving three-dimensional inhomogeneous deformations were used to verify the predictive capabilities of our model and its finite element implementation. The modeling framework can be adopted for other dynamically crosslinked rate-stiffening soft polymers and polymer gels that are microstructurally similar to PBS. △ Less

Submitted 18 July, 2023; v1 submitted 10 April, 2023; originally announced April 2023.

Journal ref: International Journal of Plasticity, Volume 168, September 2023, 103701

Towards sub-30nm Contacted Gate Pitch, Forked Contact and Dynamically-Doped Nanosheets to Enhance Si and 2D Materials Device Scaling

Authors: Aryan Afzalian, Zubair Ahmed, Julien Ryckaert

Abstract: We propose a novel Forked-Contacts, Dynamically-Doped Multigate transistor as ultimate scaling booster for both Si and 2D materials in aggressively-scaled nanosheet devices. Using accurate dissipative DFT-NEGF atomistic-simulation fundamentals and cell layout extrinsics, we demonstrate superior and optimal device characteristics and invertor energy - delays down to sub-30-nm pitches, i.e., a 10 nm… ▽ More We propose a novel Forked-Contacts, Dynamically-Doped Multigate transistor as ultimate scaling booster for both Si and 2D materials in aggressively-scaled nanosheet devices. Using accurate dissipative DFT-NEGF atomistic-simulation fundamentals and cell layout extrinsics, we demonstrate superior and optimal device characteristics and invertor energy - delays down to sub-30-nm pitches, i.e., a 10 nm scaling boost compared to the nanosheet MOSFET references. △ Less

Submitted 12 March, 2022; originally announced March 2022.

Biaxial Strain Modulated Valence Band Engineering in III-V Digital Alloys

Authors: Sheikh Z. Ahmed, Yaohua Tan, Jiyuan Zheng, Joe C. Campbell, Avik W. Ghosh

Abstract: Some III-V digital alloy avalanche photodiodes exhibit low excess noise. These alloys have low hole ionization coefficients due to presence of small 'minigaps', enhanced effective mass and large separation between light-hole and split-off bands in the valence band. In this letter, an explanation for the formation of the minigaps using a tight binding picture is provided. Furthermore, we demonstrat… ▽ More Some III-V digital alloy avalanche photodiodes exhibit low excess noise. These alloys have low hole ionization coefficients due to presence of small 'minigaps', enhanced effective mass and large separation between light-hole and split-off bands in the valence band. In this letter, an explanation for the formation of the minigaps using a tight binding picture is provided. Furthermore, we demonstrate that decreasing substrate lattice constant can increase the minigap size and mass in the transport direction. This leads to reduced quantum tunneling and phonon scattering of the holes. Finally, we illustrate the band structure modification with substrate lattice constant for other III-V digital alloys. △ Less

Submitted 7 November, 2021; originally announced November 2021.

Atomistic transport modeling, design principles and empirical rules for Low Noise III-V Digital Alloy Avalanche Photodiodes

Authors: Sheikh Z. Ahmed, Yaohua Tan, Jiyuan Zheng, Joe C. Campbell, Avik W. Ghosh

Abstract: A series of III-V ternary and quarternary digital alloy avalanche photodiodes (APDs) have recently been seen to exhibit very low excess noise. Using band inversion of an environment-dependent atomistic tight binding description of short period superlattices, we argue that a combination of increased effective mass, minigaps and band split-off are primarily responsible for the observed superior perf… ▽ More A series of III-V ternary and quarternary digital alloy avalanche photodiodes (APDs) have recently been seen to exhibit very low excess noise. Using band inversion of an environment-dependent atomistic tight binding description of short period superlattices, we argue that a combination of increased effective mass, minigaps and band split-off are primarily responsible for the observed superior performance. These properties significantly limit the ionization rate of one carrier type, either holes or electrons, making the avalanche multiplication process unipolar in nature. The unipolar behavior in turn reduces the stochasticity of the multiplication gain. The effects of band folding on carrier transport are studied using the Non-Equilibrium Green's Function Method that accounts for quantum tunneling, and Boltzmann Transport Equation model for scattering. It is shown here that carrier transport by intraband tunneling and optical phonon scattering are reduced in materials with low excess noise. Based on our calculations, we propose five simple inequalities that can be used to approximately evaluate the suitability of digital alloys for designing low noise photodetectors. We evaluate the performance of multiple digital alloys using these criteria and demonstrate their validity. △ Less

Submitted 5 September, 2021; originally announced September 2021.

Comments: 13 pages, 13 figures and 4 tables

Characterization of band offsets in Al$_x$In$_{1-x}$As$_y$Sb$_{1-y}$ alloys with varying Al composition

Authors: Jiyuan Zheng, Andrew H. Jones, Yaohua Tan, Ann K. Rockwell, Stephen March, Sheikh Z. Ahmed, Catherine A. Dukes, Avik W. Ghosh, Seth R. Bank, Joe C. Campbell

Abstract: The unprecedented wide bandgap tunability (~1 eV) of Al$_x$In$_{1-x}$As$_y$Sb$_{1-y}$ latticed-matched to GaSb enables the fabrication of photodetectors over a wide range from near-infrared to mid-infrared. In this paper, the valence band-offsets in AlxIn1-xAsySb1-y with different Al compositions are analyzed by tight-binding calculations and X-ray photoelectron spectroscopy (XPS) measurements. Th… ▽ More The unprecedented wide bandgap tunability (~1 eV) of Al$_x$In$_{1-x}$As$_y$Sb$_{1-y}$ latticed-matched to GaSb enables the fabrication of photodetectors over a wide range from near-infrared to mid-infrared. In this paper, the valence band-offsets in AlxIn1-xAsySb1-y with different Al compositions are analyzed by tight-binding calculations and X-ray photoelectron spectroscopy (XPS) measurements. The observed weak variation in valence band offsets is consistent with the lack of any minigaps in the valence band, compared to the conduction band. △ Less

Submitted 27 May, 2021; originally announced May 2021.

