玻色-爱因斯坦凝聚体中的超流现象

在玻色－爱因斯坦凝聚（BEC）的超流现象的研究中，人们通常采用平均场近似下求解Gross-Pitaveskii方程的方法，我们采用更严格的准确对角化的方法对弱排斥相互作用下两维旋转N－Boson体系的凝聚状态进行了研究，研究表明，弱相互作用下的基态并不是人们通常认为的单一凝聚态，而是一个碎裂凝聚态，通过碎裂态能谱与平均场方法给出的能谱之间的比较以及条件几率分布函数的计算，我们指出这种碎裂凝聚态有着内在的不稳定性，很容易破缺到一个单一凝聚状态；计算给出的条件几率分布可以用来揭示破缺石的状态，其分布图案与平均场近似下得到的涡旋图形相类似，我们进一步注意到过去研究工作主要集中在弱相互作用极限下和强相互作用Thomas-Fermi近似极限下这两种极端情况，为考察两种极限间的中间过渡区域，我们研究了中等相互作用强度下体系的基态性质。

SUPERFLUIDITY IN BOSE-EINSTEIN CONDENSATES

In general,the mean\|field\|approximation(MFA) is adopted to solve the Gross\|Pitaevskii equation in studies of superfluidity in Bose\|Einstein condensates. However, we use the more rigorous exact diagonalization method(EDM) to investigate the state of a condensate with weak repulsive interaction in a two\|dimensional N \|boson system under rotation. The results show that the ground state is a fragmented condensate state instead of a single condensate state, contrary to what one might expect. By comparing the energy spectrum of the fragmented state in EDM with that given by the mean\|field\|approximation and calculating the conditional probability distribution, we find that the fragmented state is intrinsically unstable and tends to decay spontaneously to a single condensate state. The conditional probability distribution reveals the state after symmetry breaking, and vortex pictures similar to those under MFA are obtained. Moreover, on the basis of previous works on superfluidity which mainly considered the two extreme limits of weak interaction and strong Thomas\|Fermi interaction we further study the ground\|state properties of the system with medium interaction strength.