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Abstract: We unify two long-memory Fokker–Planck mechanisms. Stationary solutions of the equation (; ) exist for a wide class of systems, namely for , (A, B, θ, η) being constants. We obtain that, for and arbitrary confining potential , , where . [Copyright &y& Elsevier]

Abstract: This Letter considers the curvature conditions of AW(k)-type null Cartan curves, and investigates null Cartan Bertrand curves. We show that null Cartan Bertrand curves are AW(k)-type curves in Minkowski 4-space. [Copyright &y& Elsevier]

Abstract: The entanglement backflow of two qubits coupled to two independent reservoirs is investigated. It is found that under the collective effects of the two independent reservoirs, the entanglement backflow of the qubits does not always increase with the increase of the non-Markovianity of one of the reservoirs but demonstrates an intricate behavior. Interestingly, the action of one reservoir can affect the other reservoirʼs contribution to the entanglement backflow even when the two reservoirs are independent. [Copyright &y& Elsevier]

Abstract: An interaction of vector solitons in the frame of coupled third-order nonlinear Schrödinger equations taking into account third-order linear dispersion, nonlinear dispersion, and cross-phase modulation terms is considered. Phase nature of the solitonsʼ interaction is shown. In particular, dependence of solitonsʼ trajectories on initial distance between solitons is shown. Conditions of reflection and propagation of solitons through each other are obtained. [Copyright &y& Elsevier]

Abstract: We analyze decoherence properties of entangled coherent states due to channel losses. Employing the concept of “entanglement of formation”, degradation of fidelity and degree of entanglement are calculated. We have obtained an explicit expression of concurrence concerning the symmetric noise channel and found our result is just incompatible with that of [K. Park, H. Jeong, Phys. Rev. A 82 (2010) 062325] measured by negativity in the limit of . We demonstrate that entangled coherent states with sufficient small amplitudes are more robust against channel decoherence than Bell states. [Copyright &y& Elsevier]

Abstract: We put forward a new nontrivial three-step strategy to execute joint remote state preparation via Einstein–Podolsky–Rosen pairs deterministically. At variance with all existing protocols, in ours the receiver contributes actively in both preparation and reconstruction steps, although he knows nothing about the quantum state to be prepared. [Copyright &y& Elsevier]

Abstract: The Painlevé property for the coupled Zakharov–Kuznetsov equation is verified with the WTC approach and new exact solutions of bell-type are constructed from standard truncated expansion. A symmetry transformation group theorem is also given out from a simple direct method. [Copyright &y& Elsevier]

Abstract: We demonstrate that it is possible to discern the way that has been followed to measure a quantum observable that can be expressed in terms of different products of observables, whereas no such discrimination is possible by assigning predetermined values. Specifically we show how to distinguish different routes (contexts) to measure , when and commute with each other, but A and B do not commute with and . [Copyright &y& Elsevier]

Abstract: We indicate that the proof of theorem is incorrect in Letter [Y. Xu, W. Zhou, J. Fang, W. Sun, Phys. Lett. A 374 (2010) 1673]. For correcting the mistakes, a correct version of the proof of theorem is given in this Letter. [Copyright &y& Elsevier]

Abstract: We consider the generalized Stäckel systems, the broadest class of integrable Hamiltonian systems that admit separation of variables and possess separation relations affine in the Hamiltonians. For these systems we construct in a systematic fashion hierarchies of basic separable potentials. Moreover, we show how the equations of motion for the systems under study are related through appropriately chosen reciprocal transformations and how the respective constants of motion are related through generalized Stäckel transforms. [Copyright &y& Elsevier]

Abstract: We discuss alternatives to the usual quantization of a relativistic particle which result in discrete spectra for position and time operators. [Copyright &y& Elsevier]

Abstract: Finite dimensional representations of extended Weyl–Heisenberg algebra are studied both from mathematical and applied viewpoints. They are used to define unitary phase operator and the corresponding eigenstates (phase states). It is also shown that the unitary depolarizers can be constructed in a general setting in terms of phase operators. Generation of generalized Bell states using the phase operator is presented and their expressions in terms of the elements of mutually unbiased bases are given. [Copyright &y& Elsevier]