Journal ref: Applied Physics Letters 115.12 (2019): 122105

Full band Monte Carlo simulation of AlInAsSb digital alloys

Authors: Jiyuan Zheng, Sheikh Z. Ahmed, Yuan Yuan, Andrew Jones, Yaohua Tan, Ann K. Rockwell, Stephen D. March, Seth R. Bank, Avik W. Ghosh, Joe C. Campbell

Abstract: Avalanche photodiodes fabricated from AlInAsSb grown as a digital alloy exhibit low excess noise. In this paper, we investigate the band structure-related mechanisms that influence impact ionization. Band-structures calculated using an empirical tight-binding method and Monte Carlo simulations reveal that the mini-gaps in the conduction band do not inhibit electron impact ionization. Good agreemen… ▽ More Avalanche photodiodes fabricated from AlInAsSb grown as a digital alloy exhibit low excess noise. In this paper, we investigate the band structure-related mechanisms that influence impact ionization. Band-structures calculated using an empirical tight-binding method and Monte Carlo simulations reveal that the mini-gaps in the conduction band do not inhibit electron impact ionization. Good agreement between the full band Monte Carlo simulations and measured noise characteristics is demonstrated. △ Less

Submitted 27 May, 2021; originally announced May 2021.

Journal ref: InfoMat 2.6 (2020): 1236-1240

A Physics Based Multiscale Compact Model of p-i-n Avalanche Photodiodes

Authors: Sheikh Z. Ahmed, Samiran Ganguly, Yuan Yuan, Jiyuan Zheng, Yaohua Tan, Joe C. Campbell, Avik W. Ghosh

Abstract: III-V material based digital alloy Avalanche Photodiodes (APDs) have recently been found to exhibit low noise similar to Silicon APDs. The III-V materials can be chosen to operate at any wavelength in the infrared spectrum. In this work, we present a physics-based SPICE compatible compact model for APDs built from parameters extracted from an Environment-Dependent Tight Binding (EDTB) model calibr… ▽ More III-V material based digital alloy Avalanche Photodiodes (APDs) have recently been found to exhibit low noise similar to Silicon APDs. The III-V materials can be chosen to operate at any wavelength in the infrared spectrum. In this work, we present a physics-based SPICE compatible compact model for APDs built from parameters extracted from an Environment-Dependent Tight Binding (EDTB) model calibrated to ab-initio Density Functional Theory (DFT) and Monte Carlo (MC) methods. Using this approach, we can accurately capture the physical characteristics of these APDs in integrated photonics circuit simulations. △ Less

Submitted 9 February, 2021; originally announced February 2021.

Comments: 8 pages, 11 figures

Probing Molecular Ordering in the Nematic Phases of para-Linked Bimesogen Dimers through NMR Studies of Flexible Prochiral Solutes

Authors: Leah M. Heist, Edward T. Samulski, Chris Welch, Ziauddin Ahmed, Georg H. Mehl, Alexandros G. Vanakaras, Demetri J. Photinos

Abstract: The quadrupolar splittings of perdeuteriated n-decane dissolved in nematic phases formed by mesogenic dimers of the CBnCB series, for n=7,9,10,11 are measured throughout the entire temperature range of these phases. The results of the measurements, are reported together with related measurements using the common nematic phase of 5CB as a solvent for n-decane. The data obtained from the $^{13}$C sp… ▽ More The quadrupolar splittings of perdeuteriated n-decane dissolved in nematic phases formed by mesogenic dimers of the CBnCB series, for n=7,9,10,11 are measured throughout the entire temperature range of these phases. The results of the measurements, are reported together with related measurements using the common nematic phase of 5CB as a solvent for n-decane. The data obtained from the $^{13}$C spectra of the cyanobiphenyl mesogenic units of the monomeric and dimeric solvent molecules yield the order parameter of those units. The information obtained from this set of experiments is used to elucidate the structure of the low temperature (N$_X$) and the high temperature (N) nematic phases of CBnCB dimers with n=7,9,11. The polar twisted nematic (N$_{PT}$) model is found to provide a consistent description not only of these measurements, but also of NMR measurements previously reported in the literature for these phases. These findings suggest that the high temperature nematic (N) is not a common, locally uniaxial and apolar nematic, but rather a nematic phase consisting of N$_{PT}$ clusters. The twist-bend (N$_{TB}$) model, often identified with the N$_X$ phase, is shown to be inadequate to account even qualitatively for crucial features of the experimental findings. △ Less

Submitted 19 September, 2019; originally announced September 2019.

Comments: 41 pages, 8 figures, 1 appendix, supplementary material

Journal ref: Liquid Crystals, 2020

Expectation value of $p^6$ in continuous two-piece symmetric potential wells

Authors: Zafar Ahmed, Sachin Kumar

Abstract: Earlier, potentials like square well and several other half-potential wells with discontinuous jump have been found to have the expectation value $<\! p^6 \!>$ to be divergent for all bound states. Here, we consider two-piece symmetric potential wells to prove and demonstrate that in them the expectation value of $p^6$ diverges for even states and converges for odd states. Here, $p$ denotes moment… ▽ More Earlier, potentials like square well and several other half-potential wells with discontinuous jump have been found to have the expectation value $<\! p^6 \!>$ to be divergent for all bound states. Here, we consider two-piece symmetric potential wells to prove and demonstrate that in them the expectation value of $p^6$ diverges for even states and converges for odd states. Here, $p$ denotes momentum. We also present three exactly solvable models. △ Less

Submitted 6 May, 2019; originally announced May 2019.

