Table of contents for issue 6, volume 11, New Journal of Physics

The topic of high-energy cosmic rays has recently attracted significant attention. While the AGASA and HiRes Observatories have closed after many years of successful operation, the Pierre Auger Observatory began taking data in January 2004 and the first results have been reported. Plans for the next generation of instruments are in hand: funding is now being sought for the northern phase of the Auger Observatory and plans for a space detector, JEM-EUSO, to be launched in 2013–14 are well advanced with the long-term target of a dedicated satellite for the 2020s. It therefore seemed an appropriate time to make a collection of outstanding and original research articles from the leading experimental groups and from some of the theorists who seek to interpret the hard-won data and to speculate on the origin of the highest energy cosmic rays.

This focus issue in New Journal of Physics on the topic of high energy cosmic rays, contains a comprehensive account of the work of the Yakutsk group (A A Ivanov, S P Knurenko and I Ye Sleptsov) who have used Cerenkov radiation produced by shower particles in the air to provide the basis for energy calibration. This technique contrasts with that of detecting fluorescence radiation from space that is proposed for the JEM-EUSO instrument to be placed on the International Space Station in 2013, described by Y Takahashi. Supplementing this is an article by A Santangelo and A Petrolini describing the scientific goals, requirements and main instrument features of the Super Extreme Universe Space Observatory mission (S-EUSO).

The use of fluorescence light to measure energies was the key component of the HiRes instrument and is also used extensively by the Pierre Auger Collaboration so an article, by F Arqueros, F Blanco and J Rosado, summarizing the properties of fluorescence emission, still not fully understood, is timely. M Nagano, one of the architects of the AGASA Observatory, has provided an overview of the experimental situation with regard to the energy spectrum of the highest energy cosmic rays.

The remaining contributions are of a more theoretical nature and discuss propagation (T Stanev), the time structure of multi-messenger signals (G H W Sigl), ultra-high energy cosmic ray production near black holes (A Yu Neronov, D V Semikoz and I I Tkachev), production in jets associated with black holes (C D Dermer, S Razzaque, J Finke and A Atoyan) and emission from a specific object, Cen A (M Kachelriess, S S Ostapchenko and R Tomas). Additionally the potential of high energy cosmic rays to give information about features of hadronic interactions, specifically the cross-section for p–air collisions, is discussed in the paper by R Ulrich et al.

We thank all our authors most sincerely for their efforts and Tim Smith and his editorial team for their hard work. We believe that this collection of articles will be of great value to workers in the field: further contributions to this focus issue will be published during the course of 2009.

Focus on High Energy Cosmic Rays Contents

The cosmic ray energy spectrum as measured using the Pierre Auger ObservatoryGiorgio Matthiae

The northern site of the Pierre Auger Observatory Johannes Blümer and the Pierre Auger Collaboration

Searching for new physics with ultrahigh energy cosmic rays Floyd W Stecker and Sean T Scully

On the measurement of the proton–air cross section using air shower data R Ulrich, J Blümer, R Engel, F Schüssler and M Unger

High energy radiation from Centaurus A M Kachelrieß, S Ostapchenko and R Tomàs

Ultra-high-energy cosmic rays from black hole jets of radio galaxies C D Dermer, S Razzaque, J D Finke and A Atoyan

Ultra-high energy cosmic ray production in the polar cap regions of black hole magnetospheres A Yu Neronov, D V Semikoz and I I Tkachev

Time structure and multi-messenger signatures of ultra-high energy cosmic ray sources Günter Sigl

Propagation of ultrahigh-energy cosmic rays Todor Stanev

Search for the end of the energy spectrum of primary cosmic rays M Nagano

Analysis of the fluorescence emission from atmospheric nitrogen by electron excitation, and its application to fluorescence telescopes F Arqueros, F Blanco and J Rosado

Observing ultra-high-energy cosmic particles from space: S-EUSO, the Super-Extreme Universe Space Observatory Mission A Santangelo and A Petrolini

The JEM-EUSO mission Yoshiyuki Takahashi and the JEM-EUSO Collaboration

Measuring extensive air showers with Cherenkov light detectors of the Yakutsk array: the energy spectrum of cosmic rays A A Ivanov, S P Knurenko and I Ye Sleptsov

The analysis of high-energy air shower data allows one to study the proton-air cross section at energies beyond the reach of fixed target and collider experiments. The mean depth of the first interaction point and its fluctuations are a measure of the proton-air particle production cross section. Since the first interaction point in air cannot be measured directly, various methods have been developed in the past to estimate the depth of the first interaction from air shower observables in combination with simulations. As the simulations depend on assumptions made for hadronic particle production at energies and phase space regions not accessible in accelerator experiments, the derived cross sections are subject to significant systematic uncertainties. The focus of this work is the development of an improved analysis technique that allows a significant reduction of the model dependence of the derived cross section at very high energy. Performing a detailed Monte Carlo study of the potential and the limitations of different measurement methods, we quantify the dependence of the measured cross section on the hadronic interaction model used. Based on these results, a general improvement of the analysis methods is proposed by introducing the actually derived cross section already in the simulation of reference showers. The reduction of the model dependence is demonstrated for one of the measurement methods.

We calculate, for the nearest active galactic nucleus (AGN), Centaurus A (Cen A), the flux of high-energy cosmic rays (CR) and of accompanying secondary photons and neutrinos expected from hadronic interactions in the source. We use as the two basic models for the generation of ultrahigh-energy cosmic rays (UHECR) shock acceleration in the radio jet and acceleration in the regular electromagnetic field close to the core of the AGN. While scattering on photons dominates in scenarios with acceleration close to the core, scattering on gas becomes more important if acceleration takes place along the jet. Normalizing the UHECR flux from Cen A to the observations of the Auger experiment, the neutrino flux may be marginally observable in a 1 km³ neutrino telescope, if a steep UHECR flux dN/dE∝E^-α with α=2.7 extends down to 10¹⁷ eV. The associated photon flux is close to or exceeds the observational data of atmospheric Cherenkov and γ-ray telescopes for α≳2. In particular, we find that already the present data favour either a softer UHECR injection spectrum than α=2.7 for Cen A or a lower UHECR flux than expected from the normalization to the Auger observations.

The Auger Collaboration reports (Auger Collaboration 2007 Science 318 939, The Pierre Auger Collaboration 2008 Astropart. Phys.29 188) that the arrival directions of ≳60 EeV ultra-high-energy cosmic rays (UHECRs) cluster along the supergalactic plane and correlate with active galactic nuclei (AGN) within ≈ 100 Mpc. The association of several events with the nearby radio galaxy Centaurus A supports the paradigm that UHECRs are powered by supermassive black-hole engines and accelerated to ultra-high energies in the shocks formed by variable plasma winds in the inner jets of radio galaxies. The GZK horizon length of 75 EeV UHECR protons is ≈100 Mpc, so that the Auger results are consistent with an assumed proton composition of the UHECRs. In this scenario, the sources of UHECRs are FR II radio galaxies and FR I galaxies like Cen A with scattered radiation fields that enhance UHECR neutral-beam production. Radio galaxies with jets pointed away from us can still be observed as UHECR sources due to deflection of UHECRs by magnetic fields in the radio lobes of these galaxies. A broadband ∼1 MeV–10 EeV radiation component in the spectra of blazar AGN is formed by UHECR-induced cascade radiation in the extragalactic background light. This emission is too faint to be seen from Cen A, but could be detected from more luminous blazars.