Abstract: A new exactly solvable cryptohermitian quantum chain model is proposed and analyzed. Its discrete-square-well-like Hamiltonian with the real spectrum possesses a manifestly non-Hermitian form. It is only made self-adjoint by the constructive transition to an ad hoc Hilbert space. Such a space (i.e., the closed form of its inner product, i.e., the “metric” Θ) varies with an N-plet of optional parameters. The simplicity of our model enables one to obtain the complete family of these physics-determining metrics Θ in a user-friendly band-matrix closed form. [Copyright &y& Elsevier]

Abstract: We calculate the non-Markovian dynamics of quantum correlations, including entanglement and discord, and classical correlation in a two-qubit system with Ornstein–Uhlenbeck noise and discuss the relations in these correlations. Itʼs found that the initial-state parameters and the non-Markovian properties play an important role in these dynamics behaviors. [Copyright &y& Elsevier]

Abstract: From the super-matrix Lie algebras, we consider a super-extension of the CKdV equation hierarchy in the present Letter, and propose the super-CKdV hierarchy with self-consistent sources. Furthermore, we establish the infinitely many conservation laws for the integrable super-CKdV hierarchy. [Copyright &y& Elsevier]

Abstract: An analytical formula for the Lyapunov dimension of the Lorenz attractor is presented under assumption that all the equilibria are unstable. [Copyright &y& Elsevier]

Abstract: The generalized Bretherton equation is studied. The Bäcklund transformations between traveling wave solutions of the generalized Bretherton equation and solutions of polynomial ordinary differential equation are constructed. The classification problem for meromorphic solutions of the latter equation is discussed. Several new families of exact solutions for the generalized Brethenton equation are given. [Copyright &y& Elsevier]

Abstract: The von Kárman–Howarth equation implies an infinity of invariants corresponding to an infinity of different asymptotic behaviours of the double and triple velocity correlation functions at infinite separations. Given an asymptotic behaviour at infinity for which the Birkhoff–Saffman invariant is not infinite, there are either none, or only one or only two finite invariants. If there are two, one of them is the Loitsyansky invariant and the decay of large eddies cannot be self-similar. We examine the consequences of this infinity of invariants on a particular family of exact solutions of the von Kárman–Howarth equation. [ABSTRACT FROM AUTHOR]

Abstract: We develop and illustrate methods to compute all single particle potentials that underlie the logistic map, for . We show that the switchback potentials can be obtained from the primary potential through functional transformations. We are thereby able to produce the various branches of the corresponding analytic potential functions, which have an infinite number of branch points for generic . We illustrate the methods numerically for the cases and . [ABSTRACT FROM AUTHOR]

Abstract: Based on a classical description, we demonstrate in a direct way that the acoustic Zitterbewegung could occur in an ordinary sonic crystal without involving Dirac point, similar to the case in electron systems. This study may provide a guide line for the further experimental realization of Zitterbewegung in acoustic systems. [ABSTRACT FROM AUTHOR]

Abstract: Analytical solutions are reported for the generalized non-integrable nonlinear Schrödinger equation with varying coefficients using the similarity transformation and tri-function method, which involve three free functions of spaces to generate abundant wave structures. Three types of free functions are chosen to exhibit the corresponding nonlinear wave propagations. [ABSTRACT FROM AUTHOR]

Abstract: The eruption solitons that exist under the complex cubic–quintic Ginzburg–Landau equation (CGLE) may be eliminated by the introduction of a term that in the optical context represents intrapulse Raman scattering (IRS). The later was observed in direct numerical simulations, and here we have obtained the system of ordinary differential equations and the corresponding traveling solitons that replace the eruption solutions. In fact, we have found traveling solutions for a subset of the eruption CGLE parameter region and a wide range of the IRS parameter. However, for each set of CGLE parameters they are stable solely above a certain threshold of IRS. [ABSTRACT FROM AUTHOR]

Abstract: We consider Kochen–Specker theorem for three-qubit system with eight-dimensional state space. Reexamining the proof given by Kernaghan and Peres, we make some clarifications on the orthogonality of rays and rank-two projectors found by them. Basing on their five groups of orthogonal octad, we then show a proof that requires only seventeen rays. [ABSTRACT FROM AUTHOR]

