发表机构
Virginia Tech; University of Warsaw（弗吉尼亚理工大学; 华沙大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究弱相互作用热玻色气体，证明其吉布斯态可由新型博戈留波夫随机场近似，并据此计算粒子数分布等统计量，确立微观尺度粒子数统计的普适性。
AI 中文摘要
我们研究三维环面上温度正比于玻色-爱因斯坦凝聚临界温度的弱相互作用玻色子。我们证明，当期望粒子数趋于无穷时，巨正则吉布斯态渐近地由相干态量子化的随机场描述，该随机场收敛到一个新的博戈留波夫随机场。此外，与吉布斯态相关联的点过程可以用考克斯过程近似。这些结果基于并扩展了前两位作者与Nam最近获得的吉布斯态近似。利用这些近似，我们计算了凝聚体外粒子数的极限分布、有限多个动量模式的联合占据统计以及环面宏观子集中的粒子数涨落，所有这些均由博戈留波夫场支配。我们进一步证明了相关点过程的经验测度收敛到均匀测度，以及微观粒子数统计收敛到玻色子点过程。后一结果确立了微观长度尺度上粒子数统计的普适性。
英文摘要
We study weakly interacting bosons on the three-dimensional torus at temperatures proportional to the critical temperature for Bose--Einstein condensation. We show that, as the expected particle number tends to infinity, the grand canonical Gibbs state is asymptotically described by the coherent state quantization of a random field that converges to a novel Bogoliubov random field. Moreover, the point process associated with the Gibbs state can be approximated by a Cox process. These results are based on and extend the approximation of the Gibbs state recently obtained by the first two authors and Nam. Using these approximations, we compute limiting distributions of the number of particles outside the condensate, the joint occupation statistics of finitely many momentum modes, and particle-number fluctuations in macroscopic subsets of the torus, all governed by the Bogoliubov field. We further prove convergence of the empirical measure of the associated point process to the uniform measure and convergence of the microscopic particle-number statistics to the boson point process. The latter result establishes the universality of particle-number statistics on microscopic length scales.
Comments54 pages