We develop a model of ultra-high energy cosmic ray (UHECR) production via acceleration in a rotation-induced electric field in vacuum gaps in the magnetospheres of supermassive black holes (BHs). We show that if the poloidal magnetic field near the BH horizon is misaligned with the BH rotation axis, charged particles, which initially spiral into the BH along the equatorial plane, penetrate into the regions above the BH ‘polar caps’ and are ejected with high energies to infinity. We show that in such a model acceleration of protons near a BH of typical mass 3×10⁸ solar masses is possible only if the magnetic field is almost aligned with the BH rotation axis. We find that the power of anisotropic electromagnetic emission from an UHECR source near a supermassive BH should be at least 10–100 times larger than the UHECR power of the source. This implies that if the number of UHECR sources within the 100 Mpc sphere is ∼100, the power of electromagnetic emission that accompanies proton acceleration in each source, 10^42–43 erg s⁻¹, is comparable to the typical luminosities of active galactic nuclei (AGN) in the local Universe. We also explore the acceleration of heavy nuclei, for which the constraints on the electromagnetic luminosity and on the alignment of the magnetic field in the gap are relaxed.

The latest results on the sky distribution of ultra-high energy cosmic ray sources have consequences for their nature and time structure, if either deflection is moderate or if their density is comparable to or larger than the average density of active galaxies. If the sources accelerate predominantly nuclei of atomic number A and charge Z and emit continuously, their luminosity in cosmic rays above ≃6×10¹⁹ eV can be no more than a fraction of ≃5×10^-4 Z^-2 of their total power output. Such sources could produce a diffuse neutrino flux that gives rise to several events per year in neutrino telescopes of km³ size. Continuously emitting sources should be easily visible in photons below ∼100 GeV, but TeV γ-rays may be absorbed within the source. For episodic sources that accelerate cosmic rays in areas moving with a Lorentz factor Γ, the bursts or flares have to last at least ≃0.1 Γ^-4 A^-4 yr. A considerable fraction of the flare luminosity could then go into highest energy cosmic rays, in which case the rate of flares per source has to be less than ≃5×10^{- 3} Γ⁴ A⁴ Z² yr^-1. Episodic sources should typically have detectable variability both at FERMI/GLAST and TeV energies, but neutrino fluxes may be hard to detect. Finally, in contrast to γ-rays, power and density requirements make it unlikely that the ultra-high energy cosmic rays leave the source environment strongly beamed.

We briefly describe the energy loss processes of ultrahigh-energy protons, heavier nuclei and γ-rays in interactions with the universal photon fields of the Universe. We then discuss the modification of the accelerated cosmic-ray energy spectrum in propagation by the energy loss processes and the charged cosmic-ray scattering in the extragalactic magnetic fields. The energy lost by the ultrahigh-energy cosmic rays goes into γ-rays and neutrinos that carry additional information about the sources of highest energy particles. The new experimental results of the HiRes and the Auger collaborations are discussed in view of the predictions from propagation calculations.

The experiments on the search for the end of the cosmic-ray energy spectrum with the particle detector array technique and the optical (Čerenkov and/or fluorescence) technique are summarized. In the highest observed energy region, the suppression of the flux above about 6×10¹⁹ eV, which corresponds to the so-called ‘Greisen–Zatsepin–Kuz'min (GZK) cutoff energy’, is confirmed by the new results from the High-Resolution Fly's Eye (HiRes) and the Pierre Auger Observatory (Auger). Summarizing the spectra observed from 10¹⁴ to 10²⁰ eV with world wide experiments, there is still room for further investigations on the energy scale and the flux of primary cosmic rays. In order to establish the energy scale, it is necessary not only to understand the optical technique further, but also to determine the primary species in the highest energy region. Also, it is important to make more detailed measurements on the energy spectrum in the 10¹⁷–10¹⁸ eV region. To observe the super-GZK events and the anticipated recovery of the spectrum above the GZK cutoff, the search for the end of cosmic-ray energy spectrum will be continued even after a century since the discovery of cosmic rays in 1912.

A microscopic analysis of the processes involved in the fluorescence emission of nitrogen molecules induced by electronic collisions is carried out for a large range of incident energies (eV to GeV) and pressures (Pa to atmospheric conditions). The contribution of secondary electrons to that fluorescence is calculated by means of detailed Monte Carlo simulations. For this purpose, a novel analytical approximation of the energy spectrum of secondary electrons is used. The results of the simulations are shown to be useful for the interpretation of available experimental data. For instance, they account for the pressure dependence of the fluorescence observed in laboratory experiments. The conditions under which emitted fluorescence is proportional to deposited energy are also studied. Finally, these calculations provide an absolute value of the fluorescence yield consistent with available experimental data.

The experimental search for ultra-high-energy cosmic messengers, from E∼10¹⁹ eV to beyond E∼10²⁰ eV, at the very end of the known energy spectrum, constitutes an extraordinary opportunity to explore a largely unknown aspect of our universe. Key scientific goals are the identification of the sources of ultra-high-energy particles, the measurement of their spectra and the study of galactic and local intergalactic magnetic fields. Ultra-high-energy particles might, also, carry evidence of unknown physics or of exotic particles that are relics of the early universe.

To meet this challenge a significant increase in the integrated exposure is required. This implies a new class of experiments with larger acceptances and good understanding of the systematic uncertainties. Space-based observatories can reach the instantaneous aperture and the integrated exposure necessary to systematically explore the ultra high-energy universe.

In this paper, we focus on the Super Extreme Universe Space Observatory (-EUSO), a mission concept developed in the framework of the first Announcement of Opportunity of the ‘Cosmic Vision 2015–2025’ program, the long-term science plan of the European Space Agency. -EUSO will observe from space, in a free flyer configuration, the extensive air showers produced by ultra-high-energy primaries that traverse the Earth atmosphere. From a variable altitude orbit of 800–1100 km, -EUSO will have an instantaneous geometrical aperture of A_geo⩾2×10⁶ km² sr with an estimated duty cycle in the range 10–20%. In this paper, after briefly summarizing the science case of the mission, we describe the scientific goals and requirements of the -EUSO concept. We then introduce the -EUSO observational approach and describe the main instrument and mission features. We conclude by discussing the expected performance of the mission.

JEM-EUSO is a space science mission to explore the extreme energies and physics of the Universe. Its instrument will watch the darkside of the earth and will detect UV photons emitted from the extensive air shower caused by an ultra-high energy cosmic ray (UHECR above 10¹⁸ eV), or an extremely high energy cosmic ray (EHECR) particle (e.g. above about 10²⁰ eV). Such a high-rigidity particle as the latter arrives almost in a straight line from its origin through the magnetic fields of our Milky Way Galaxy and is expected to allow us to trace the source location by its arrival direction. This can open the door to new astronomy with charged particles. In its 5 years of operation including the tilted mode, Extreme Universe Space Observatory an Japanese Experiment Module (JEM-EUSO) will detect at least 1000 events with E>7×10¹⁹ eV with the Greisen–Zatsepin–Ku'zmin (GZK) suppression spectrum. It can determine the energy spectrum and source locations of GZK to super-GZK regions with a statistical accuracy of several percent. JEM-EUSO is planned to be deployed by H2 transfer vehicle (HTV) and will be attached to the Japanese Experiment Module/ Exposure Facility (JEM/EF) of International Space Station. JAXA has selected JEM-EUSO as one of the mission candidates of the second phase utilization of JEM/EF for launch in the early-to-mid 2010s.

