冷原子系统中不同色散准粒子波包动力学的模拟

基于光晶格中的超冷原子气体，研究了不同色散关系的准粒子动力学行为.分别采用数值时间劈裂谱方法和海森堡绘景解析求解运动方程的方法，针对有初速度和无初速度的准粒子动力学问题进行了数值模拟, 并深入讨论了色散关系中准动量幂次对准粒子动力学行为的影响.结果表明:在系统的准粒子色散关系中，当准动量幂次为奇数时，系统会出现相对论Zitterbewegung (ZB)振荡现象; 而当幂次为偶数时，准粒子动力学过程中不会出现ZB现象.此外，准动量幂次越大，则准粒子漂移对波包初速度的敏感度越高.

Simulation of Wave Packet Dynamics of Quasiparticles with Different Dispersions in Cold Atomic System

The dynamic propertic of quasi-particles with different dispersion relations is investigated based on ultra-cold atomic gases in optical lattices. Numerical simulation of quasi-particle dynamics with and without the initial velocity is conducted by means of the numerical time-splitting spectrum and Heisenberg scenario analytic solution to equations of motion, and a thorough discussion is made on the effect of quasi-momentum power in dispersion relations on the dynamics of quasi-particles. The results show that relativistic Zitterbewegung(ZB) oscillation occurs in the system given that the quasi-momentum power in dispersion relations of the quasi-particles is an odd number. However, ZB does not occur in the process of quasi-particle dynamics with an even power. Besides, the greater the power of the quasi-momentum, the higher sensitivity of the quasi-particle drift to the initial velocity of the wave packets.