Comments: 9 pages 4 figures and no tables. arXiv admin note: text overlap with arXiv:1803.01597

Solvable model of bound states in the continuum (BIC) in one dimension

Authors: Zafar Ahmed, Sachin Kumar, Dona Ghosh, Tarit Goswami

Abstract: Historically, most of the quantum mechanical results have originated in one dimensional model potentials. However, Von-Neumann's Bound states in the Continuum (BIC) originated in specially constructed, three dimensional, oscillatory, central potentials. One dimensional version of BIC has long been attempted, where only quasi-exactly-solvable models have succeeded but not without instigating degene… ▽ More Historically, most of the quantum mechanical results have originated in one dimensional model potentials. However, Von-Neumann's Bound states in the Continuum (BIC) originated in specially constructed, three dimensional, oscillatory, central potentials. One dimensional version of BIC has long been attempted, where only quasi-exactly-solvable models have succeeded but not without instigating degeneracy in one dimension. Here, we present an exactly solvable bottomless exponential potential barrier $V(x)=-V_0[\exp(2|x|/a)-1]$ which for $E<V_0$ has a continuum of non-square-integrable, definite-parity, degenerate states. In this continuum, we show a surprising presence of discrete energy, square-integrable, definite-parity, non-degenerate states. For $E>V_0$, there is again a continuum of complex scattering solutions $ψ(x)$ whose real and imaginary parts though solutions of Schr{ö}dinger equation yet their parities cannot be ascertained as $Cψ(x)$ is also a solution where $C$ is an arbitrary complex non-real number. △ Less

Submitted 13 June, 2019; v1 submitted 31 January, 2019; originally announced January 2019.

Comments: There is no Ref. [16] in the paper, please read [15] for [16]

Journal ref: Phys. Scr. 94 (2019) 105214

Modeling tunnel field effect transistors - from interface chemistry to non-idealities to circuit level performance

Authors: Sheikh Z. Ahmed, Yaohua Tan, Daniel S. Truesdell, Benton H. Calhoun, Avik W. Ghosh

Abstract: We present a quasi-analytical model for Tunnel Field Effect Transistors (TFETs) that includes the microscopic physics and chemistry of interfaces and non-idealities. The ballistic band-to-band tunneling current is calculated by modifying the well known Simmons equation for oxide tunneling, where we integrate the Wentzel-Kramers-Brillouin (WKB) tunneling current over the transverse modes. We extend… ▽ More We present a quasi-analytical model for Tunnel Field Effect Transistors (TFETs) that includes the microscopic physics and chemistry of interfaces and non-idealities. The ballistic band-to-band tunneling current is calculated by modifying the well known Simmons equation for oxide tunneling, where we integrate the Wentzel-Kramers-Brillouin (WKB) tunneling current over the transverse modes. We extend the Simmons equation to finite temperature and non-rectangular barriers using a two-band model for the channel material and an analytical channel potential profile obtained from Poisson's equation. The two-band model is parametrized first principles by calibrating with hybrid Density Functional Theory calculations, and extended to random alloys with a band unfolding technique. Our quasi-analytical model shows quantitative agreement with ballistic quantum transport calculations. On top of the ballistic tunnel current we incorporate higher order processes arising at junctions coupling the bands, specifically interface trap-assisted tunneling and Auger generation processes. Our results suggest that both processes significantly impact the off-state characteristics of the TFETs - Auger in particular being present even for perfect interfaces. We show that our microscopic model can be used to quantify the TFET performance on the atomistic interface quality. Finally, we use our simulations to quantify circuit level metrics such as energy consumption. △ Less

Submitted 19 June, 2018; v1 submitted 16 June, 2018; originally announced June 2018.

Pearson's correlation coefficient in the theory of networks: A comment

Authors: Zafar Ahmed, Sachin Kumar

Abstract: In statistics, the Pearson correlation coefficient $r_{x,y}$ determines the degree of linear correlation between two variables and it is known that $-1 \le r_{x,y} \le 1$. In the theory of networks, a curious expression proposed in [PRL {\bf 89} 208701 (2002)] for degree-degree correlation coefficient $r_{j_i,k_i}, i\in [1,M]$ has been in use. We realize that the suggested form is the conventional… ▽ More In statistics, the Pearson correlation coefficient $r_{x,y}$ determines the degree of linear correlation between two variables and it is known that $-1 \le r_{x,y} \le 1$. In the theory of networks, a curious expression proposed in [PRL {\bf 89} 208701 (2002)] for degree-degree correlation coefficient $r_{j_i,k_i}, i\in [1,M]$ has been in use. We realize that the suggested form is the conventional Pearson's coefficient for $\{(j_i,k_i), (k_i,j_i)\}$ for $2M$ data points and hence it is rightly dedicated to undirected networks. △ Less

Submitted 21 March, 2018; v1 submitted 16 March, 2018; originally announced March 2018.

Comments: Important changes in the abstract and in the text

Gaussian pseudo-Orthogonal Ensemble of Real Random Matrices

Authors: Sachin Kumar, Amit Kumar, S M Yusuf

Abstract: Here, using two real non-zero parameters $λ$ and $μ$, we construct Gaussian pseudo-orthogonal ensembles of a large number $N$ of $n \times n$ ($n$ even and large) real pseudo-symmetric matrices under the metric $η$ using $ \altmathcal {N}=n(n+1)/2$ elements independently drawn from a Gaussian random population and investigate the statistical properties of the eigenvalues. When $λμ>0$, we show that… ▽ More Here, using two real non-zero parameters $λ$ and $μ$, we construct Gaussian pseudo-orthogonal ensembles of a large number $N$ of $n \times n$ ($n$ even and large) real pseudo-symmetric matrices under the metric $η$ using $ \altmathcal {N}=n(n+1)/2$ elements independently drawn from a Gaussian random population and investigate the statistical properties of the eigenvalues. When $λμ>0$, we show that the pseudo-symmetric matrix is similar to a real symmetric matrix, consequently, all the eigenvalues are real and so the spectral distributions satisfy Wigner's statistics. But when $λμ<0$ the eigenvalues are either real or complex conjugate pairs. We find that these real eigenvalues exhibit intermediate statistics. We show that the diagonalizing matrices ${ \cal D}$ of these pseudo-symmetric matrices are pseudo-orthogonal under a constant metric $ζ$ as $ \altmathcal{D}^t ζ\altmathcal{D}= ζ$, and hence they belong to a pseudo-orthogonal group. These pseudo-symmetric matrices serve to represent the parity-time (PT)-symmetric quantum systems having exact (un-broken) or broken PT-symmetry. △ Less