The energy spectrum of cosmic rays in the range E∼10¹⁵ eV to 6×10¹⁹ eV is studied in this paper using air Cherenkov light detectors of the Yakutsk array. The total flux of photons produced by the relativistic electrons (including positrons as well, hereafter) of extensive air showers in the atmosphere is used as an energy estimator of the primary particle initiating a shower. The resultant differential flux of cosmic rays exhibits, in agreement with previous measurements, a knee and ankle feature at energies of 3×10¹⁵ and ∼10¹⁹ eV, respectively. A comparison of observational data with simulations is made in the knee and ankle regions in order to choose the models of galactic and extragalactic components of cosmic rays that describe well the energy spectrum measured.

The radiation of a relativistic electron interacting with a co-propagating tightly focused high-power laser is investigated. High-order fields (HOFs) existing in a tight focus (a few micrometers or so) affect the dynamics of electrons rather significantly so as to enhance radiation intensity by several orders of magnitude. In the case of a co-propagating interaction geometry, the second-order field plays an important role in radiation enhancement. It is demonstrated that when HOFs are included, the radiation efficiency is increased by a factor of up to 100 000 for w₀ = 2 and 5 μm, with a laser intensity of 2.2×10²⁰ W cm⁻², compared with that when HOFs are not included. The enhancement is larger for smaller electron energies and laser beam waists.

It has also been shown that when an electron bunch interacts with a high-intensity tightly-focused femtosecond laser pulse in a co-propagation geometry, attosecond (∼300 as) x-ray pulses can be produced. The photon energy can reach about 40 keV for an electron energy of 2 GeV. The physical scheme investigated in this work can be used for an ultrafast (attosecond or femtosecond) x-ray source in the range of 10–100 keV.

An optical technique devised for the detection of the ultrasharp angular resonance of long-range surface plasmons (LRSPs) is described. The LRSPs propagate along an 8 nm-thick palladium (Pd) film deposited on a one-dimensional photonic crystal structure and bordering a gas environment at another Pd film interface. At such a small metal film thickness, the scattering attenuation losses prevail over dissipation losses inside the film and we use this scattering as an input signal to pick up the angle of the surface plasmon resonance by a closed feedback loop via an angle-scanning piezomirror. As an implementation of this technique, we detected a 0.5% hydrogen concentration in nitrogen at room temperature with a signal/noise ratio of approximately 100 and response and recovery times of about 5 and 15 s, respectively.

We numerically study the critical behavior of the XY model on the Erdős–Rényi random graph and a growing random network model, representing the uncorrelated and the correlated random networks, respectively. We also checked the dependence of the critical behavior on the choice of order parameters: the ordinary unweighted and the degree-weighted magnetization. On the Erdős–Rényi random network, the critical behavior of the XY model is found to be of the second order with the estimated exponents consistent with the standard mean-field theory for both order parameters. On the growing random network, on the contrary, we found that the critical behavior is not of the standard mean-field type. Rather, it exhibits behavior reminiscent of that in the infinite-order phase transition for both order parameters, such as the lack of discontinuity in specific heat and the non-divergent susceptibility at the critical point, as observed in the percolation and the Potts models on some growing network models.

A proper understanding of the mechanism for cuprate superconductivity can emerge only by comparing materials in which physical parameters vary one at a time. Here, we present a variety of bulk, resonance and scattering measurements on the (Ca_xLa_1−x) (Ba_1.75−xLa_0.25+x) Cu₃O_y high temperature superconductors, in which this can be done. We determine the superconducting, Néel, glass and pseudopage critical temperatures. In addition, we clarify which physical parameter varies, and, equally important, which does not, with each chemical modification. This allows us to demonstrate that a single energy scale, set by the superexchange interaction J, controls all the critical temperatures of the system. J, in turn, is determined by the in plane Cu–O–Cu buckling angle.

High charge (Z) and energy (E) (HZE) nuclei are the main contributors to the uncertainty of radiation risk in space. They ionize a large number of molecules when they interact with matter, initiating a complex succession of events that leads to the radiation track structure. Radiation tracks are often studied by Monte-Carlo simulations that provide detailed information on energy deposition and production of radiolytic species that damage cellular components. These simulations require total and differential elastic and inelastic cross sections. Most ionized electrons have low energy; therefore, most calculations and experiments have been performed on electrons below 1 MeV. Electrons of ∼1–100 MeV are also produced; they interact with many target molecules when they slow down and determine the radial extension of HZE tracks. Much less work has been done in this energy range. In this paper, a simulation code named RETRACKS uses interaction cross sections (including bremsstrahlung) to calculate the stopping power, range and average energy needed to produce an ion pair (W) for electrons up to 100 MeV. It was also used previously with the RITRACKS program to calculate the radial dose of HZE ions. These cross sections should allow the simulation of higher energy HZE ions, which will help improve our models of space radiation risk.

Graphene forms from a relatively dense, tightly bound C-adatom gas when elemental C is deposited on or segregates to the Ru(0001) surface. Nonlinearity of the graphene growth rate with C-adatom density suggests that growth proceeds by addition of C atom clusters to the graphene edge. The generality of this picture has now been studied by use of low-energy electron microscopy (LEEM) to observe graphene formation when Ru(0001) and Ir(111) surfaces are exposed to ethylene. The finding that graphene growth velocities and nucleation rates on Ru have precisely the same dependence on adatom concentration as for elemental C deposition implies that hydrocarbon decomposition only affects graphene growth through the rate of adatom formation. For ethylene, that rate decreases with increasing adatom concentration and graphene coverage. Initially, graphene growth on Ir(111) is like that on Ru: the growth velocity is the same nonlinear function of adatom concentration (albeit with much smaller equilibrium adatom concentrations, as we explain with DFT calculations of adatom formation energies). In the later stages of growth, graphene crystals that are rotated relative to the initial nuclei nucleate and grow. The rotated nuclei grow much faster. This difference suggests firstly, that the edge-orientation of the graphene sheets relative to the substrate plays an important role in the growth mechanism, and secondly, that attachment of the clusters to the graphene is the slowest step in cluster addition, rather than formation of clusters on the terraces.

Entanglement is arguably the key quantum-mechanical resource for improving the performance of communication, precision measurement and computing systems beyond their classical-physics limits. Yet entanglement is fragile, being very susceptible to destruction by the decoherence arising from loss and noise. Surprisingly, Lloyd (2008 Science 321 1463) recently proved that a very large performance gain accrues from use of entanglement in single-photon target detection within an entanglement-destroying lossy, noisy environment when compared to what can be achieved with unentangled single-photon states. We extend Lloyd's analysis to the full multiphoton input Hilbert space. We show that the performance of Lloyd's single-photon‘quantum illumination’ system is, at best, equal to that of a coherent-state transmitter of the same average photon number, and may be substantially worse. We demonstrate that the coherent-state system derives its advantage from the coherence between a sequence of weak—single photon on average—transmissions, a possibility that was not allowed for in Lloyd's work. Nevertheless, as shown by Tan et al (2008 Phys. Rev. Lett. 101 253601), quantum illumination may offer a significant, although more modest, performance gain when operation is not limited to the single-photon regime.

