International Journal of Modern Physics B

The ubiquitous presence of complexity in nature makes it necessary to seek new mathematical tools which can probe physical systems beyond linear or perturbative approximations. The random matrix theory is one such tool in which the statistical behavior of a system is modeled by an ensemble of its replicas. This paper is an attempt to review the basic aspects of the theory in a simplified language, aimed at students from diverse areas of physics.

Using symmetry consideration and previous results in anomalous and spin Hall effect it is argued and shown that the effect of spin–orbit (SO) scattering is of nonperturbative nature. Moreover it is shown to be of higher relevance compared to potential disorder scattering and therefore should be taken into account first. Therefore building upon symmetry consideration we derive an (nonperturbative) exact T-Matrix operator for SO scattering. It is shown that due to SO scattering local spin polarization (local moment) appears which is missing in standard perturbative schemes. This has important consequence for anomalous velocity and spin accumulation which are illustrated. The appearance of local moment has a nontrivial effect on SU(2) gauge symmetry which is also discussed. This exact T-matrix will be helpful on building detailed Boltzmann type of theories which has the potential to clarify the intrinsic or extrinsic nature of anomalous and spin Hall effect.

In this paper, we derive tight bounds for the eavesdropping attacks on continuous variable quantum key distribution (CV-QKD) protocol that involves nonmaximally entangled states. We show that deriving bounds on the eavesdropper's accessible information based on the Heisenberg uncertainty yields upper bounds, but those bounds are not tight. For this reason, we follow different techniques to derive the desired tight bounds. The new bounds are tight for all CV-QKD protocols that involve two-mode entangled state. Our derivations are applied to direct and reverse reconciliation schemes of protocol implementation, respectively.

In this paper, a combination method is developed to construct the explicit and exact solutions of nonlinear evolution equations (NEEs). As illustrative examples, the explicit and exact solutions of some physically significant NEEs, comprising the generalized BBM–Burgers equation, generalized KdV–Burgers equation and generalized Benney equation are successfully presented by this means.

In this paper we have studied information dynamics of both internal and external noises driven harmonic oscillator. Based on the Fokker–Planck description of the stochastic processes and the Schwarz inequality principle we have calculated upper bound of rate of change of information entropy with time and its deviation from the time derivative of the entropy. The bound and the deviation monotonically decreases to zero during the relaxation of a given nonequilibrium state to a stationery state. The relaxation time increase with increase of noise correlation time of the internal colored thermal noise but it is independent on the correlation time of the external colored noise. However, an extremum behavior appears in the variation of the bound as a function of parameter of the system such as damping strength, noise correlation time of thermal and nonthermal noises etc.

In this paper, a generalized (lag, anticipated and complete) projective synchronization for a general class of chaotic systems is defined. A systematic, powerful and concrete scheme is developed to investigate the generalized (lag, anticipated and complete) projective synchronization between the drive system and response system based on the adaptive control method and feedback control approach. The hyperchaotic Chen system and hyperchaotic Lorenz system are chosen to illustrate the proposed scheme. Numerical simulations are provided to show the effectiveness of the proposed schemes. In addition, the scheme can also be extended to research generalized (lag, anticipated and complete) projective synchronization between nonidentical discrete-time chaotic systems.