标题： 相互作用原子系统中非对角长程序与无限排列循环的同时出现 显示英文标题

标题： Simultaneous occurrence of off-diagonal long-range order and infinite permutation cycles in systems of interacting atoms

摘要： 基于论文“量子配分函数的傅里叶公式”，arXiv:2106.10032 [math-ph]，我们证明在由正类型对势相互作用的相同玻色子无限系统中，当且仅当一定比例的粒子形成无限排列循环时，存在非对角长程序。 特别是，当发散循环长度随着$N$，粒子数，的增长至少与$N^{2/d}$在$d\geq 3$维度中的增长速度相同时，就会发生玻色-爱因斯坦凝聚。 这一结果扩展了已知的理想玻色气体的类似结论。 显示英文摘要

摘要： Based on the paper "Fourier formula for quantum partition functions", arXiv:2106.10032 [math-ph], we show that in an infinite system of identical bosons interacting via a positive-type pair potential there is off-diagonal long-range order if and only if a nonzero fraction of the particles form infinite permutation cycles. In particular, there is Bose-Einstein condensation if and only if the diverging cycle lengths increase at least as fast with $N$, the number of particles, as $N^{2/d}$ in $d\geq 3$ dimensions. This extends a similar result known for the ideal Bose gas.