We demonstrate a general and efficient informational cooling technique for atoms that is an experimental realization of a one-dimensional Maxwell's demon. The technique transfers atoms from a magnetic trap into an optical trap via a single spontaneous Raman transition that is discriminatively driven near each atom's classical turning point. In this way, nearly all of the atomic ensemble's kinetic energy in one dimension is removed. We develop a simple analytical model to predict the efficiency of transfer between the traps and provide evidence that the performance is limited only by particle dynamics in the magnetic trap. Transfer efficiencies up to 2.2% are reported. We show that efficiency can be traded for phase-space compression, and we report compression up to a factor of 350. Our results represent a 15-fold improvement over our previous demonstration of the cooling technique.

We revisit the question of the nature of odd-frequency superconductors, first proposed by Berezinskii in 1974 (JETP Lett. 20 287). We start with the notion that the order parameter of odd-frequency superconductors can be thought of as a time derivative of the odd-time pairing operator. This leads to the notion of the composite boson condensate (Abrahams et al 1995 Phys. Rev. B 52 1271; Balatsky and Bonca 1993 Phys. Rev. B 48 7445). To elucidate the nature of broken symmetry states in odd-frequency superconductors, we consider a wave function that properly captures the coherent condensate of composite charge 2e bosons in an odd-frequency superconductor. We consider the Hamiltonian that describes the equal-time composite boson condensation as proposed earlier by Abrahams et al (1995 Phys. Rev. B 52 1271). We propose a Bardeen–Cooper–Schrieffer (BCS)-like wave function that describes a composite condensate comprised of a spin-0 Cooper pair and a spin-1 magnon excitation. We derive the quasi-particle dispersion, the self-consistent equation for the order parameter and the density of states. We show that the coherent wave function approach recovers all the known proprietaries of odd-frequency superconductors: the quasi-particle excitations are gapless and the superconducting transition requires a critical coupling.

In the original BB84 protocol by Bennett and Brassard, an eavesdropper is detected because his attempts to intercept information result in a quantum bit error rate (QBER) of at least 25%. Here we design an alternative quantum key distribution protocol, where Alice and Bob use two mutually unbiased bases with one of them encoding a ‘0’ and the other one encoding a ‘1’. The security of the scheme is due to a minimum index transmission error rate (ITER) introduced by an eavesdropper that increases significantly for higher-dimensional photon states. This allows for more noise in the transmission line, thereby increasing the possible distance between Alice and Bob without the need for intermediate nodes.

The quantum electrons dynamics in a thin metal film is studied numerically using the self-consistent Wigner–Poisson equations. The initial equilibrium is computed from the Kohn–Sham equations at finite temperature, and then mapped into the phase-space Wigner function. The time-dependent results are compared systematically with those obtained previously with a classical approach (Vlasov–Poisson equations). It is found that, for large excitations, the quantum and classical dynamics display the same low-frequency oscillations due to ballistic electrons bouncing back and forth on the film surfaces. However, below a certain excitation energy (roughly corresponding to one quantum of plasmon energy ), the quantum and classical results diverge, and the ballistic oscillations are no longer observed. These results provide an example of a quantum–classical transition that may be observed with current pump–probe experiments on thin metal films.

We show a classical analog of the original nonlocal dispersion cancelation effect in intensity interferometry with stationary light obeying Gaussian statistics. The dispersion compensation is due to the uncorrelation of the spectral components of the radiation. Although this classical counterpart phenomenon is not nonlocal in a strict quantum mechanical sense, it suggests that some second-order interference devices relying on temporal entanglement do not require a quantum light source.

Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an alternate approach to defining a set of quasi-probability representations, based on a more natural generalization of a classical representation, is equivalent to our earlier approach based on frames, and therefore is also subject to our no-go theorem for a non-negative representation. Furthermore, we clarify the relationship between the contextuality of quantum theory and the necessity of negativity in quasi-probability representations and discuss their relevance as criteria for non-classicality. We also provide a comprehensive overview of known quasi-probability representations and their expression within the frame formalism.

An exact algorithm is used to investigate the distributions of the degeneracies of low-energy excited states for the bimodal Ising spin glass on the brickwork lattice. Since the distributions are extreme and do not self-average, we base our conclusions on the most likely values of the degeneracies. Our main result is that the degeneracy of the first excited state per ground state and per spin is finite in the thermodynamic limit. This is very different from the same model on a square lattice where a divergence proportional to the linear lattice size is expected. The energy gap for the brickwork lattice is obviously 2J on finite systems and predicted to be the same in the thermodynamic limit. Our results suggest that a 2J gap is universal for planar bimodal Ising spin glasses. The distribution of the second contribution to the internal energy has a mode close to zero and we predict that the low-temperature specific heat is dominated by the leading term proportional to T⁻²exp (−2J/kT).

We propose to use ferromagnetic systems for entanglement generation and distribution together with perfect state transfer between distant parties in a qubit chain. The scheme relies on an effective two-qubit dynamics, realized by leaving two empty sites in a uniformly filled chain. This allows long-range interacting qubit chains to serve as quantum channels for both tasks with optimal performances. Remarkably, the entanglement between sender and receiver sites is independent of both the transmission distance and the system size. This property opens new perspectives for short- and mid-range quantum communication with qubit chains.

The simple alkali metal Na that crystallizes in a body-centred cubic structure at ambient pressure exhibits a wealth of complex phases at extreme conditions as found by experimental studies. The analysis of the mechanism of stabilization of some of these phases, namely, the low-temperature Sm-type phase and the high-pressure cI16 and oP8 phases, shows that they satisfy the criteria for the Hume-Rothery mechanism. These phases appear to be stabilized due to a formation of numerous planes in a Brillouin–Jones zone in the vicinity of the Fermi sphere of Na, which leads to the reduction of the overall electronic energy. For the oP8 phase, this mechanism seems to work if one assumes that Na becomes a divalent metal at this density. The oP8 phase of Na is analysed in comparison with the MnP-type oP8 phases known in binary compounds, as well as in relation to the NiAs-type hP4 structure.

We study the statistics of return intervals between large heartbeat intervals (above a certain threshold Q) in 24 h records obtained from healthy subjects. We find that both the linear and the nonlinear long-term memory inherent in the heartbeat intervals lead to power-laws in the probability density function P_Q(r) of the return intervals. As a consequence, the probability W_Q(t; Δt) that at least one large heartbeat interval will occur within the next Δt heartbeat intervals, with an increasing elapsed number of intervals t after the last large heartbeat interval, follows a power-law. Based on these results, we suggest a method of obtaining a priori information about the occurrence of the next large heartbeat interval, and thus to predict it. We show explicitly that the proposed method, which exploits long-term memory, is superior to the conventional precursory pattern recognition technique, which focuses solely on short-term memory. We believe that our results can be straightforwardly extended to obtain more reliable predictions in other physiological signals like blood pressure, as well as in other complex records exhibiting multifractal behaviour, e.g. turbulent flow, precipitation, river flows and network traffic.

Calculations based on density functional theory with generalized gradient approximation for exchange and correlation potential show that N-doped ZnO thin films and nanowires are magnetic. In neutral state, a total moment of 1 μ_B per N atom is introduced with 0.3–0.6 μ_B from N 2p orbitals. The mechanism contributing to magnetism in N-doped ZnO systems, however, is different from that in conventional transition metal-doped ZnO. Here magnetism is due to the holes in N 2p states induced by the substitution of oxygen with nitrogen. The N atoms show no tendency for clustering either on the ZnO thin film surfaces or on the NW surfaces, but they prefer the surface sites over the bulk sites. This study provides physical insight into the origin of magnetism in the new magnetic materials with no magnetic elements.