Submitted 11 July, 2025; v1 submitted 13 February, 2018; originally announced February 2018.

Comments: Changes of text at some place for better consistency of terminology used in work

Expectation values of $p^2$ and $p^4$ in the square well potential

Authors: Zafar Ahmed, Dona Ghosh, Sachin Kumar, Joseph Amal Nathan

Abstract: Position and momentum representations of a wavefunction $ψ(x)$ and $φ(p)$, respectively are physically equivalent yet mathematically in a given case one may be easier or more transparent than the other. This disparity may be so much so that one has to device a special strategy to get the quantity of interest in one of them. We revisit finite square well (FSW) in this regard. Circumventing the the… ▽ More Position and momentum representations of a wavefunction $ψ(x)$ and $φ(p)$, respectively are physically equivalent yet mathematically in a given case one may be easier or more transparent than the other. This disparity may be so much so that one has to device a special strategy to get the quantity of interest in one of them. We revisit finite square well (FSW) in this regard. Circumventing the the problems of discontinuity of second and higher derivatives of $ψ(x)$ we obtain simple analytic expressions of $<\!p^2\!>$ and $<\!p^4\!>$. But it is the surprising fall-off of $φ(p)$ as $p^{-6}$ that reveals and restricts $<\!p^s\!>$ to be finite and non-zero only for $s=2,4$. In finding $<\!p^s\!>(s=2,4)$ from $φ(p)$, $p$-integrals are improper which for time-being, have been evaluated numerically to show the agreement between two representations. △ Less

Submitted 17 January, 2018; v1 submitted 15 January, 2018; originally announced January 2018.

Comments: 5 pages and six figures, Eq. (7) and the text below it are corrected, text added below Eq. (15)

Coherent scattering from semi-infinite non-Hermitian potentials

Authors: Zafar Ahmed, Dona Ghosh, Sachin Kumar

Abstract: When two identical (coherent) beams are injected at a semi-infinite non-Hermitian medium from left and right, we show that both reflection $(r_L,r_R)$ and transmission $(t_L,t_R)$ amplitudes are non-reciprocal. In a parametric domain, there exists Spectral Singularity (SS) at a real energy $E=E_*$ and the determinant of the time-reversed two port S-matrix i.e., $|\det(S)|=|t_L t_R-r_L r_R|$ vanish… ▽ More When two identical (coherent) beams are injected at a semi-infinite non-Hermitian medium from left and right, we show that both reflection $(r_L,r_R)$ and transmission $(t_L,t_R)$ amplitudes are non-reciprocal. In a parametric domain, there exists Spectral Singularity (SS) at a real energy $E=E_*$ and the determinant of the time-reversed two port S-matrix i.e., $|\det(S)|=|t_L t_R-r_L r_R|$ vanishes sharply at $E=E_*$ displaying the phenomenon of Coherent Perfect Absorption (CPA). In the complimentary parametric domain, the potential becomes either left or right reflectionless at $E=E_z$. But we rule out the existence of Invisibility despite $r_R(E_i)=0$ and $t_R(E_i)=1$ in these new models. We present two simple exactly solvable models where the expressions for $E_*$, $E_z$, $E_i$ and the parametric conditions on the potential have been obtained in explicit and simple forms. Earlier, the novel phenomena of SS and CPA have been found to occur only in the scattering complex potentials which are spatially localized (vanish asymptotically) and having $t_L=t_R$. △ Less

Submitted 24 January, 2018; v1 submitted 25 September, 2017; originally announced September 2017.

Comments: Six pages, 3 figures, no table, language improved

Journal ref: Phys. Rev. A 97, 023828 (2018)

Engineering Multiple Topological Phases in Nanoscale Van der Waals Heterostructures: Realisation of $α$-Antimonene

Authors: Tobias Märkl, Pawel J. Kowalczyk, Maxime Le Ster, Ishan Vardhan Mahajan, Harry Pirie, Zuned Ahmed, Guang Bian, Xiaoxiong Wang, Tai-Chang Chiang, Simon Anthony Brown

Abstract: Van der Waals heterostructures have recently been identified as providing many opportunities to create new two-dimensional materials, and in particular to produce materials with topologically interesting states. Here we show that it is possible to create such heterostructures with multiple topological phases in a single nanoscale island. We discuss their growth within the framework of diffusion-li… ▽ More Van der Waals heterostructures have recently been identified as providing many opportunities to create new two-dimensional materials, and in particular to produce materials with topologically interesting states. Here we show that it is possible to create such heterostructures with multiple topological phases in a single nanoscale island. We discuss their growth within the framework of diffusion-limited aggregation, the formation of moiré patterns due to the differing crystallographies of the materials comprising the heterostructure, and the potential to engineer both the electronic structure as well as local variations of topological order. In particular we show that it is possible to build islands which include both the hexagonal $β$- and rectangular $α$-forms of antimonene, on top of the topological insulator $α$-bismuthene. This is the first experimental realisation of $α$-antimonene, and we show that it is a topologically non-trivial material in the quantum spin Hall class. △ Less

Submitted 27 August, 2017; originally announced August 2017.

