Revised research about chaotic dynamics in Manko et al. spacetime

A recent work by Dubeibe et al. [Phys. Rev. D 75, 023008 (2007)] stated that chaos phenomenon of test particles in gravitational field of rotating neutron stars which are described by Manko, Sanabria-Gomez, and Manko (Manko et al.) metric can only occur when the stars have oblate deformation. But the chaotic motions they found are limited in a very narrow zone which is very close to the center of the massive bodies. This paper argues that this is impossible because the region is actually inside of the stars, so the motions cannot exist at this place. In this paper, we scan all parameters space and find chaos and unstable fixed points outside of stars with big mass-quadrupole moments. The calculations show that chaos can only occur when the stars have prolate deformation. Because real deformation of stars should be oblate, all orbits of test particles around the rotating neutron stars described by Manko et al. solutions are regular. The case of nonzero dipolar magnetic moment has also been taken into account in this study.Comment: 6 pages, 5 figure

Ground states of hard-core bosons in one dimensional periodic potentials

With Girardeau's Fermi-Bose mapping, we find the exact ground states of hard-core bosons residing in a one dimensional periodic potential. The analysis of these ground states shows that when the number of bosons $N$ is commensurate with the number of wells $M$ in the periodic potential, the boson system is a Mott insulator whose energy gap, however, is given by the single-particle band gap of the periodic potential; when $N$ is not commensurate with $M$, the system is a metal (not a superfluid). In fact, we argue that there may be no superfluid phase for any one-dimensional boson system in terms of Landau's criterion of superfluidity. The Kronig-Penney potential is used to illustrate our results.Comment: 6 pages, 6 figure

Tunneling Time in the Landau-Zener Model

We give a general definition for the tunneling time in the Landau-Zener model. This definition allows us to compute numerically the Landau-Zener tunneling time at any sweeping rate without ambiguity. We have also obtained analytical results in both the adiabatic limit and the sudden limit. Whenever applicable, our results are compared to previous results and they are in good agreement.Comment: 7pages, 9 figure

GPG-stability of Runge-Kutta methods for generalized delay differential systems

AbstractThe GPG-stability of Runge-Kutta methods for the numerical solutions of the systems of delay differential equations is considered. The stability behaviour of implicit Runge-Kutta methods (IRK) is analyzed for the solution of the system of linear test equations with multiple delay terms. After an establishment of a sufficient condition for asymptotic stability of the solutions of the system, a criterion of numerical stability of IRK with the Lagrange interpolation process is given for any stepsize of the method

Adiabatic Theory of Nonlinear Evolution of Quantum States

We present a general theory for adiabatic evolution of quantum states as governed by the nonlinear Schrodinger equation, and provide examples of applications with a nonlinear tunneling model for Bose-Einstein condensates. Our theory not only spells out conditions for adiabatic evolution of eigenstates, but also characterizes the motion of non-eigenstates which cannot be obtained from the former in the absence of the superposition principle. We find that in the adiabatic evolution of non-eigenstates, the Aharonov-Anandan phases play the role of classical canonical actions.Comment: substantial revision, 5 pages and 3 figure

Local U(1) symmetry in Y(so(5)) associated with Massless Thirring Model and its Bethe Ansatz

The Massless Thirring model associated with SO(5) is solved in terms of the local U(1) symmetry. The local U(1) symmetry is related to q-deformation of four-component field operators due to the nonlinear interaction for differently internal degree of freedom. The Bethe ansatz wavefunction is also discussed. In addition, the local U(1) symmetry in the Yangian associated with SO(5)(Y(SO(5))) is explored.Comment: 10 pages, no figure

A Quantum Tweezer for Atoms

We propose a quantum tweezer for extracting a desired number of neutral atoms from a reservoir. A trapped Bose-Einstein condensate (BEC) is used as the reservoir, taking advantage of its coherent nature, which can guarantee a constant outcome. The tweezer is an attractive quantum dot, which may be generated by red-detuned laser light. By moving with certain speeds, the dot can extract a desired number of atoms from the BEC through Landau-Zener tunneling. The feasibility of our quantum tweezer is demonstrated through realistic and extensive model calculations.Comment: 4 pages, 6 figures Revised versio