An indium-induced one-dimensional (1D) surface reconstruction on a Si(557) surface was studied by the combined approach of scanning tunneling microscopy (STM) and first principles calculations. Low-energy electron diffraction revealed a (1×3) phase with a triple-period along the step edge direction, which was also confirmed by STM. The STM images showed that the 1D structure consists of two atomic chains. One is located on the terrace and consists of triple-period bright protrusions. The other shows a weak ×3 modulation at the step edge. Five atomic structure models based on the In adatom of a In/Si(111)- surface were considered to figure out the underlying structure of the STM images of the In/Si(557)-1×3 surface. Interestingly, a heterogeneous In–Si adatom chain model reproduced most of the features of STM images and was the most stable energetically at a wide range of In chemical potential.

We report a systematic study of dc electric fields produced by sinusoidal high frequency ac currents in Nb superconducting films subject to a constant magnetic field perpendicular to the film plane. At frequencies in the 100 kHz to MHz range appears a new rectification effect which has not been previously observed at lower frequencies. We have observed the dc electric field generated in this regime in films without intentionally created anisotropic pinning centres, i.e. plain films, both in strip geometry as in cross-shape geometry, and also in films with symmetric periodic pinning centres. The electric field appears in both directions along and transverse to the alternating current and is essentially different at opposite film sides. It depends strongly on the intensity of the magnetic field and may exceed by nearly an order of magnitude the rectified electric fields recently reported at lower frequencies (few kHz) in systems with artificially induced anisotropic vortex pinning. The effect has a non-monotonic dependence on the drive current frequency, being maximum around a few 100 kHz to MHz, and shows a complicated temperature dependence. It is found to be different in long strips and cross shape samples. In the case of films with symmetric periodic pinning centres the rectified voltage shows a lower magnitude than in plain films, and shows an interesting structure when the applied magnetic field crosses the matching fields. We are only able to put forward tentative ideas to explain this phenomenon, which irrespective of its explanation should be taken into account in experimental studies of rectification effects in superconductors.

The low-energy spectrum of a particle in planar honeycomb lattices is conical, which leads to the unusual electronic properties of graphene. In this paper, we calculate the quasi-energy spectra of a charged particle in honeycomb lattices driven by a strong ac field, which is of fundamental importance for its time-dependent dynamics. We find that depending on the amplitude, direction and frequency of the external field, many interesting phenomena may occur, including band collapse, renormalization of the velocity of ‘light’, gap opening etc. Under suitable conditions, by increasing the magnitude of the ac field, a series of phase transitions from gapless phases to gapped phases appear alternately. At the same time, the Dirac points may disappear or change to a line. We suggest possible realization of the system in honeycomb optical lattices.

The scattering mechanisms governing the transport properties of high mobility AlInN/AlN/GaN two-dimensional electron gas (2DEG) heterostructures with various AIN spacer layer thicknesses from zero to 2 nm were presented. The major scattering processes including acoustic and optical phonons, ionized impurity, interface roughness, dislocation and alloy disorder were applied to the temperature-dependent mobility data. It was found that scattering due mainly to alloy disorder limits the electron mobility for samples having spacer layer thicknesses up to 0.3 nm. On the other hand, alloy scattering is greatly reduced as the AlN spacer layer thickness increases further, and hence the combination of acoustic, optical and interface roughness become operative with different degrees of effectiveness over different temperature ranges. The room-temperature electron mobility was observed to increase gradually as the AlN spacer layer increases. A peak electron mobility of 1630 cm² V⁻¹ s⁻¹ was realized for the sample consisting of a 1 nm AlN spacer layer. Then, the electron mobility decreased for the sample with 2 nm AlN. Moreover, the measured 2DEG densities were also compared with the theoretical predictions, which include both piezoelectric and spontaneous polarization components existing at AlN/GaN interfaces. The experimental sheet carrier densities for all AlInN/AlN/GaN HEMT structures were found to be in excellent agreement with the theoretical predictions when the parasitic (unintentional) GaN layer deposited between AlN and AlInN was taken into account. From these analyses, 1 nm AlN spacer layer thickness is found to be the optimum thickness required for high electron mobility and hence low sheet resistance once the sheet carrier density is increased to the theoretically expected value for the sample without unintentional GaN layer.

This study examines the effect that dipole–dipole charge interactions between fractal aggregates have on the growth of dust grains. Aggregates in a plasma or radiative environment will have charge distributed over their extended surface, which leads to a net dipole moment for the charged grains. A self-consistent N-body code is used to model the dynamics of interacting charged aggregates. The aggregates are free to rotate due to collisions and dipole–dipole electrostatic interactions. These rotations are important in determining the growth rate and subsequent geometry (fractal dimension) of the grains. In contrast to previous studies which have only taken charge-dipole interactions into account, like-charged grains are found to coagulate more efficiently than neutral grains due to preferential incorporation of small aggregates into mid-sized aggregate structures. The charged aggregates tend to be more compact than neutral aggregates, characterized by slightly higher fractal dimensions.

We construct a method for verifying mode entanglement of N-mode W states. The ideal W state contains exactly one excitation symmetrically shared between N modes, but our method takes the existence of higher numbers of excitations into account, as well as the vacuum state and other deviations from the ideal state. Moreover, our method distinguishes between full N-party entanglement and states with M-party entanglement with M<N, including mixtures of the latter. We specialize to the case N=4 for illustrative purposes. In the optical case, where excitations are photons, our method can be implemented using linear optics.

We consider non-interacting multi-qubit systems as controllable probes of an environment of defects/impurities modelled as a composite spin-boson environment. The spin-boson environment consists of a small number of quantum-coherent two-level fluctuators (TLFs) damped by independent bosonic baths. A master equation of the Lindblad form is derived for the probe-plus-TLF system. We discuss how correlation measurements in the probe system encode information about the environment structure and could be exploited to efficiently discriminate between different experimental preparation techniques, with particular focus on the quantum correlations (entanglement) that build up in the probe as a result of the TLF-mediated interaction. We also investigate the harmful effects of the composite spin-boson environment on initially prepared entangled bipartite qubit states of the probe and on entangling gate operations. Our results offer insights in the area of quantum computation using superconducting devices, where defects/impurities are believed to be a major source of decoherence.

We consider a gas of ultracold two-level atoms confined in a cavity, taking account of atomic center-of-mass motion and cavity-mode variations. We use the generalized Dicke model (DM), and analyze separately the cases of a Gaussian, and a standing wave mode shape. Owing to the interplay between external motional energies of the atoms and internal atomic and field energies, the phase-diagrams exhibit novel features not encountered in the standard DM, such as the existence of first- and second-order phase transitions between normal and superradiant phases. Due to the quantum description of atomic motion, internal and external atomic degrees of freedom are highly correlated leading to modified normal and superradiant phases.

