Resistivity of two-dimensional systems in a magnetic field at the filling factor ν = 1/2

Experimental data on the diagonal resistivity ρ _xx of GaAs/AlGaAs heterostructures in a magnetic field at the filling factor ν = 1/2 have been compared with the existing theoretical predictions [B. I. Halperin et al., Phys. Rev. B 47, 7312 (1993) and F. Evers et al., Phys. Rev. B 60, 8951 (1999)]. The experimental results have been found to follow the relation ρ _xx (1/2) ∝ n ^?2 d ^?1.64, which disagrees with the predictions.     

Specific Heat Anomalies in Solids Described by a Multilevel Model

In the field of condensed matter physics, specific heat measurements can be considered as a pivotal experimental technique for characterizing the fundamental excitations involved in a certain phase transition. Indeed, phase transitions involving spin (de Souza et al. Phys. B Condens. Matter 404, 494 (2009) and Manna et al. Phys. Rev. Lett. 104, 016403 (2010)), charge (Pregelj et al. Phys. Rev. B 82, 144438 (2010)), lattice (Jesche et al. Phys. Rev. B 81, 134525 (2010)) (phonons) and orbital degrees of freedom, the interplay between ferromagnetism and superconductivity (Jesche et al. Phys. Rev. B 86, 020501 (2012)), Schottky-like anomalies in doped compounds (Lagos et al. Phys. C Supercond. 309, 170 (1998)), electronic levels in finite correlated systems (Macedo and Lagos J. Magn. Magn. Mater. 226, 105 (2001)), among other features, can be captured by means of high-resolution calorimetry. Furthermore, the entropy change associated with a first-order phase transition, no matter its nature, can be directly obtained upon integrating the specific heat over T, i.e., C(T)/T, in the temperature range of interest. Here, we report on a detailed analysis of the two-peak specific heat anomalies observed in several materials. Employing a simple multilevel model, varying the spacing between the energy levels Δ_i = (E_i?E₀) and the degeneracy of each energy level g_i, we derive the required conditions for the appearance of such anomalies. Our findings indicate that a ratio of \({\Delta }_{2}/{\Delta }_{1}\thickapprox \) 10 between the energy levels and a high degeneracy of one of the energy levels define the two-peaks regime in the specific heat. Our approach accurately matches recent experimental results. Furthermore, using a mean-field approach, we calculate the specific heat of a degenerate Schottky-like system undergoing a ferromagnetic (FM) phase transition. Our results reveal that as the degeneracy is increased the Schottky maximum in the specific heat becomes narrow while the peak associated with the FM transition remains unaffected.     

Hypersurface-homogeneous Universe filled with perfect fluid in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) theory of gravity

The exact solutions of the field equations with respect to hypersurface-homogeneous Universe filled with perfect fluid in the framework of f(R, T) theory of gravity (Harko et al, Phys. Rev. D 84, 024020 (2011)) is derived. The physical behaviour of the cosmological model is studied.     

Crossover from polaron to band conduction upon doping CaMnO<Subscript>3</Subscript> with La ions

In studying the specular reflection IR spectra of manganite polycrystals with electron doping Ca_1?x La _x MnO₃ (0 ≤ x ≤ 0.050) at room temperature, a crossover from polaron to band conduction is observed at x = 0.030. It has been shown that the observed changes in the electronic subsystem is associated with the crossover in the behavior of the magnetization and magnetoresistance in the magnetically ordered and paramagnetic phases that occurs at the same concentration and is described in [C. Chiorescu et al., Phys. Rev. B 73, 014406 (2006)].     

Observation of quantum noise in the polarization of laser light in a rubidium-vapor cell

Experimental observation of quantum noise in the polarization of laser light that has passed through a dense Rb⁸⁷ atomic vapor is reported. The step-like noise spectrum is observed. Factors responsible for the form of the observed spectrum and the absence of noise “squeezing” predicted by Matsko et al. [Phys. Rev. A 63, 043814 (2001)] are discussed.     

On the phase boundaries of the integer quantum hall effect

It has been pointed out that, according to the two-parameter scaling theory, the magnetic-field position of the phases of the integer quantum Hall effect (IQHE) at ω_cτ ? 1 is not determined by the filling factor ν = nh/eB. The position of the IQHE phases is given by the bare Hall conductivity σ _xy ⁰ . In this regard, it has been shown that the diagonal resistivity in the magnetic field measured by Sakr et al. [Phys. Rev. B 64, 161308 (2001)] does not exhibit transitions between the σ _xy = 3, 4 and 6 IQHE states on the one hand and the dielectric state on the other hand in contrast to the assertion by Sakr et al.     

