International Journal of Modern Physics B

The aim of this paper is to provide better understanding of a few approaches that have been proposed for treating nonequilibrium (time-dependent) processes in statistical mechanics with the emphasis on the interrelation between theories. The ensemble method, as it was formulated by Gibbs, has great generality and broad applicability to equilibrium statistical mechanics. Different macroscopic environmental constraints lead to different types of ensembles, with particular statistical characteristics. In the present work, the statistical theory of nonequilibrium processes which is based on nonequilibrium ensemble formalism is discussed. We also outline the reasoning leading to some other useful approaches to the description of the irreversible processes. The kinetic approach to dynamic many-body problems, which is important from the point of view of the fundamental theory of irreversibility, is alluded to. Appropriate references are made to papers dealing with similar problems arising in other fields. The emphasis is on the method of the nonequilibrium statistical operator (NSO) developed by Zubarev. The NSO method permits one to generalize the Gibbs ensemble method to the nonequilibrium case and to construct a nonequilibrium statistical operator which enables one to obtain the transport equations and calculate the transport coefficients in terms of correlation functions, and which, in the case of equilibrium, goes over to the Gibbs distribution. Although some space is devoted to the formal structure of the NSO method, the emphasis is on its utility. Applications to specific problems such as the generalized transport and kinetic equations, and a few examples of the relaxation and dissipative processes, which manifest the operational ability of the method, are considered.

In this paper, four kinds of optical solitary wave solutions, including bright, dark optical solitary waves and new types of solitary waves (W-shaped and M-shaped), for the generalized higher-order nonlinear Schrödinger equation (GHONLSE) with variable coefficients are considered under certain parametric conditions. Among these solutions, the W-shaped and M-shaped solitary waves, which cannot exist in the variable-coefficient nonlinear Schrödinger equation (vNLSE), are first given for the GHONLSE with variable coefficients. As examples, we analyze the properties of these solitary wave solutions in some periodic distributed amplification systems. When α₁(z)=0, these bright and dark optical solitary wave solutions agree with the corresponding solutions in Refs. 25, 26 and 27, and the W-shaped solitary wave is in agreement with the corresponding result in Ref. 29. When α₃(z)–α₇(z) are constants and α₁(z)=α₂(z)=0, the W-shaped and M-shaped solitary waves in Refs. 14 and 15 can be recovered, respectively. Under the absence of the higher-order terms (α₄(z), α₆(z), α₇(z)) and α₁(z)=0, we provide the same results as reported in Refs. 22 and 23. This means that our results have more general forms than the earlier reports.

The complex perovskite oxide barium iron antimonate, BaFe_1/2Sb_1/2O₃ (BFS) is synthesized by a solid-state reaction technique for the first time. The X-ray diffraction of the sample at room temperature shows a monoclinic phase. The field dependences of dielectric response and the loss tangent of the sample are measured in a frequency range from 50 Hz to 1 MHz and in a temperature range from 143 to 463 K. An analysis of the loss factor with frequency is performed by the scaling behavior of the dielectric loss spectra. The frequency dependence of the loss peaks are found to obey the Arrhenius law with an activation energy ≃0.81 eV. The scaling behavior of the dielectric loss spectra suggests that the distribution of relaxation times is temperature-independent. The frequency-dependent electrical data are also analyzed in the framework of conductivity and electric modulus formalisms. The scaling behavior of the imaginary electric modulus shows the temperature-independent nature of the distribution of relaxation times. All these formalisms resulted in the qualitative similarities in the relaxation time. The relationship between relaxation parameters and electrical conduction indicates the hopping motion of electrons from Fe(II) to Fe(III) ions in BFS.

The effect of the external velocity field on the transverse impedance of normal liquid ³He has been considered. It is shown that there is an additional frequency dependent term proportional to the current-current correlation function. Vertex corrections to the collisional self-energy have to be treated in order to turn the simple relaxation time into viscous transport time, which is necessary for a quantitative description of the problem.

