Yunbo Zhang

Absorption Cross Section of Scalar Field in Supergravity Background

Abstract It has recently been shown that the equation of motion of a massless scalar field in the background of some specific p -branes can be reduced to a modified Mathieu equation. In the following the absorption rate of the scalar by a D3 brane in ten dimensions is calculated in terms of modified Mathieu functions of the first kind, using standard Mathieu coefficients. The relation of the latter to Dougall coefficients (used by others) is investigated. The S -matrix obtained in terms of modified Mathieu functions of the first kind is easily evaluated if known rapidly convergent low energy expansions of these in terms of products of Bessel functions are used. Leading order terms, including the interesting logarithmic contributions, can be obtained analytically.

Quantum-classical phase transition of escape rates in biaxial spin particles

By using a stereographic projection of the unit sphere of magnetization vector onto a complex plane for the equations of motion, the effect of an external magnetic field for integrability of the system is discussed. The properties of the Jest solutions and the scattering data are then investigated through introducing transformations other than the Riemann surface in order to avoid double-valued functions of the usual spectral parameter. The exact multisoliton solutions are investigated by means of the Binet-Cauchy formula. The results showed that under the action of an external magnetic field nonlinear magnetization depends essentially on two parameters: its center moves with a constant velocity, while its shape changes with another constant velocity; its amplitude and width vary periodically with time, while its shape is also dependent on time and is unsymmetric with respect to its center. The orientation of the nonlinear magnetization in the plane orthogonal to the anisotropy axis changes with an external magnetic field. The total magnetic momentum and the integral of the motion coincident with its z component depend on time. The mean number of spins derivated from the ground state in a localized magnetic excitations is dependent on time. The asymptotic behavior of multisoliton solutions, the total displacement of center, and the phase shift of the jth peak an also analyzed. [S0163-1829(99)07121-0].

Ground-state properties of one-dimensional ultracold Bose gases in a hard-wall trap

We investigate the ground state of the system of N bosons enclosed in a hard-wall trap interacting via a repulsive or attractive delta-function potential. Based on the Bethe ansatz method, the explicit ground state wave function is derived and the corresponding Bethe ansatz equations are solved numerically for the full physical regime from the Tonks limit to the strongly attractive limit. It is shown that the solution takes a different form in different regime. We also evaluate the one body density matrix and second-order correlation function of the ground state for finite systems. In the Tonks limit the density profiles display the Fermi-like behavior, while in the strongly attractive limit the Bosons form a bound state of N atoms corresponding to the N-string solution. The density profiles show the continuous crossover behavior in the entire regime. Further, the correlation function indicates that the Bose atoms bunch closer as the interaction constant decreases.

Quantum walks of two interacting anyons in one-dimensional optical lattices

We investigate continuous-time quantum walks of two indistinguishable anyons in one-dimensional lattices with both on-site and nearest-neighbor interactions based on the fractional Jordan-Wigner transformation. It is shown that the two-body correlations in position space are symmetric about the initial sites of two quantum walkers in the Bose limit (

Ground-state properties of hard-core anyons in one-dimensional optical lattices

\chi=0

Topological defects in spinor condensates

) and Fermi limit (

Stability and free expansion of a dipolar Fermi gas

\chi=1

Ground-state properties of a few-boson system in a one-dimensional hard-wall split potential

), while in momentum space this happens only in the Bose limit. An interesting asymmetry arises in the correlation for most cases with the statistical parameter

Macroscopic quantum coherence in spinor condensates confined in an anisotropic potential

\chi

Quantum phases of the Bose-Hubbard model in optical superlattices

varying in between. It turns out that the origin of this asymmetry comes from the fractional statistics that anyons obey. On the other hand, the two-body correlations of hard-core anyons in position spaceshow uniform behaviors from anti-bunching to co-walking regardless of the statistical parameter. The momentum correlations in the case of strong interaction undergo a smooth process of two stripes smoothly merging into a single one, i.e. the evolution of fermions into hard-core bosons.