Resonant scattering of an X-ray photon by a heavy atom

The influence of many-body and relativistic effects on the absolute values and shape of the double differential cross section for the resonant scattering of a linearly polarized X-ray photon by a free xenon atom near the K-shell ionization threshold has been theoretically analyzed. The evolution of the spatially extended structure of the scattering cross section to the K _{α, β} structure of the X-ray spectrum of the xenon atom emission has been demonstrated. The calculations have been performed in the dipole approximation for the anomalous dispersion component of the total inelastic scattering amplitude and in the impulse approximation for the contact component of this amplitude. The contribution of the Rayleigh (elastic) scattering component is taken into account using the methods developed in Hopersky et al., J. Phys. B 30, 5131 (1997). The effects of the radial relaxation of the electron shells, spin-orbit splitting, double excitation/ionization of the atomic ground state, as well as the Auger and radiative decays of the produced main vacancies, are considered. Using the results obtained by Tulkki, Phys. Rev. A 32, 3153 (1985) and Biggs et al., At. Data Nucl. Data Tables 16, 201 (1975), the nonrelativistic Hartree-Fock wavefunctions are changed to the relativistic Dirac-Hartree-Fock wavefunctions of the single-particle scattering states when constructing the process probability amplitude. The calculations are predicting and are in good agreement with the synchrotron experiment on the measurement of the absolute values and shape of the double differential cross section for the resonant scattering of an X-ray photon by a free xenon atom reported by Czerwinski et al., Z. Phys. A 322, 183 (1985).     

Discrete breathers in alpha-uranium

Uranium is an important radioactive material used in the field of nuclear energy and it is interesting from the scientific point of view because it possesses unique structure and properties. There exist several experimental reports on anomalies of physical properties of uranium that have not been yet explained. Manley et al. [Phys. Rev. Lett. 96, 125501 (2006); Phys. Rev. B 77, 214305 (2008)] speculate that the excitation of discrete breathers (DBs) could be the reason for anisotropy of thermal expansion and for the deviation of heat capacity from the theoretical prediction in the high temperature range. In the present work, with the use of molecular dynamics, the existence of DBs in α-uranium is demonstrated and their properties are studied. It is found that DB frequency lies above the phonon band and increases with DB amplitude. DB is localized on half a dozen of atoms belonging to a straight atomic chain. DB in uranium, unlike DBs in fcc, bcc and hcp metals, is almost immobile. Thus, the DB reported in this study cannot contribute to thermal conductivity and the search for other types of DBs in α-uranium should be continued. Our results demonstrate that even metals with low-symmetry crystal lattices such as the orthorhombic lattice of α-uranium can support DBs.     

Positions of the magnetoroton minima in the fractional quantum Hall effect

The multitude of excitations of the fractional quantum Hall state are very accurately understood, microscopically, as excitations of composite fermions across their Landau-like Λ levels. In particular, the dispersion of the composite fermion exciton, which is the lowest energy spin conserving neutral excitation, displays filling-factor-specific minima called “magnetoroton” minima. Simon and Halperin employed the Chern-Simons field theory of composite fermions [Phys. Rev. B 48, 17368 (1993)] to predict the magnetoroton minima positions. Recently, Golkar et al. [Phys. Rev. Lett. 117, 216403 (2016)] have modeled the neutral excitations as deformations of the composite fermion Fermi sea, which results in a prediction for the positions of the magnetoroton minima. Using methods of the microscopic composite fermion theory we calculate the positions of the roton minima for filling factors up to 5/11 along the sequence s/ (2s + 1) and find them to be in reasonably good agreement with both the Chern-Simons field theory of composite fermions and Golkar et al.’s theory. We also find that the positions of the roton minima are insensitive to the microscopic interaction in agreement with Golkar et al.’s theory. As a byproduct of our calculations, we obtain the charge and neutral gaps for the fully spin polarized states along the sequence s/ (2s ± 1) in the lowest Landau level and the n = 1 Landau level of graphene.     

The Second Order Upper Bound for the Ground Energy of a Bose Gas

Consider N bosons in a finite box Λ=[0,L]³?R ³ interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives the following upper bound on the ground state energy per particle

$\overline{\lim}_{\rho\to0}\overline{\lim}_{L\to\infty,\,N/L^3\to \rho}\biggl(\frac{e_0(\rho)-4\pi a\rho}{(4\pi a)^{5/2}(\rho)^{3/2}}\biggr )\leq\frac{16}{15\pi^2},$

where a is the scattering length of the potential. Previously, an upper bound of the form C16/15π ² for some constant C>1 was obtained in (Erdös et al. in Phys. Rev. A 78:053627, 2008). Our result proves the upper bound of the prediction by Lee and Yang (Phys. Rev. 105(3):1119–1120, 1957) and Lee et al. (Phys. Rev. 106(6):1135–1145, 1957).

