International Journal of Modern Physics B

A review of models describing the interactions of ultra-cold atoms and laser light is given. Both semi-classical and fully quantum models are presented with particular attention given to the introduction of local field effects. Some possible effects of self-localization and guiding, consequences of such interactions, are discussed.

In this paper, the Caudrey–Dodd–Gibbon–Kotera–Sawada (CDGKS) equation is analytically investigated using the Hirota bilinear method. Based on the bilinear form of the CDGKS equation, its N-soliton solution in explicit form is derived with the aid of symbolic computation. Besides the soliton solutions, several integrable properties such as the Bäcklund transformation, the Lax pair and the nonlinear superposition formula are also derived for the CDGKS equation.

This paper studies the effect of Casimir force on the pull-in instability of electrostatically actuated torsional nano/micro actuators. Dependence of the actuator's pull-in angle and pull-in voltage on several design parameters are investigated and it is found that Casimir force can considerably reduce the stability limits of the torsional actuators. Nonlinear equilibrium equation is solved numerically and analytically using straight forward perturbation expansion method. It is observed that a fourth-order perturbation approximation can precisely model the behavior of a torsional actuator. The results of this paper can be used for safe and stable design of torsional nano/micro actuators.

The microscopic structure and dynamics of liquid Mg_xBi_1-x(x = 0.5, 0.6, 0.7) alloys together with pure liquid Mg and Bi metals were investigated by means of ab initio molecular dynamics simulations. We present results of structure properties including pair correlation function, structural factor, bond-angle distribution function and bond order parameter, and their composition dependence. The dynamical and electronic properties have also been studied. The structure factor and pair correlation function are in agreement with the available experimental data. The calculated bond-angle distribution function and bond order parameter suggest that the stoichiometric composition Mg₃Bi₂ exhibits a different local structure order compared with other concentrations, which help us understand the appearance of the minimum electronic conductivity at this composition observed in previous experiments.

According to two dependent solutions to a generalized Riccati equation together with the equation itself, a multiple Riccati equations rational-exponent method is proposed and applied to Whitham–Broer–Kaup equation. It shows that this method is a more concise and efficient approach and can uniformly derive many types of combined solutions to nonlinear partial differential equations.

We have studied structural, mechanical and dynamical properties of PdC and CdC compounds to predict the most stable structure. We have focused on seven binary structure types as rock salt (RS), caesium chloride (CsCl), zinc blende (ZB), wurtzite (WZ), tungsten carbide (WC), cadmium telluride (CdTe) and nickel arsenide (NiAs). For modelling exchange-correlation effects we have used generalized gradient (GGA) approximation based on Perdew–Burke–Ernzhorf functional (PBE). The polycrystalline elastic moduli such as Young's and shear moduli, Poisson's ratio, sound velocities, Debye temperatures and shear anisotropic factors have been presented for mechanically stable structures using second-order elastic constants calculated from the stress-strain relations. The results show that PdC is thermodynamically, mechanically and dynamically stable in ZB structure. On the other hand, while CdC is energetically in favor of RS structure, it is mechanically and dynamically stable in ZB structure.

We present a derivation of the quantum hydrodynamic (QHD) equations for neutral bosons. We consider the short-range interaction between particles. This interaction consist of a binary interaction U( r_i, r_j) and a three-particle interaction (TPI) U( r_i, r_j, r_k) and the last one does not include binary interaction between particles. From QHD equations for Bose–Einstein condensate we derive a nonlinear Schrödinger equation. This equation was derived for zero temperature and contains the nonlinearities of the third and the fifth degree. Explicit form of the constant of the TPI is obtained. First of all, developed method we used for studying of dispersion of the linear waves. Dispersion characteristics of the linear waves are compared for different particular cases. We make comparison of the two-particle interaction in the third order by the interaction radius (TOIR) and TPI at the zero temperature. We consider influence of the temperature on the dispersion of the elementary excitations. For this aim we derive a system of the QHD equations at nonzero temperature. Obtained system of equation is an analog of the well-known two-fluid hydrodynamics. Moreover, it is generalization of the two-fluid hydrodynamics equations due to TPI. Explicit expressions of the velocities for the first and the second sound via the concentration of superfluid and noncondensate components is calculated.

Double perovskites (DPs) of the form A₂BB′ O₆ usually involve a transition metal ion, B, with a large magnetic moment, and a nonmagnetic ion B′. While many DPs are ferromagnetic, studies on the underlying model reveal the possibility of antiferromagnetic (AF) phases as well driven by electron delocalization. In this paper we present a comprehensive study of the magnetic ground state and T_c scales of the minimal DP model in three dimensions using a combination of spin-fermion Monte Carlo and variational calculations. The effective magnetic lattice in three dimensions is face centered cubic (FCC) and so geometrically frustrated. This promotes noncollinear spiral states and "flux" like phases in addition to collinear AF order. We map out the possible magnetic phases for varying electron density, "level separation" ϵ_B - ϵ_B', and the crucial B′ B′ (next neighbour) hopping t′.

The eigenvalue spectrum of the fractional quantum harmonic oscillator is calculated numerically, solving the fractional Schrödinger equation based on the Riemann and Caputo definition of a fractional derivative. The fractional approach allows a smooth transition between vibrational and rotational type spectra, which is shown to be an appropriate tool to analyze IR spectra of diatomic molecules.