论文标题
相互作用的循环集合和玻色气体
Interacting loop ensembles and Bose gases
论文作者
论文摘要
我们研究了晶格上热平衡中的相互作用的胶体气体。我们建立了这种气体的大规范吉布斯状态的融合到其平均场（经典场）和大型（经典粒子）极限。前者是具有四分之一自我交往的复杂标量场的经典字段理论。后者是具有两体相互作用的点粒子的经典理论。我们的分析基于表示相互作用的随机回路的组合，Bose气体的Ginibre循环集合和经典标量场理论的Symanzik循环集合。对于足够小的相互作用，我们的结果也具有无限的体积。
We study interacting Bose gases in thermal equilibrium on a lattice. We establish convergence of the grand canonical Gibbs states of such gases to their mean-field (classical field) and large-mass (classical particle) limits. The former is a classical field theory for a complex scalar field with quartic self-interaction. The latter is a classical theory of point particles with two-body interactions. Our analysis is based on representations in terms of ensembles of interacting random loops, the Ginibre loop ensemble for Bose gases and the Symanzik loop ensemble for classical scalar field theories. For small enough interactions, our results also hold in infinite volume.