     

Spin dynamics of semiconductor electrons in a hybrid ferromagnet/semiconductor structure

We analyze the recent experimental study by R.J. Epstein et al. [Phys. Rev. B 65, 121202 (2002)] on the spin dynamics of semiconductor electrons in a hybrid ferromagnet/semiconductor structure by using a simple model based on the Bloch equations. A comparison between the model calculations and the experimental observations shows that the spin relaxation rate is strongly anisotropic. We interpret this anisotropy as a manifestation of the exchange interaction between metallic and semiconductor electrons at the ferromagnet/semiconductor interface.     

Method for calculating photoionization cross sections of fullerenes in the local density and random phase approximations

A method for calculating the photoionization cross sections of fullerenes taking into account many-electron correlations on the basis of the local density and random phase approximations is proposed and implemented. Calculations are made specifically for fullerenes C₆₀ and C₂₀. It is shown that the photoionization spectrum of C₆₀ acquires a plasmon resonance whose position and magnitude are in good agreement with experimental results [I.V. Hertel, H. Steger, J. de Vries et al., Phys. Rev. Lett. 68, 784 (1992)] and with the results of other calculations [M.J. Puska and R.N. Nieminen, Phys. Rev. A47, 1181 (1993)]. The emergence of a giant resonance is predicted in the photoionization spectrum of fullerene C₂₀ with the center at a photon energy on the order of 27 eV, which corresponds to the frequency of resonant surface plasmon oscillations in a conducting sphere.     

Quantum-Secret-Sharing Scheme Based on Local Distinguishability of Orthogonal Seven-Qudit Entangled States

The concept of judgment space was proposed by Wang et al. (Phys. Rev. A 95, 022320, 2017), which was used to study some important properties of quantum entangled states based on local distinguishability. In this study, we construct 15 kinds of seven-qudit quantum entangled states in the sense of permutation, calculate their judgment space and propose a distinguishability rule to make the judgment space more clearly. Based on this rule, we study the local distinguishability of the 15 kinds of seven-qudit quantum entangled states and then propose a (k, n) threshold quantum secret sharing scheme. Finally, we analyze the security of the scheme.     

The Amigó paradigm of forbidden/missing patterns: a detailed analysis

We deal here with the issue of determinism versus randomness in time series (TS), withthe goal of identifying their relative importance in a given TS. To this end we extend (i)the use of ordinal patterns based probability distribution functions associated to a TS[C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002)] and (ii) theso-called Amigó paradigm of forbidden/missing patterns [J.M. Amigó et al., Europhys. Lett.79, 50001 (2007)], to analyze deterministic finite TS contaminated withstrong additive noises of different correlation-degree. Useful information on thedeterministic component of the original time series is obtained with the help of theso-called causal entropy-complexity plane [O.A. Rosso et al., Phys. Rev. Lett.99, 154102 (2007)].     

Effect of diffusion on the velocity of stationary impact ionization waves in semiconductors

The known theory of stationary plane impact ionization waves in gases [U. Ebert et al., Phys. Rev. E 55, 1530 (1997)] has been generalized to the bipolar case characteristic of semiconductors, where a medium is ionized by hot charge carriers of both signs. In this case, the velocity u of bipolar waves (in contrast to monopolar waves) is determined by the processes in the leading region of the front at any nonzero impact ionization rates and for any propagation directions. This property makes it possible to derive analytical formulas for u as a function of material parameters, initial perturbation, and external field strength by analyzing a boundary value problem linearized near an unstable state. In the highest achievable fields (e.g., in streamers), diffusion must give rise to an increase in u by a factor of about 3 as compared to the average drift velocity at typical parameters of semiconductors.     

Amplification of longitudinal ultrasonic waves by a moving vortex structure in type II superconductors

A moving vortex structure can amplify (generate) longitudinal acoustic waves when the velocity of its motion exceeds a certain critical velocity. The critical velocity is determined by the logarithmic derivative of the viscosity coefficient of the vortex structure with respect to the magnetic field and may be much smaller than the speed of sound. In particular, this effect suggests an alternative explanation for the plateau observed in the current-voltage characteristic of superconducting bridges in a perpendicular magnetic field [S.G. Doettinger et al., Phys. Rev. Lett. 73, 1691 (1994)].     