Abstract: We propose a program for determining the reference for the covariant Hamiltonian boundary term quasi-local energy and test it on spherically symmetric spacetimes. For different observers the quasi-local energy can be positive, zero, or even negative, however the maximum value is positive for both the Schwarzschild and FLRW spacetimes. [ABSTRACT FROM AUTHOR]

Abstract: The non-exponential relaxation is shown to result from the temporal subordination of an initial, exponentially decaying state by inverse tempered α-stable processes. In contrast to the ordinary α-stable processes the tempered α-stable ones are characterized by the finiteness of their moments. This approach establishes a direct link between the Cole–Cole and the Cole–Davidson relaxation laws. [Copyright &y& Elsevier]

Abstract: In this Letter, we give special solutions of second and fourth Painlevé hierarchies derived by Gordoa, Joshi, and Pickering. We show that for certain choice of the parameters each nth member of these hierarchies has a special solution in terms of an nth order differential equation. Furthermore we derive a relation between these two hierarchies. [Copyright &y& Elsevier]

Abstract: It is shown that the Dirac equation with scalar and vector quadratic potentials and a Coulomb-like tensor potential can be solved exactly. The bound state solutions for equal vector and scalar potentials are obtained. The limit of zero tensor coupling is investigated. The case of equal vector and scalar potentials with opposite sign is also studied. The pseudospin symmetry and its breaking by the tensor interaction are discussed. [Copyright &y& Elsevier]

Abstract: In this Letter, we consider the general expressions of peaked traveling wave solutions for CH and CH-γ equations. The orbital stability of these peakons are directly proved in the norm. Some previous results are extended. [Copyright &y& Elsevier]

Abstract: A mathematical technique based on an auxiliary equation and the symbolic computation system Matlab is developed to construct the exact solutions for a generalized Camassa–Holm equation and a nonlinear dispersive equation with variable coefficients. It is shown that the variable coefficients of the derivative terms in the equations cause the qualitative change in the physical structures of the solutions. [Copyright &y& Elsevier]

Abstract: This Letter proposes two different attacks on a recently proposed chaotic cryptosystem for images and videos in [S. Lian, Chaos Solitons Fractals (2007), doi: 10.1016/j.chaos.2007.10.054]. The cryptosystem under study displays weakness in the generation of the keystream. The encryption is made by generating a keystream mixed with blocks generated from the plaintext and the ciphertext in a CBC mode design. The so obtained keystream remains unchanged for every encryption procedure. Guessing the keystream leads to guessing the key. Two possible attacks are then able to break the whole cryptosystem based on this drawback in generating the keystream. We propose also to change the description of the cryptosystem to be robust against the described attacks by making it in a PCBC mode design. [Copyright &y& Elsevier]

Abstract: In this Letter, the -expansion method [M.L. Wang, X.Z. Li, J.L. Zhang, Phys. Lett. A 372 (2008) 417] is improved and a generalized -expansion method is proposed to seek exact solutions of nonlinear evolution equations. We choose the -dimensional Nizhnik–Novikov–Vesselov equation, the -dimensional Broer–Kaup equation and the -dimensional Kadomstev–Petviashvili equation to illustrate the validity and advantages of the proposed method. Many new and more general non-travelling wave solutions and coefficient function solutions are obtained. [Copyright &y& Elsevier]

Abstract: The dynamics of Josephson junction equation in case of damping is investigated numerically. In this case the second-order system can be asymptotically reduced in the large to a one-dimensional circle map. We study the parametric dependence of the resonances of this system and plot the resonant regions in two-dimensional parameter space. The periodic variation of the widths of harmonic regions with increase of the periodic driving force is observed. In the limit of infinite damping, we study a first order system through suitable re-scaling and the same property is observed. We conjecture this may caused by the competition between the periodic potential and the periodic external driving in these systems. [Copyright &y& Elsevier]

Abstract: Monte Carlo simulation using the Wang–Landau algorithm has been performed in an one-dimensional Lebwohl–Lasher model. Both one-dimensional and two-dimensional random walks have been carried out. The results are compared with the exact results which are available for this model. [Copyright &y& Elsevier]

Abstract: With the aid of symbolic computation, we demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schrödinger equations. This system includes the modified Hubbard model and the system of coupled nonlinear Schrödinger derived by Lazarides and Tsironis. Four types of solutions for this system are given explicitly, namely: new bright–bright, new dark–dark, new bright–dark and new dark–bright solitons. [Copyright &y& Elsevier]

