Theoretical study on the Quantum Statistical Aspects of BEC

A4小组由研究BEC物理的理论家组成。(1)上田等人研究了吸引相互作用下的BEC物理。吸引BEC的状态最多是一个亚稳态，最终会崩溃。他们研究了BEC坍塌的机制，发现在临界温度附近的BEC产生宏观量子隧穿，然后BEC坍塌。他还发现，在排斥性BEC中保证的循环量子化在吸引性BEC中只得到部分满足。循环的量子化被认为是超流性的一个标志。在一个有吸引力的BEC量子化的故障增加了新的见解BEC的基本性质。他们还研究了当相互作用从排斥转变为吸引时BEC的动力学。他们的发现是：（i）当一个大的BEC从排斥相互作用转换到吸引相互作用时，各种非线性模式（壳结构，层状结构，.）预计会出现。(ii)他们研究了当相互作用是排斥时产生的涡旋的动力学。他们发现了各种动力学不稳定性，这是相互作用强度的函数。不稳定性导致涡破裂，涡坍缩。(iii)研究表明，在吸引BEC中，如果相互作用势的符号和振幅被调制，则二维亮是稳定的。Ohmi和町田研究了多状态BEC的相分离、相变动力学、产生涡旋的新方法以及涡旋的稳定性。

The A4 group consisted of theoreticians working on the physics of BEC. (1) Ueda's group studied on the physics of BEC under attractive interaction. The state of the attractive BEC is at best a metastable state and eventually collapses. They studied the mechanism of the BEC collapsing and found that a BEC near the critical temperature grows macroscopic quantum tunneling, and then the BEC collapses. The found also the quantization of circulation that was guaranteed in a repulsive BEC was only partially satisfied in an attractive BEC. The quantization of circulation is know as a signature of superfluidity. The breakdown of the quantization in an attractive BEC adds new insight on the fundamental properties of BEC. They studied also the dynamics of BEC when the interaction is switched from repulsive to attractive. Their findings are (i) when a large BEC is switched from repulsive to attractive interaction, various nonlinear pattern (shell structure, layered structure,....) is expected to appear. (ii) They studied the dynamics of vortex generated when the interaction is repulsive. They found various dynamical instabilities that was a function of the interaction strength. The instabilities cause fracture of the vortex, and the vortex collapses. (iii) They showed in an attractive BEC two-dimensional bright is stabilized if the sign and amplitude of the interaction potential is modulated. Ohmi and Machida studied on me phase separation of multi-state BEC, dynamics of the phase transition, a new method of generating vortices, and on the stability of vortices.