It has recently been speculated that the solar neutrino mixing angle is connected to the golden ratio φ. Two such proposals have been made, cot θ₁₂=φ and cos θ₁₂=φ/2. We compare these ansätze and discuss a model leading to cos θ₁₂=φ/2 based on the dihedral group D₁₀. This symmetry is a natural candidate because the angle in the expression cos θ₁₂=φ/2 is simply π/5, or 36°. This is the exterior angle of a decagon and D₁₀ is its rotational symmetry group. We also estimate radiative corrections to the golden ratio predictions.

Polarization-encoding provides a promising approach for the practical quantum key distribution (QKD) system due to the simple encoding and decoding method. Here we present a long-term stable polarization-encoding QKD with a real-time polarization control. The polarization of the signal photons in the optical fiber was maintained stable by using time-division-multiplexed reference pulses for feedback control. We implemented this technique in the QKD experiment in 50 km fiber to show that it could facilitate polarization-encoded quantum communication. The system operated stably for ∼460 min, and the quantum bit error rate was ∼5.27%. The raw key generating rate in this system was kept stable at ∼500 bits s^-1. The advantages and disadvantages of the previous polarization-control schemes were also rigorously analyzed.

Single photon detectors (SPDs) based on passively quenched avalanche photodiodes can be temporarily blinded by relatively bright light, of intensity less than 1 nW. A bright-light regime suitable for attacking a quantum key distribution system containing such detectors is described in this paper. In this regime, all SPDs in the receiver Bob are uniformly blinded by continuous illumination coming from the eavesdropper Eve. When Eve needs a certain detector in Bob to produce a click, she modifies the polarization (or other parameters used to encode quantum states) of the light she sends to Bob such that the target detector stops receiving light, while the other detector(s) continue to be illuminated. The target detector regains single photon sensitivity and, when Eve modifies the polarization again, produces a single click. Thus, Eve has full control of Bob and can perform a successful intercept–resend attack. To check the feasibility of the attack, three different models of passively quenched detectors have been tested. In the experiment, I have simulated the intensity diagrams the detectors would receive in a real QKD system under attack. Control parameters and side effects are considered. It appears that the attack could be practically possible.

In the reaction–diffusion process on random scale-free (SF) networks with the degree exponent γ, the particle density decays with time in a power law with an exponent α when initial densities of each species are the same. The exponent α is known as α>1 for 2<γ<3 and α=1 for γ⩾3. Here, we examine the reaction process on fractal SF networks, finding that α<1 even for 2<γ<3. This slowly decaying behavior originates from the segregation effect: fractal SF networks contain local hubs, which are repulsive to each other. Those hubs attract particles and accelerate the reaction, creating particle domains containing the same species of particles. Then, the reaction takes place at the non-hub boundaries between those domains, and the particle density decays slowly. Since many real SF networks are fractal, the segregation effect has to be taken into account in the reaction kinetics among heterogeneous particles.

A self-consistent fluid model developed for simulations of micro-gravity dusty plasma experiments has for the first time been used to model asymmetric dusty plasma experiments in a modified Gaseous Electronics Conference (GEC) reference cell with gravity. The numerical results are directly compared with experimental data and the experimentally determined dependence of global discharge parameters on the applied driving potential and neutral gas pressure is found to be well matched by the model. The local profiles important for dust particle transport are studied and compared with experimentally determined profiles. The radial forces in the midplane are presented for the different discharge settings. The differences between the results obtained in the modified GEC cell and the results first reported for the original GEC reference cell are pointed out.

We evaluate the information capacities of a lossy bosonic channel with correlated noise. The model generalizes the one recently discussed by Pilyavets et al (2008 Phys. Rev. A 77 052324), where memory effects come from the interaction with correlated environments. Environmental correlations are quantified by a multimode squeezing parameter, which vanishes in the memoryless limit. We show that a global encoding/decoding scheme, which involves input-entangled states among different channel uses, is always preferable with respect to a local one in the presence of memory. Moreover, in a certain range of the parameters, we provide an analytical expression for the classical capacity of the channel showing that a global encoding/decoding scheme allows it to be attained. All the results can be applied to a broad class of bosonic Gaussian channels.

Optical trapping of liquid aerosols from polydisperse samples provides unique problems for measuring their radii. Perhaps the most precise method, cavity-enhanced Raman spectroscopy (CERS), is limited to relatively large aerosols (>2 μm in radius). Determining particle perimeters in video microscopy lacks precision and, although simple, can be ambiguous. Here we demonstrate a simple and precise method based on studying the Brownian motion of droplets as they approach a nearby surface. We obtain results with greater precision and reliability than video microscopy, and with no size limitation conclude the technique could compete with CERS in terms of precision and accuracy.

The Stranski–Krastanow growth of SiGe islands by deposition of SiGe alloys instead of pure Ge allows us to control both the Ge concentration and gradient in the islands. In contrast to the commonly found increasing Ge content with island height, growth conditions for islands with nearly constant and even decreasing Ge profile along the growth direction were found. Atomic force microscopy, transmission electron microscopy and high-resolution x-ray diffraction were employed to determine the islands' size, shape, lateral distance and Ge composition. Efficient photoluminescence is emitted from these islands. We show that for islands with higher Ge contents at the bottom than at the apex, transitions between heavy holes and electron Δ_xy states in the compressive Si regions around the island's circumference dominate the photoluminescence spectra instead of the usually observed recombination between heavy holes and electrons in the Δ_z valleys in the tensile Si above the island's apex. The relative importance of the Δ_xy transitions is enhanced for lateral island distances less than 10 nm, where overlapping strain fields of neighbouring islands increase the compressive strain in the Si region between them. At intense photoexcitation, recombinations between electrons in the Δ_z valleys and light holes within the islands appear in the photoluminescence spectra. These so far, for SiGe islands, unobserved transitions were identified by a quantitative modelling of the band structure within the islands and in the surrounding Si matrix based on full 3D simulations using the nextnano³ package with the experimentally obtained island shape and composition as input parameters.

Silver dimers were fabricated on Ag(111) by single-atom manipulation using the tip of a cryogenic scanning tunnelling microscope. An unoccupied electronic resonance was observed to shift toward the Fermi level with decreasing atom–atom distance as monitored by spatially resolved scanning tunnelling spectroscopy. Density functional calculations were used to analyse the experimental observations and revealed that the coupling between the adsorbed atoms is predominantly direct rather than indirect via the Ag(111) substrate. While the substrate influence is small owing to the surface-projected sp band gap, the direct interaction is most likely due to the large extension of the p wave functions at the adsorbate atoms contributing to the resonance.

One important issue implied by the finite nature of real-world networks regards the identification of their more external (border) and internal nodes. The present work proposes a formal and objective definition of these properties, founded on the recently introduced concept of node diversity. It is shown that this feature does not exhibit any relevant correlation with several well-established complex networks measurements. A methodology for the identification of the borders of complex networks is described and illustrated with respect to theoretical (geographical and knitted networks) as well as real-world networks (urban and word association networks), yielding interesting results and insights in both cases.

We report on spectroscopy and time-of-flight measurements using an 18 keV fast-pulsed photoelectron source of adjustable intensity, ranging from single photoelectrons per pulse to 5 photoelectrons per μs at pulse repetition rates of up to 10 kHz. Short pulses between 40 ns and 4 μs in length were produced by switching light emitting diodes with central output wavelengths of 265 and 257 nm, in the deep ultraviolet (or UV-C) regime, at kHz frequencies. Such photoelectron sources can be useful calibration devices for testing the properties of high-resolution electrostatic spectrometers, like the ones used in current neutrino mass searches.

