Tunneling of Boseben-Einstein condensate and interference effect in a harmonic trap with a Gaussian energy barrier

The tunneling effect of Bose-Einstein condensate (BEC) in a harmonic trap with a Gaussian energy barrier is studied in this paper. The initial condensate evolves into two separate moving condensates after the tunneling time under certain conditions. The interference pattern between the two moving condensates is given as a comparison and as a further demonstration of the existence of the global phase.     

立方五次方非线性Schrdinger方程的动力学性质研究

采用辛算法数值求解了一维立方五次方非线性Schrdinger方程,研究了不同非线性参数下非线性Schrdinger方程的动力学性质.数值结果表明,随着立方非线性参数的增加,系统经历了拟周期状态、混沌状态和周期状态,且在五次方项的调制下,呼吸子解可以退化为单孤子解.     

Solution of Dirac equation around a charged rotating black hole

The aim of this paper is to solve the radial parts of a Dirac equation in Kerr-Newman （KN） geometry. The potential is replaced by a collection of step functions, then the reflection and transmission coefficients as well as the solution of the wave equation are obtained by using a quantum mechanical method. The result shows that the waves with different values of mass will be scatted off very differently.     

非线性Schrdinger方程的动力学行为分析

采用辛算法数值求解非线性Schr dinger方程的周期初值问题,建立不同的相空间来分析其动力学特性.首先比较分析了不同的相空间中立方非线性Schr dinger方程在不同立方非线性参数下的长时间演化的动力学特性,然后讨论了相空间中立方-五次方非线性Schr dinger方程在不同立方和五次方非线性参数下的长时间演化的动力学特性,数值结果显示,对于不同的立方非线性参数,随着五次方非线性参数的增加,动力学行为的演化路径是不一样的.     

Gross-Pitaevskii方程的数值解及其动力学研究

采用辛-打靶法求解了简谐势阱中碱金属玻色-爱因斯坦凝聚原子在T=0时的基态波函数,检验了波函数的稳定性,并研究了当简谐势阱突然改变时波函数随时间演化的动力学.     

Nonlinear resonance phenomenon of one-dimensional Bose–Einstein condensate under periodic modulation

We investigate the effect of an external periodic modulation on the one-dimensional （1D） Bose-Einstein conden- sate with harmonic trapping potential. By numerically solving the Gross-Pitaevskii equation with symplectic algorithm, the nonlinear resonance phenomenon is shown and the corresponding Fourier spectrum is given. The autoresonance phe- nomenon is also presented under almost periodic external modulation, and it shows that the condensate eventually evolves into quasi-periodic oscillation.     

Research on the discrete variational method for a Birkhoffian system

In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.     

Dynamics of cubic–quintic nonlinear Schr?dinger equation with different parameters

We study the dynamics of the cubic–quintic nonlinear Schr?dinger equation by the symplectic method. The behaviors of the equation are discussed with harmonically modulated initial conditions, and the contributions from the quintic term are discussed. We observe the elliptic orbit, homoclinic orbit crossing, quasirecurrence, and stochastic motion with different nonlinear parameters in this system. Numerical simulations show that the changing processes of the motion of the system and the trajectories in the phase space are various for different cubic nonlinear parameters with the increase of the quintic nonlinear parameter.     

改进打靶法求解Gross-Pitaevskii方程及三个凝聚体的干涉

用改进的打靶法求解零温简谐势阱中中性原子玻色-爱因斯坦凝聚的一维Gross-Pitaevskii方程,给出不同非线性参数时凝聚体基态的本征值.用辛算法研究三个凝聚体在撤掉陷俘势后产生的干涉,和三个凝聚体处于同-陷俘势中的干涉及周期性演化,讨论不同的相对相位对凝聚体干涉的影响.     

Tunneling of Bose-Einstein condensate and interference effect in a harmonic trap with a Gaussian energy barrier

The tunneling effect of Bose-Einstein condensate (BEC) in a harmonic trap with a Gaussian energy barrier is studied in this paper. The initial condensate evolves into two separate moving condensates after the tunneling time under certain conditions. The interference pattern between the two moving condensates is given as a comparison and as a further demonstration of the existence of the global phase.