Comments: 6 pages, 3 figures, plus Supplementary material (9 pages, 6 figures)

Journal ref: 2018 2D Mater. 5 011002

Solvable models of an open well and a bottomless barrier in 1-D

Authors: Zafar Ahmed, Dona Ghosh, Sachin Kumar, Nihar Turumella

Abstract: We present one dimensional potentials $V(x)= V_0[e^{2|x|/a}-1]$ as solvable models of a well $(V_0>0)$ and a barrier ($V_0<0$). Apart from being new addition to solvable models, these models are instructive for finding bound and scattering states from the analytic solutions of Schr{ö}dinger equation. The exact analytic (semi-classical and quantal) forms for bound states of the well and reflection/… ▽ More We present one dimensional potentials $V(x)= V_0[e^{2|x|/a}-1]$ as solvable models of a well $(V_0>0)$ and a barrier ($V_0<0$). Apart from being new addition to solvable models, these models are instructive for finding bound and scattering states from the analytic solutions of Schr{ö}dinger equation. The exact analytic (semi-classical and quantal) forms for bound states of the well and reflection/transmission $(R/T)$ co-efficients for the barrier have been derived. Interestingly, the crossover energy $E_c$ where $R(E_c)=1/2=T(E_c)$ may occur below/above or at the barrier-top. A connection between poles of these co-efficients and bound state eigenvalues of the well has also been demonstrated. △ Less

Submitted 19 June, 2017; v1 submitted 16 June, 2017; originally announced June 2017.

Comments: Fig. 6(b) changed, Section IV modified after Eq. 16, some typos corrected

Journal ref: Eur. J. Phys. 39 (2018) 025404

Pseudo-symmetric random matrices: semi-Poisson and sub-Wigner statistics

Authors: Sachin Kumar, Zafar Ahmed

Abstract: Real non-symmetric matrices may have either real or complex conjugate eigenvalues. These matrices can be seen to be pseudo-symmetric as $ηM η^{-1} = M^t$, where the metric $η$ could be secular (a constant matrix) or depending upon the matrix elements of $M$. Here, we construct ensembles of a large number $N$ of pseudo-symmetric $n \times n$ ($n$ large) matrices using ${\cal N}$… ▽ More Real non-symmetric matrices may have either real or complex conjugate eigenvalues. These matrices can be seen to be pseudo-symmetric as $ηM η^{-1} = M^t$, where the metric $η$ could be secular (a constant matrix) or depending upon the matrix elements of $M$. Here, we construct ensembles of a large number $N$ of pseudo-symmetric $n \times n$ ($n$ large) matrices using ${\cal N}$ $(n(n+1)/2 \le {\cal N} \le n^2)$ independent and identically distributed (iid) random numbers as their elements. Based on our numerical calculations, we conjecture that for these ensembles the Nearest Level Spacing Distributions (NLSDs: $p(s)$) are sub-Wigner as $p_{abc}(s)=a s e^{-bs^c} (0<c <2)$ and the distributions of their eigenvalues fit well to $D(ε)= A[\mbox{tanh}\{(ε+B)/C \}-\mbox{tanh}\{(ε-B)/C\}]$ (exceptions also discussed). These sub-Wigner NLSD are encountered in Anderson metal-insulator transition and topological transitions in a Josephson junction. Interestingly, $p(s)$ for $c=1$ is called semi-Poisson and we show that it lies close to the form $p(s)=0.59 s K_0(0.45 s^2)$ derived for the case of $2 \times 2$ pseudo-symmetric matrix where the eigenvalues are most aptly conditionally real: $E_{1,2}=a \pm \sqrt{b^2-c^2}$ which represent characteristic coalescing of eigenvalues in PT(Parity-Time)-symmetric systems. △ Less

Submitted 10 August, 2017; v1 submitted 25 May, 2017; originally announced May 2017.

Comments: 7 pages, 5 figures and 1 table, 3 New Refs. added, to appear in Phys. Rev. E

Journal ref: Phys. Rev. E 96, 022157 (2017)

Spectral statistics for ensembles of various real random matrices

Authors: Sachin Kumar, Zafar Ahmed

Abstract: We investigate spacing statistics $p(s)$ and distribution of eigenvalues $D(ε)$ for ensembles of various real random matrices (of order $n \times n, n=2$ and $n>>2$) where the matrix-elements have various Probability Distribution Function (PDF: $f(x)$) including Gaussian. We construct ensembles of $1000$, $100 \times 100$ real random matrices $R$, $C$ (cyclic) and $T$ (tridiagonal) and real symmet… ▽ More We investigate spacing statistics $p(s)$ and distribution of eigenvalues $D(ε)$ for ensembles of various real random matrices (of order $n \times n, n=2$ and $n>>2$) where the matrix-elements have various Probability Distribution Function (PDF: $f(x)$) including Gaussian. We construct ensembles of $1000$, $100 \times 100$ real random matrices $R$, $C$ (cyclic) and $T$ (tridiagonal) and real symmetric matrices: ${\cal R}'$, ${\cal R}=R+R^t$, ${\cal Q}=RR^t$, ${\cal C}$ (cyclic), ${\cal T}$ (tridiagonal), $T'$ (pseudo-symmetric Tridiagonal), $Θ$ (Toeplitz) , ${\cal D}=CC^t$ and ${\cal S}=TT^t$. We find that the spacing distribution of the adjacent levels of matrices ${\cal R}$ and ${\cal R}'$ under any symmetric PDF of matrix elements is $p_{AB}(s)=A s e^{-Bs^2}$ which approximately conforms to the Wigner surmise as $A/2 \approx B \approx π/4$. But under asymmetric PDFs we observe $A/2 \approx B >>π/4$, where $A,B$ are also sensitive to the choice of the matrix and the PDF. More interestingly, the real symmetric matrices ${\cal C}, {\cal T}, {\cal Q}$, $Θ$ (excepting ${\cal D}$ and ${\cal S}$) and $T'$ (pseudo-symmetric tridiagonal) all conform to the Poisson distribution $p_μ(s) =μe^{-μs}$, where $μ$ depends upon the choice of the matrix and PDF. Let complex eigenvalues of $R$, $C$ and $T$ be $E^c_n$. We show that all $p(s)$ arising due to $\Re(E^c_n)$, $\Im(E^c_n)$ and $|E^c_n|$ of $R$, $C$ and $T$ are also of Poisson type: $μe^{-μs}$. We observe $p(s)$ as half-Gaussian for two real eigenvalues of $C$. For real matrices $R, C, T$, we associate new types of $p(s)$ with them. Lastly, we study the distribution $D(ε)$ of eigenvalues of symmetric matrices (of large order) discussed above. △ Less

