Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods
Paulsamy Muruganandam and Sadhan K Adhikari
我们建议一种用于解决三维时间依赖性Gross-Pitaevskii(GP)方程的伪光谱方法,并用它来研究由原子散射长度的周期性变化引起的被困玻色-爱因斯坦凝结物的共振动力学。 当散射长度的振荡频率是沿 x、y 或 z 方向的诱捕频率之一的均匀倍数时,冷凝物的相应大小执行共振振荡。 使用分化矩阵的概念,偏差GP方程被简化为一组耦合的普通微分方程,该方程由四阶自适应步大小的控制Runge-Kutta方法解决。 伪光谱方法与同一问题的有限差法形成对比,其中时间演变由Crank-Nicholson算法执行。 后一种方法被说明更适合三维站立波光学晶格捕获电位。
We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross-Pitaevskii (GP) equation and use it to study the resonance dynamics of a trapped Bose-Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y, or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of ...