超稳弱不完美玻色气体的大偏差
Large Deviations in the Superstable Weakly Imperfect Bose Gas
摘要：
超稳定弱不完全玻色气体{（WIBG）}最初是为了解决超流性的Bogoliubov理论的不一致性而导出的。它的巨正则热力学最近得到了解决，但不是在{（一阶）}相变的{点}。本文提出了使用大偏差形式主义，特别是Kac分布函数的分析，以缩小这一差距。结果表明，作为化学势的函数，玻色凝聚体密度在相变{点}处的不连续性作为粒子密度的函数消失。事实上，玻色凝聚体在第一临界粒子密度处开始不断地增长，但每个粒子的自由能保持不变，直到达到第二临界密度。在较高的粒子密度下，玻色凝聚密度以及每个粒子的自由能都单调增加。
英文摘要：
The superstable Weakly Imperfect Bose Gas {(WIBG)} was originally derived to solve the inconsistency of the Bogoliubov theory of superfluidity. Its grand-canonical thermodynamics was recently solved but not at {point of} the {(first order)} phase transition. This paper proposes to close this gap by using the large deviations formalism and in particular the analysis of the Kac distribution function. It turns out that, as a function of the chemical potential, the discontinuity of the Bose condensate density at the phase transition {point} disappears as a function of the particle density. Indeed, the Bose condensate continuously starts at the first critical particle density and progressively grows but the free-energy per particle stays constant until the second critical density is reached. At higher particle densities, the Bose condensate density as well as the free-energy per particle both increase {monotonously}.
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