Submitted 10 April, 2017; originally announced April 2017.

Comments: 12 pages, 11 figures and 4 tables

Journal ref: Acta Polytechnica 57,418, 2017

Molecular organization in the twist-bend nematic phase by resonant X-ray scattering at the Se K-edge and by SAXS, WAXS and GIXRD

Authors: W. D. Stevenson, Z. Ahmed, X. B. Zeng, C. Welch, G. Ungar, G. H. Mehl

Abstract: Using a novel Se-labelled dimer mixed with DTC5C7 aligned by magnetic field, the twist-bend nematic phase (Ntb) in dimers was studied by hard X-ray resonant scattering and by small and wide angle X-ray scattering (SAXS, WAXS). Resonant diffraction spots indicated a helix with a 9-12 nm pitch in the Ntb phase. Unprecedentedly high helix orien-tation enabled deconvolution of global and local order p… ▽ More Using a novel Se-labelled dimer mixed with DTC5C7 aligned by magnetic field, the twist-bend nematic phase (Ntb) in dimers was studied by hard X-ray resonant scattering and by small and wide angle X-ray scattering (SAXS, WAXS). Resonant diffraction spots indicated a helix with a 9-12 nm pitch in the Ntb phase. Unprecedentedly high helix orien-tation enabled deconvolution of global and local order parameters. This, combined with simultaneous resonant and non-resonant SAXS and WAXS data, allowed us to construct a modified model of the Ntb phase matching twisted molecular conformations and the local heliconical director field. △ Less

Submitted 4 December, 2016; originally announced December 2016.

Comments: Main text: 5 pages, 4 figures Supporting information: 27 pages, 9 figures, 5 tables

Comparative analysis of anisotropic material properties of uniaxial nematics formed by flexible dimers and rod-like monomers

Authors: Greta Cukrov, Youssef Mosaddeghian Golestani, Jie Xiang, Yu. A. Nastishin, Z. Ahmed, C. Welch, G. H. Mehl, Oleg D. Lavrentovich

Abstract: We report temperature dependencies of material properties such as dielectric anisotropy, birefringence, splay (K11), twist (K22), and bend (K33) elastic constants of the uniaxial nematic (N) phase formed by flexible dimers of DTC5C9 and compare their behavior to that of a corresponding monomer MCT5. DTC5C9 forms a twist-bend nematic (Ntb) at temperatures below the N phase. Anisotropic properties o… ▽ More We report temperature dependencies of material properties such as dielectric anisotropy, birefringence, splay (K11), twist (K22), and bend (K33) elastic constants of the uniaxial nematic (N) phase formed by flexible dimers of DTC5C9 and compare their behavior to that of a corresponding monomer MCT5. DTC5C9 forms a twist-bend nematic (Ntb) at temperatures below the N phase. Anisotropic properties of MCT5 are typical of the rod-like mesogens. In particular, birefringence increases as the temperature is reduced, following the classic behavior, described by Haller. The elastic constants also follow the standard behavior, with their ratios being practically temperature-independent. In contrast, DTC5C9 shows a dramatic departure from the standard case. Birefringence changes non-monotonously with temperature, decreasing on approaching the N-Ntb phase transition. decreases strongly to 0.4 pN near the N - Ntb transition, although remains finite. The ratios of the elastic constants in DTC5C9 show a strong temperature dependence that can be associated with the bend-induced changes in the orientational distribution function. The measured elastic properties are consistent with the tendency of the dimeric molecules to adopt bent configurations that give rise to the Ntb phase. △ Less

Submitted 23 September, 2016; originally announced September 2016.

Comments: This is an Accepted Original Manuscript of an article to be published by Taylor & Francis in Liquid Crystals. Contents: 26 pages, 10 figures

Journal ref: Liq. Cryst. 44, 219 (2017)

Light scattering study of the "pseudo-layer" compression elastic constant in a twist-bend nematic liquid crystal

Authors: Z. Parsouzi, Shokir A. Pardaev, C. Welch, Z. Ahmed, G. H. Mehl, A. R. Baldwin, J. T. Gleeson, O. D. Lavrentovich, D. W. Allender, J. V. Selinger, A. Jakli, S. Sprunt