When a liquid drop impacts a smooth, solid, dry surface, the drop forms a radially spreading lamella, which can lead to a splash. Previous studies have focused almost exclusively on impacts perpendicular to a surface; yet it is common for drops to impact on angled or moving surfaces. The asymmetry of such impacts leads to an azimuthal variation of the ejected rim, and under certain conditions only part of the rim breaks up to form droplets. We show that the tangential component of impact can act to enhance or suppress a splash. We develop a new model to predict when this type of splashing will occur. The model accounts for our observations of the effects of tangential velocity and agrees well with previous experimental data.

We study wavenumber locking and pattern formation resulting from weak spatially periodic one-dimensional forcing of two-dimensional systems. We consider systems that produce stationary or traveling stripe patterns when unforced and apply forcing aligned with the stripes. Forcing at close to twice the pattern wavenumber selects, stabilizes, or creates resonant stripes locked at half the forcing wavenumber. If the mismatch between the forcing and pattern wavenumber is high we find that the pattern still locks but develops a wave vector component perpendicular to the forcing direction and forms rectangular and oblique patterns. When the unforced system supports traveling waves, resonant rectangular patterns remain stationary but oblique patterns travel in a direction orthogonal to the traveling waves.

Secular variation of the Earth's main magnetic field is believed to originate in the Earth's core. (The main field is operationally defined as comprising spherical harmonics of degree l⩽10.) I propose a different mechanism of secular variation: ocean water being a conductor of electricity, the magnetic field induced by the ocean as it flows through the Earth's main field may depend on time and manifest itself globally as secular variation. This proposal is supported by calculation of secular variation using the induction equation of magnetohydrodynamics, the observed main field and the ocean flow field. The predicted secular variation is in rough agreement with that observed. Additional support is provided by the striking temporal correlation (hitherto unsuspected) between the intensity of the North Atlantic oceanic circulation and the rate of secular variation in Western Europe; this explains, in particular, the geomagnetic jerks, and the recently discovered correlation between secular variation and climate. Spatial correlation between ocean currents and secular variation is also strong.

Practical recipes are presented for simulating high-temperature and nonequilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass macroscopic test masses as the limiting case of large-j spins. The simulation technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an equivalent continuous measurement and control process, and finally, projection of the trajectory onto state-space manifolds having reduced dimensionality and possessing a Kähler potential of multilinear algebraic form. These state-spaces can be regarded as ruled algebraic varieties upon which a projective quantum model order reduction (MOR) is performed. The Riemannian sectional curvature of ruled Kählerian varieties is analyzed, and proved to be non-positive upon all sections that contain a rule. These manifolds are shown to contain Slater determinants as a special case and their identity with Grassmannian varieties is demonstrated. The resulting simulation formalism is used to construct a positive P-representation for the thermal density matrix. Single-spin detection by magnetic resonance force microscopy (MRFM) is simulated, and the data statistics are shown to be those of a random telegraph signal with additive white noise. Larger-scale spin-dust models are simulated, having no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low dimensionality Kähler state-space manifolds is demonstrated. The reconstruction of quantum trajectories from sparse random projections is demonstrated, the onset of Donoho–Stodden breakdown at the Candès–Tao sparsity limit is observed, a deterministic construction for sampling matrices is given and methods for quantum state optimization by Dantzig selection are given.

A quantum phase transition between the symmetric (polar) phase and the phase with broken symmetry can be induced in a ferromagnetic spin-1 Bose–Einstein condensate in space (rather than in time). We consider such a phase transition and show that the transition region in the vicinity of the critical point exhibits scalings that reflect a compromise between the rate at which the transition is imposed (i.e. the gradient of the control parameter) and the scaling of the divergent healing length in the critical region. Our results suggest a method for the direct measurement of the scaling exponent ν.

Typical quantum communication schemes are such that to achieve perfect decoding the receiver must share a reference frame (RF) with the sender. Indeed, if the receiver only possesses a bounded-size quantum token of the sender's RF, then the decoding is imperfect, and we can describe this effect as a noisy quantum channel. We seek here to characterize the performance of such schemes, or equivalently, to determine the effective decoherence induced by having a bounded-size RF. We assume that the token is prepared in a special state that has particularly nice group-theoretic properties and that is near-optimal for transmitting information about the sender's frame. We present a decoding operation, which can be proven to be near-optimal in this case, and we demonstrate that there are two distinct ways of implementing it (corresponding to two distinct Kraus decompositions). In one, the receiver measures the orientation of the RF token and reorients the system appropriately. In the other, the receiver extracts the encoded information from the virtual subsystems that describe the relational degrees of freedom of the system and token. Finally, we provide explicit characterizations of these decoding schemes when the system is a single qubit and for three standard kinds of RF: a phase reference, a Cartesian frame (representing an orthogonal triad of spatial directions), and a reference direction (representing a single spatial direction).

If the bare interaction between two electrons is dressed in the two-dimensional (2D) electron gas by the many-body environment, pairing may occur. Here, we study numerically the existence and character of bound states in cases where the basic dressing is described by superimposing normalized holes centered around both electrons. Beyond this modeling, a possible modification of the interaction energy at short range is considered by a repulsive potential term. The effect of the ionic polarizability on pair interaction is approximated by a static dielectric constant. A many-body analysis of pairing, employing the spherical harmonics representation of the Bethe–Salpeter ladder-solution for the two-particle scattering amplitude in 2D, is given as well. Pairing occurs due to attractive spherical harmonics in our interparticle potential.

The effect of a background pressure of adsorbable species on sputtering and surface damage in grazing incidence ion erosion of Pt(111) is investigated by scanning tunneling microscopy and molecular dynamics simulations. The background pressure implies a partial surface coverage with adsorbates, which in turn causes an enhancement of the erosion rate by a factor of up to 40 compared to the clean case. Partial pressures of molecular oxygen and carbon monoxide were maintained during ion erosion with 5 keV Ar⁺ for various grazing angles between 81° and 87° and temperatures ranging from 400 to 550 K.

A finite array of N globally coupled Stratonovich models exhibits a continuous nonequilibrium phase transition. In the limit of strong coupling, there is a clear separation of timescales of centre of mass and relative coordinates. The latter relax very fast to zero and the array behaves as a single entity described by the centre of mass coordinate. We compute analytically the stationary probability distribution and the moments of the centre of mass coordinate. The scaling behaviour of the moments near the critical value of the control parameter a_c(N) is determined. We identify a crossover from linear to square root scaling with increasing distance from a_c. The crossover point approaches a_c in the limit N→∞ which reproduces previous results for infinite arrays. Our results are obtained in both the Fokker–Planck and the Langevin approach and are corroborated by numerical simulations. For a general class of models we show that the transition manifold in the parameter space depends on N and is determined by the scaling behaviour near a fixed point of the stochastic flow.

