有限体系中的Bose-Einstein凝聚

Bose-Einstein Condensation in Finite System

用巨正则系综 ,研究了一个可解的束缚在有限体积中没有相互作用的原子体系的Bose Einstein凝聚(BEC) .它比通常意义下的无限体系中的BEC在某些概念上有所延伸 .在有限体系中 ,由于体系的化学势 μ≤ 0的条件不再一定成立 ,可能出现 μ >0的“汽”态 (粒子在能级上完全按Bose Einstein统计分布的状态 ) ,即非BEC状态 .因此 ,在温度T <TC 情况下 ,需要同时讨论 μ >0的“汽”态和 μ =0的BEC状态 ,计算了“汽”态和BEC状态的吉布斯自由能 ,探讨了出现BEC的条件 ,同时还计算了BEC温度TC 随粒子密度的关系 .计算结果显示没有相互作用的Bose气体模型大致上可以相当好地解释超冷原子体系的BEC实验 .

Based on grand canonical assembles statistics,the Bose Einstein Condensation (BEC) in non interacting bound atomic system is studied.Some basic concepts of BEC in conventional infinite Bose system are extended.The condition of chemical potential μ ≤0 will not be guarantted for the present finite bound system,and the 'vapour state' with μ >0,the state without condensation at any eigenstate,might be possible in principle even below a critical temperature T C .Gibbs functions for both the 'gas state' and the BEC state at temperature T<T C have been calculated.The condition for BEC to appear is presented.The relation of BEC temperature T C with the density of particles is estimated and the result is qualitatively in good agreement with the experimental results.