Abstract: This Letter applies He''s parameter-expansion method (PEM) to a nonlinear oscillation of a mass attached to a stretched wire. The method, taking full advantage of the perturbation method, does not depend upon small parameter assumption. One iteration step provides an approximate solution which is valid for the whole solution domain. The method can be easily extended to other nonlinear oscillations. [Copyright &y& Elsevier]

Abstract: Properties of localized states on array of BEC confined to a potential, representing superposition of linear and nonlinear optical lattices are investigated. For a shallow lattice case the coupled mode system has been derived. We revealed new types of gap solitons and studied their stability. For the first time a moving soliton solution has been found. Analytical predictions are confirmed by numerical simulations of the Gross–Pitaevskii equation with jointly acting linear and nonlinear periodic potentials. [Copyright &y& Elsevier]

Abstract: The tanh–coth method and the sech method are used to construct many exact solutions for Jaulent–Miodek equation. Travelling wave solutions are determined. Complex solutions are obtained as well. The power of the proposed methods is confirmed. [Copyright &y& Elsevier]

Abstract: We discuss the method of automatic search of critical point (MASCP) in the context of self-organizing criticality (SOC). The system analyzed is a contact process that presents a non-equilibrium phase transition between two states: active state and inactive state (the so-called absorbing state). The lattice sites represent infected and healthy individuals. We apply the technique MASCP to the propagation of epidemy in an unidimensional lattice at the criticality (space-domain). We take the thechnique MASCP to study SOC behavior. The time-series of density of infected individuals is analyzed using two complementary tools: Fourier analysis and detrended fluctuation analysis. We find numeric evidence that the time evolution that drives the system to the critical point in MASCP is not a SOC problem, but Gaussian noise. A SOC problem is characterized by an interaction-dominated system that goes spontaneously to the critical point. In fact MASCP goes by itself to a stationary point but it is not an interaction-dominated process, but a mean-field interaction process. [Copyright &y& Elsevier]

Abstract: We investigate the chirping effects in a semiconductor quantum well medium. Our results show that the redshift and the blueshift can be obtained in the spectra driven by the few-cycle laser pulse due to the chirping effects. Moreover, the redshift and the blueshift depend sensitively on the carrier-envelope phase (CEP) of the fundamental few-cycle laser pulse, which provides a useful route to extract the CEP information by the spectral signal. [Copyright &y& Elsevier]

Abstract: The relativistic problem of fermions subject to a PT-symmetric potential in the presence of position-dependent mass is reinvestigated. The influence of the PT-symmetric potential in the continuity equation and in the orthonormalization condition are analyzed. In addition, a misconception diffused in the literature on the interaction of neutral fermions is clarified. [Copyright &y& Elsevier]

Abstract: Lie symmetries along with either Noether theorem or Jacobi Last Multiplier yield all the conserved quantities that one may seek and even more. We show that three new conserved quantities derived in Jian-Hui Fang, Ming-Jiang Zhang, Wei-Wei Zhang (2010) can be algorithmically obtained by these old methods. Even more than three. [Copyright &y& Elsevier]

Abstract: We study asymptotical behaviour of resonances for a quantum graph consisting of a finite internal part and external leads placed into a magnetic field, in particular, the question whether their number follows the Weyl law. We prove that the presence of a magnetic field cannot change a non-Weyl asymptotics into a Weyl one and vice versa. On the other hand, we present examples demonstrating that for some non-Weyl graphs the “effective size” of the graph, and therefore the resonance asymptotics, can be affected by the magnetic field. [ABSTRACT FROM AUTHOR]

Abstract: We consider violation of CHSH inequality for states before and after entanglement swapping. We present a pair of initial states which do not violate CHSH inequality however the final state violates CHSH inequality for some results of Bell measurement performed in order to swap entanglement. [ABSTRACT FROM AUTHOR]

Abstract: In the Letter “Cluster synchronization in the adaptive complex dynamical networks via a novel approach” [Phys. Lett. A 375 (2011) 1559], there are several errors in the proof of theorems. [Copyright &y& Elsevier]

Abstract: We combine Taub''s and Ray''s variational approaches to relativistic hydrodynamics of perfect fluids into another simple formulation. [Copyright &y& Elsevier]