Single-crystalline Ni-doped ZnO nanorods have been synthesized through a chemical method. The average length and diameter of these nanorods are in the ranges of 400–700 nm and 25–40 nm, respectively. Structural analyses reveal that the Ni-doped ZnO nanorods are of pure wurtzite hexagonal phase and grow along the preferred c-axis direction. X-ray photoelectron spectroscopy (XPS) gives evidence that the Ni dopant is in the +2 valence oxidation state and is uniformly distributed in the nanorods. Full multiple-scattering ab initio calculations of Ni K-edge x-ray absorption near edge structure (XANES) analysis reveal that Ni impurity atoms are substitutionally incorporated into ZnO host without formation of secondary phases (Ni metal and Ni₂O₃). The comparison of experimental and simulated XANES spectra on Ni K edge shows the presence of the oxygen vacancy (native defect) in the prepared nanorods. Photoluminescence spectrum shows two emission peaks, which are ascribed to near band edge (NBE) transitions and broadened intensive green emission associated with oxygen-vacancy defects. Furthermore, the magnetic measurements reveal that the nanorods exhibit intrinsic room-temperature ferromagnetism. Ferromagnetic ordering is interpreted by the overlapping of polarons mediated through oxygen vacancy based on the bound magnetic polaron (BMP) model.

The role of magnetic reconnection on the evolution of the Kelvin–Helmholtz instability is investigated in a plasma configuration with a velocity shear field. It is shown that the rate at which the large-scale dynamics drives the formation of steep current sheets, leading to the onset of secondary magnetic reconnection instabilities, and the rate at which magnetic reconnection occurs compete in shaping the final state of the plasma configuration. These conclusions are reached within a two-fluid plasma description on the basis of a series of two-dimensional numerical simulations. Special attention is given to the role of the Hall term. In these simulations, the boundary conditions, the symmetry of the initial configuration and the simulation box size have been optimized in order not to affect the evolution of the system artificially.

While the BB84 protocol is in principle secure, real implementations suffer from imperfections. Here, we analyse a free space BB84 transmitter, operating with polarization encoded attenuated pulses. We report on measurements of all degrees of freedom of the transmitted photons in order to estimate potential side channels of the state preparation at Alice.

The emission intensity of diamond samples containing negatively charged nitrogen-vacancy centres are measured as a function of magnetic field along the ⟨111⟩ direction for various temperatures. At low temperatures the responses are sample and stress dependent and can be modelled in terms of the previous understanding of the ³E excited state fine structure which is strain dependent. At room temperature the responses are largely sample and stress independent, and modelling involves invoking a strain independent excited state with a single zero field spin-level splitting of 1.42 GHz. The change in behaviour is attributed to a temperature dependent averaging process over the components of the excited state orbital doublet. It decouples orbit and spin and at high temperature the spin levels become independent of any orbit splitting. One significant implication of this averaging is that it simplifies the development of room temperature applications.

Finite-element micromagnetic simulations are employed to study the chiral symmetry breaking of magnetic vortices, caused by the surface roughness of thin-film magnetic structures. An asymmetry between vortices with different core polarizations has been experimentally observed for square-shaped platelets. For example, the threshold fields for vortex core switching were found to differ for core up and down. This asymmetry was, however, not expected for these symmetrically shaped structures, where both core polarizations should behave symmetrically. Three-dimensional finite element simulations are employed to show that a small surface roughness can break the symmetry between vortex cores pointing up and down. A relatively small sample roughness is found to be sufficient to reproduce the experimentally observed asymmetries. It arises from the lack of mirror-symmetry of the rough thin-film structures, which causes vortices with different handedness to exhibit asymmetric dynamics.

We report on analytical and numerical studies of the magnetic quantum oscillations of the diagonal conductivity σ_xx in a two-dimensional conductor with a weak square superlattice modulation under conditions of the integer quantum Hall (IQHE) effect. The quantum Hall effect in such a system differs from the conventional IQHE, in which the finite width of the Landau bands is due to disorder only. The superlattice modulation potential yields a fractal splitting of the Landau levels into Hofstadter minibands. For rational flux through a unit cell, the minibands have a finite width and intrinsic dispersion relations. We consider a regime, now accessible experimentally, in which disorder does not wash out the fractal internal gap structure of the Landau bands completely. We found the following distinctions from the conventional IQHE produced by the superlattice: (i) the peaks in diagonal conductivity are split due to the Hofstadter miniband structure of Landau bands; (ii) the number of split peaks in the bunch, their positions and heights depend irregularly on the magnetic field and the Fermi energy; (iii) the gaps between the split Landau bands (and related quantum Hall plateaus) become narrower with the superlattice modulation than without it.

Recent experiments have demonstrated that it is possible to create macroscopic-ordered one- and two-dimensional nanostructures on (111) noble metal surfaces exploiting long-range substrate-mediated interaction. Here, we report on the systematic theoretical studies of magnetic properties of these atomic structures in the externally applied magnetic field. The spin dynamics is investigated by means of the kinetic Monte Carlo method based on transition-state theory. For the characteristic values of (i) magnetic anisotropy energy of adatoms and (ii) exchange coupling between adatoms in the considered class of nanostructures, we reveal the hysteresis-like behavior at low temperatures (typically at 1–3 K).

Fe films with thickness varying between 5 and 100 nm were grown on flat MgO(001) substrates while rotating the substrates. Hysteresis loops with one step and two steps were observed and interpreted in terms of a magnetization reversal mechanism with either two successive or two separate 90° domain wall (DW) nucleations, respectively. This recently introduced, novel mechanism for 180° magnetic transitions was used to quantitatively evaluate both the uniaxial magnetic anisotropy (UMA), which accompanies the intrinsic fourfold in-plane magnetic anisotropy, and the DW nucleation energy. The strength of both the UMA and the DW nucleation energy turns out to be inversely proportional to the thickness of the Fe layers for Fe/MgO(001). This suggests that the extra UMA and the DW nucleation/propagation for Fe layers are pure interface related effects. By comparing six 15 nm thick Fe/MgO(001) films deposited under different conditions, it is found that these interface related effects originate from the presence of atomic steps due to the substrate miscut and from the presence of strain relaxation resulting from lattice mismatch.

We present the results of high resolution core level photoelectron spectroscopy employed to investigate the electronic structure of clean and oxygen covered Ir(111) surface. Ir 4f_7/2 core level spectra are shown to be very sensitive to the local atomic environment. For the clean surface we detected two distinct components shifted by 550 meV, originated by surface and bulk atoms. The larger Gaussian width of the bulk component is explained as due to experimentally unresolved subsurface components. In order to determine the relevance of the phonon contribution we examined the thermal behaviour of the core level lineshape using the Hedin–Rosengren theory. From the phonon-induced spectral broadening we found the Debye temperature of bulk and surface atoms to be 298 and 181 K, respectively, which confirms the softening of the vibrational modes at the surface. Oxygen adsorption leads to the appearance of new surface core level components at −200 meV and +230 meV, which are interpreted as due to first-layer Ir atoms differently coordinated with oxygen. The coverage dependence of these components demonstrates that the oxygen saturation corresponds to 0.38 ML, in good agreement with recent density functional theory calculations.

When a neutral gas impinges on a stationary magnetized plasma an enhancement in the ionization rate occurs when the neutrals exceed a threshold velocity. This is commonly known as the critical ionization velocity effect. This process has two distinct timescales: an ion–neutral collision time and electron acceleration time. We investigate the energization of an ensemble of electrons by their self-electric field in an applied magnetic field. The evolution of the electrons is simulated under different magnetic field and density conditions. It is found that electrons can be accelerated to speeds capable of electron impact ionization for certain conditions. In the magnetically dominated case the energy distribution of the excited electrons shows that typically 1% of the electron population can exceed the initial electrostatic potential associated with the unbalanced ensemble of electrons.