Abstract: The nematic twist-bend (TB) phase, exhibited by certain achiral thermotropic liquid crystalline (LC) dimers, features a nanometer-scale, heliconical rotation of the average molecular long axis (director) with equally probable left- and right-handed domains. On meso to macroscopic scales, the TB phase may be considered as a stack of equivalent slabs or "pseudo-layers", each one helical pitch in thi… ▽ More The nematic twist-bend (TB) phase, exhibited by certain achiral thermotropic liquid crystalline (LC) dimers, features a nanometer-scale, heliconical rotation of the average molecular long axis (director) with equally probable left- and right-handed domains. On meso to macroscopic scales, the TB phase may be considered as a stack of equivalent slabs or "pseudo-layers", each one helical pitch in thickness. The long wavelength fluctuation modes should then be analogous to those of a smectic-A phase, and in particular the hydrodynamic mode combining "layer" compression and bending ought to be characterized by an effective layer compression elastic constant $B_{eff}$ and average director splay constant $K_1^{eff}$. The magnitude of $K_1^{eff}$ is expected to be similar to the splay constant of an ordinary nematic LC, but due to the absence of a true mass density wave, $B_{eff}$ could differ substantially from the typical value of $\sim 10^6$ Pa in a conventional smectic-A. Here we report the results of a dynamic light scattering study, which confirms the "pseudo-layer" structure of the TB phase with $B_{eff}$ in the range $\sim 10^3-10^4$ Pa. We show additionally that the temperature dependence of $B_{eff}$ at the TB to nematic transition is accurately described by a coarse-grained free energy density, which is based on a Landau-deGennes expansion in terms of a heli-polar order parameter that characterizes the TB state and is linearly coupled to bend distortion of the director. △ Less

Submitted 14 September, 2016; originally announced September 2016.

Comments: 9 pages, 7 figures

Energy of mixing and entropy of mixing for Cu$_{x}$Al$_{1-x}$ liquid binary alloys

Authors: Fysol Ibna Abbas, G. M. Bhuiyan, A. Z. Ziauddin Ahmed

Abstract: The free energy of mixing and the entropy of mixing for Cu$_{x}$Al$_{1-x}$ liquid binary alloys have been systematically investigated by using the electronic theory of metals along with the perturbation approach at a thermodynamic state $T=1373$ K. The interionic interaction and a reference liquid are the fundamental components of the theory. The interionic interaction is described by a local pseu… ▽ More The free energy of mixing and the entropy of mixing for Cu$_{x}$Al$_{1-x}$ liquid binary alloys have been systematically investigated by using the electronic theory of metals along with the perturbation approach at a thermodynamic state $T=1373$ K. The interionic interaction and a reference liquid are the fundamental components of the theory. The interionic interaction is described by a local pseudopotential. A liquid of hard spheres (HS) of two different effective diametres is used to describe the reference system for alloys. The results of the calculations for energy of mixing agree well with the available experimental data. Calculation of entropy of mixing is parameter free and, the agreement with experiment, in this case, is found to be fairly good. △ Less

Submitted 20 July, 2016; originally announced July 2016.

Comments: 23 pages in pdf file, 11 figures

Role of carbon nanotube diameter on thermal interfacial resistance through the analysis of vibrational mismatch: A Molecular Dynamics approach

Authors: Ajinkya Sarode, Zeeshan Ahmed, Pratik Basarkar, Atul Bhargav, Debjyoti Banerjee

Abstract: Carbon nanotube (CNT) have been known to increase the heat transfer at the solid-liquid interfaces, but have a limitation due to the interfacial thermal resistance. Vibrational mismatch at the interface leads to this interfacial thermal resistance, which plays an important role in energy transfer at the boundary. Negligible work has been reported on the influence of CNT diameter on the resistance… ▽ More Carbon nanotube (CNT) have been known to increase the heat transfer at the solid-liquid interfaces, but have a limitation due to the interfacial thermal resistance. Vibrational mismatch at the interface leads to this interfacial thermal resistance, which plays an important role in energy transfer at the boundary. Negligible work has been reported on the influence of CNT diameter on the resistance through the vibrational mismatch study. Molecular dynamics simulations have been performed to investigate the effect of CNT diameter on interfacial resistance between carbon nanotube (CNT) and water molecules. This work is an effort to understand the heat transfer phenomenon at the interface by quantifying the vibrational mismatch. Analysis of the vibrational spectra of CNT and water molecules is done to study the effect of CNT diameter on interfacial resistance. Starting with the initial configuration, and equilibrating the system of CNT and water molecules at 300 K and 1 atm, the CNT temperature is raised to 700 K by velocity rescaling. This system is now allowed to relax as a micro-canonical ensemble. Based on the lumped capacitance analysis, the time constant of the CNT temperature response is determined, which is then used to compute the interfacial thermal resistance. The interfacial thermal resistance is observed to be relatively higher for the larger diameter nanotube. This is attributed to the higher vibrational mismatch existing for larger diameter CNT as a result of low overlapping region between vibrational density states of CNT and water molecules. For smaller diameter CNT, the interfacial thermal resistance is low which results in the efficient heat transfer at the interface thus, emphasizing the indispensable role of larger diameter CNTs in the cooling applications. △ Less

Submitted 2 October, 2016; v1 submitted 11 July, 2016; originally announced July 2016.

Comments: 11 pages, 6 figures, Molecular dynamics simulation performed using LAMMPS

Dirichlet spectrum of the paradigm model of complex PT-symmetric potential: $V(x)=-(ix)^N$

