论文标题
$ su（1,1）$对称性冷原子气的量子动态
Quantum Dynamics of Cold Atomic Gas with $SU(1,1)$ Symmetry
论文作者
论文摘要
在量子动力学的最新进展中，我们以$ su（1,1）$对称性进行了研究。我们没有为时间依赖的哈密顿量的演化运算符执行时间订购的积分，而是表明时间演化运算符可以表示为$ su（1,1）$组元素。由于$ su（1,1）$组描述了双曲线表面上的“旋转”，因此可以在庞加莱磁盘上可视化动力学，这是上部倍增倍曲底的立体投影。例如，我们介绍了Bose-Einstein凝结的复兴以及庞加莱磁盘上的比例不变的费米气体的轨迹。进一步考虑了振荡晶格中的量子气，我们还通过时间依赖性的单粒子色散研究了系统的动力学。希望我们的结果可以在当前的实验中进行检查。
Motivated by recent advances in quantum dynamics, we investigate the dynamics of the system with $SU(1,1)$ symmetry. Instead of performing the time-ordered integral for the evolution operator of the time-dependent Hamiltonian, we show that the time evolution operator can be expressed as an $SU(1,1)$ group element. Since the $SU(1,1)$ group describes the "rotation" on a hyperbolic surface, the dynamics can be visualized on a Poincaré disk, a stereographic projection of the upper hyperboloid. As an example, we present the trajectory of the revival of Bose-Einstein condensation and that of the scale-invariant Fermi gas on the Poincaré disk. Further considering the quantum gas in the oscillating lattice, we also study the dynamics of the system with time-dependent single-particle dispersion. Our results are hopefully to be checked in current experiments.