Atomic structure effects of a target on the polarization properties of high harmonics in the region of the cooper minimum

Recently, a scheme based on the method of weak measurements to register the trajectories of photons passing through a nested Mach–Zehnder interferometer was proposed [L. Vaidman, Phys. Rev. A 87, 052104 (2013)] and then realized [A. Danan, D. Farfurnik, S. Bar-Ad, et al., Phys. Rev. Lett. 111, 240402 (2013)]. Interpreting the results of the experiment, the authors concluded that “the photons do not always follow continuous trajectories.” It is shown in this work that these results can be easily and clearly explained in terms of traditional classical electrodynamics or quantum mechanics implying the continuity of all possible paths of photons. Consequently, a new concept of disconnected trajectories proposed by the authors of work [Phys. Rev. Lett. 111, 240402 (2013)] is unnecessary.     

Schwarzian derivative as a proof of the chaotic behaviour

In recent years, a sufficient condition for determining chaotic behaviours of the non-linear systems has been characterized by the negative Schwarzian derivative (Hac?bekiro?lu et al, Nonlinear Anal.: Real World Appl. 10, 1270 (2009)). In this work, the Schwarzian derivative has been calculated for investigating the quantum chaotic transition points in the high-temperature superconducting frame of reference, which is known as a nonlinear dynamical system that displays some macroscopic quantum effects. In our previous works, two quantum chaotic transition points of the critical transition temperature, T _c, and paramagnetic Meissner transition temperature, T _PME, have been phenomenologically predicted for the mercury-based high-temperature superconductors (Onba?l? et al, Chaos, Solitons and Fractals 42, 1980 (2009); Aslan et al, J. Phys.: Conf. Ser. 153, 012002 (2009); Çataltepe, Superconductor (Sciyo Company, India, 2010)). The T _c, at which the one-dimensional global gauge symmetry is spontaneously broken, refers to the second-order phase transition, whereas the T _PME, at which time reversal symmetry is broken, indicates the change in the direction of orbital current in the system (Onba?l? et al, Chaos, Solitons and Fractals 42, 1980 (2009)). In this context, the chaotic behaviour of the mercury-based high-temperature superconductors has been investigated by means of the Schwarzian derivative of the magnetic moment versus temperature. In all calculations, the Schwarzian derivatives have been found to be negative at both T _c and T _PME which are in agreement with the chaotic behaviour of the system.     

Comment on “Concrete Representation and Separability Criteria for Symmetric Quantum State”

Recently, Li et al. (Int. J. Theor. Phys. 53(9), 2923–2930 (2014)) presented the concrete representation of density matrix of symmetric quantum states . Moreover , according to this concrete representation of the density matrix for symmetric quantum states, Li et al. (Int. J. Theor. Phys. 53(9), 2923–2930 (2014)) have established Theorem 4.1. In this Comment, we would like to point out that Theorem 4.1 given by Li et al. (Int. J. Theor. Phys. 53(9), 2923–2930 (2014)) is incorrect in general.     

Asymptotics of work distributions in a stochastically driven system

We determine the asymptotic forms of work distributions at arbitrary times T, in a class of driven stochastic systems using a theory developed by Nickelsen and Engel (EN theory) [D. Nickelsen and A. Engel, Eur. Phys. J. B 82, 207 (2011)], which is based on the contraction principle of large deviation theory. In this paper, we extend the theory, previously applied in the context of deterministically driven systems, to a model in which the driving is stochastic. The models we study are described by overdamped Langevin equations and the work distributions in path integral form, are characterised by having quadratic augmented actions. We first illustrate EN theory, for a deterministically driven system – the breathing parabola model, and show that within its framework, the Crooks fluctuation theorem manifests itself as a reflection symmetry property of a certain characteristic polynomial, which also determines the exact moment-generating-function at arbitrary times. We then extend our analysis to a stochastically driven system, studied in references [S. Sabhapandit, EPL 89, 60003 (2010); A. Pal, S. Sabhapandit, Phys. Rev. E 87, 022138 (2013); G. Verley, C. Van den Broeck, M. Esposito, New J. Phys. 16, 095001 (2014)], for both equilibrium and non-equilibrium steady state initial distributions. In both cases we obtain new analytic solutions for the asymptotic forms of (dissipated) work distributions at arbitrary T. For dissipated work in the steady state, we compare the large T asymptotic behaviour of our solution to the functional form obtained in reference [New J. Phys. 16, 095001 (2014)]. In all cases, special emphasis is placed on the computation of the pre-exponential factor and the results show excellent agreement with numerical simulations. Our solutions are exact in the low noise (β →?∞) limit.