Authors: Zafar Ahmed, Sachin Kumar, Dhruv Sharma

Abstract: So far the spectra $E_n(N)$ of the paradigm model of complex PT(Parity-Time)-symmetric potential $V_{BB}(x,N)=-(ix)^N$ is known to be analytically continued for $N > 4$. Consequently, the well known eigenvalues of the Hermitian cases ($N=6,10$) cannot be recovered. Here, we illustrate Kato's theorem that even if a Hamiltonian $H(λ)$ is an analytic function of a real parameter $λ$, its eigenvalues… ▽ More So far the spectra $E_n(N)$ of the paradigm model of complex PT(Parity-Time)-symmetric potential $V_{BB}(x,N)=-(ix)^N$ is known to be analytically continued for $N > 4$. Consequently, the well known eigenvalues of the Hermitian cases ($N=6,10$) cannot be recovered. Here, we illustrate Kato's theorem that even if a Hamiltonian $H(λ)$ is an analytic function of a real parameter $λ$, its eigenvalues $E_n(λ)$ may not be analytic at finite number of Isolated Points (IPs). In this light, we present the Dirichlet spectra $E_n(N)$ of $V_{BB}(x,N)$ for $2\le N<12$ using the numerical integration of Schr{ö}dinger equation with $ψ(x=\pm \infty)=0$ and the diagonalization of $H=p^2/2μ+V_{BB}(x,N)$ in the harmonic oscillator basis. We show that these real discrete spectra are consistent with the most simple two-turning point CWKB (C refers to complex turning points) method provided we choose the maximal turning points (MxTP) [$-a+ib,a+ib, a, b \in {\cal R}$] such that $|a|$ is the largest for a given energy among all (multiple) turning points. We find that $E_n(N)$ are continuous function of $N$ but non-analytic (their first derivative is discontinuous) at IPs $N=4,8$; where the Dirichlet spectrum is null (as $V_{BB}$ becomes a Hermitian flat-top potential barrier). At $N=6$ and $10$, $V_{BB}(x,N)$ becomes a Hermitian well and we recover its well known eigenvalues. △ Less

Submitted 12 July, 2017; v1 submitted 15 June, 2016; originally announced June 2016.

Comments: Final Version just appeared in Annals of Physics (N.Y.) 383 (2017) 635-644

Journal ref: Annals of Physics (N.Y.) 383 (2017) 635-644

The Design and Investigation of the Self-Assembly of Dimers with two Nematic Phases

Authors: Z. Ahmed, C. Welch, G. H. Mehl

Abstract: A series of non-symmetric dimers were synthesised containing either cyanobiphenyl or difluoroterphenyl moieties on one side and a range of long, short, bent, polar or apolar mesogens on the other side of the molecules. The dielectric anisotropy of the mesogens was varied systematically. The systems were characterised by differential scanning calorimetry (DSC), optical polarizing microscopy (OPM) a… ▽ More A series of non-symmetric dimers were synthesised containing either cyanobiphenyl or difluoroterphenyl moieties on one side and a range of long, short, bent, polar or apolar mesogens on the other side of the molecules. The dielectric anisotropy of the mesogens was varied systematically. The systems were characterised by differential scanning calorimetry (DSC), optical polarizing microscopy (OPM) and detailed X-ray diffraction (XRD) studies, both in the nematic and the Nx phase. The results are compared and structure properties relationships are discussed. A model for the assembly in the Nx phase is developed discussing Ntb structures, coaxial helices, swiss roll structures and chiral domain formation. △ Less

Submitted 6 September, 2015; originally announced September 2015.

Do the short helices exist in the nematic TB phase?

Authors: Ewa Gorecka, Miroslaw Salamonczyk, Anna Zep, Damian Pociecha, Chris Welch, Ziauddin Ahmed, Georg H. Mehl

Abstract: Dimeric compounds forming twist-bend nematic, Ntb, phase show unusual optical texture related to the formation of arrays of focal conic defects. Some of the focal conics show submicron internal structure with 8 nm periodicity, which is very close to that found in the crystalline phase of the material, suggesting surface freezing. Dimeric compounds forming twist-bend nematic, Ntb, phase show unusual optical texture related to the formation of arrays of focal conic defects. Some of the focal conics show submicron internal structure with 8 nm periodicity, which is very close to that found in the crystalline phase of the material, suggesting surface freezing. △ Less

Submitted 23 October, 2014; originally announced October 2014.

Spin Waves in 2D ferromagnetic square lattice stripe

Authors: Maher Z. Ahmed

Abstract: In this work, the area and edges spin wave calculations were carried out using the Heisenberg Hamiltonian and the tridiagonal method for the 2D ferromagnetic square lattice stripe, where the SW modes are characterized by a 1D in-plane wave vector $q_x$. The results show a general and an unexpected feature that the area and edge spin waves only exist as optic modes. This behavior is also seen in 2D… ▽ More In this work, the area and edges spin wave calculations were carried out using the Heisenberg Hamiltonian and the tridiagonal method for the 2D ferromagnetic square lattice stripe, where the SW modes are characterized by a 1D in-plane wave vector $q_x$. The results show a general and an unexpected feature that the area and edge spin waves only exist as optic modes. This behavior is also seen in 2D Heisenberg antiferromagnetic square lattice. This absence of the acoustic modes in the 2D square lattice is explained by the fact that the geometry constrains for NN exchange inside the square lattice allow only optical modes. We suggest that this unexpected behavior of spin waves in the 2D square lattice may be useful in realizing an explanation for HTS. △ Less

Submitted 19 October, 2011; originally announced October 2011.

Comments: 19 pages,8 figures

Brownian motion model of random matrices revisited

Authors: Sudhir R. Jain, Zafar Ahmed

Abstract: We present a modified Brownian motion model for random matrices where the eigenvalues (or levels) of a random matrix evolve in "time" in such a way that they never cross each other's path. Also, owing to the exact integrability of the level dynamics, we incorporate long-time recurrences into the random walk problem underlying the Brownian motion. From this model, we derive the Coulomb interactio… ▽ More We present a modified Brownian motion model for random matrices where the eigenvalues (or levels) of a random matrix evolve in "time" in such a way that they never cross each other's path. Also, owing to the exact integrability of the level dynamics, we incorporate long-time recurrences into the random walk problem underlying the Brownian motion. From this model, we derive the Coulomb interaction between the two eigenvalues. We further show that the Coulomb gas analogy fails if the confining potential, $V(E)$ is a transcendental function such that there exist orthogonal polynomials with weighting function, $\exp [-βE]$, where $β$ is a symmetry parameter. △ Less

Submitted 23 April, 1998; originally announced April 1998.

Comments: 3 pages, LaTeX