The scattering intensity (SI) for an electron resonant Raman scattering (ERRS) process in a free-standing semiconductor quantum wire of cylindrical geometry associated with bulk longitudinal optical (LO) phonon modes or the surface optical (SO) phonon modes is calculated for T=0 K. The Fröhlich interaction is considered to illustrate the theory for a GaAs system. Electron states are confined within a free-standing quantum wire (FSW). Single parabolic conduction and valence bands are assumed. The selection rules are studied. Numerical results and a discussion are also presented for various radii of the cylindrical quantum wires.

I investigate persistent currents and the sign of these currents in a low-field limit (ϕ→0) for n-fold twisted Moebius strips threaded by a slowly varying magnetic flux ϕ and describe the effects of the total number of electrons N_e, chemical potential μ, number of twists n, and disorder on these quantities. Transverse hopping strength (v_⊥) of the electrons plays an important role in the periodicity of the persistent current. It is observed that for Moebius strips with an odd number of twists the current shows ϕ₀/2 flux-quantum periodicity only when v_⊥=0, but if the electrons are allowed to hop along the transverse direction, then current shows ϕ₀ flux periodicity for both odd- and even-fold twisted Moebius strips. The sign of the low-field currents also has strong dependence on the number of twists n. For zero transverse hopping strength (v_⊥ = 0) the sign of the currents can be predicted exactly in odd-fold twisted Moebius strips that are characterized by fixed N_e only. For impurity free systems, the current shows only diamagnetic sign irrespective of N_e, i.e., whether the systems contain odd or even N_e. In the presence of impurity, the current shows diamagnetic and paramagnetic sign, respectively, for the systems with odd and even N_e. On the other hand, for non-zero transverse hopping strength (v_⊥≠0), the sign of the low-field currents cannot be predicted exactly. Then it strongly depends on N_e, μ, and the specific realization of disordered configurations.

This paper analyzes anti-synchronization of three-dimensional autonomous chaotic systems and achieves the anti-synchronization of a class of three-dimensional autonomous chaotic systems, i.e., Lorenz system, Chen system, and Lü system with one another via active control. Numerical simulations are demonstrated to verify the effectiveness of the proposed method.

The photoexcited carrier lifetime in ZnSe and CdSe (direct band gap crystals) and CdI₂ and PbI₂ (indirect band gap crystals) has been investigated by the use of a single beam Z-scan technique at 532 nm. The carrier lifetime (τ) is determined to be (1.7 ± 0.5) ns in the case of direct band gap and (1.2 ± 0.03) ps in the case of indirect band gap crystals. Lower values of τ in the case of indirect band gap crystals can be attributed to the reduction in value of the carrier density (N).

Using a variational approach, the binding energy of shallow hydrogenic impurities in a semimagnetic parabolic quantum dot is calculated within the effective mass approximation. The binding energy is computed for Cd_1-xinMn_xinTe/Cd_1-xoutMn_xoutTe structures as a function of the dot size in an external magnetic field. The results show that the impurity binding energy (i) increases with the reduction in dot sizes (ii) decreases when the magnetic field is increased for a given dot and (iii) increases to a maximum value at 100 Å and then decreases as the size of the dot increases beyond 100 Å for a realistic model. Spin polaronic shifts are estimated using a mean field theory. These results are compared with the existing literatures.

We show, both semi-classically as well as quantum–mechanically that the vacuum becomes birefringent in the presence of a counterpropagating light beam. For the KJ laser energy, this effect is not observable. However, with several Mega joule laser pulses, this effect will be detectable.

Based on the property of a passive system, the essential conditions under which a hyperchaotic Lorenz system could be equivalent to a passive system via smooth state feedback are derived, making the minimum phase hyperchaotic Lorenz system globally asymptotically stabilized at zero and at any desired equilibrium points. The results of simulation on Matlab and the circuit experiment on EWB confirm the effectiveness of the proposed hyperchaos control method.

By adding a rotating magnetic field in one incoming lead, we calculate the shot noise with different incident states in a 4-lead beam-splitter. The result shows that the shot noise of singlet and triplet states oscillates with the external magnetic field and depends on the symmetric properties of the incident states. Thus, the singlet, entangled triplet, and polarized states can be distinguished by adjusting the magnetic field.