The heat capacity (C) of a mesoscopic nonsuperconducting fermion system treated as a canonical ensemble of independent particles is studied in a wide range of particle numbers and temperatures which vary from values close to zero up to the Fermi energy. The temperature evolution of C is naturally divided into four stages. On the first one the heat capacity exponentially increases with temperature and at a resonance temperature reaches either a local maximum or an irregularity in its growth. This resonance temperature being measured can give information concerning the level spacings in the immediate proximity of the Fermi energy. On the second stage the progressive suppression of the level density oscillations takes place. During this stage oscillations of C v.s. particle number N can be distinctly observed. These oscillations give the N-variations of the temperature averaged level density. The growth of C on the third stage of the evolution is governed by the T-linear law if the particle number is large enough (N>1000). It is found that the Sommerfeld factor in the linear law for such small systems shows more complicated N-dependence as compared with large systems where C is strictly proportional to N. For temperatures tending to the Fermi energy the deviations from the T-linearity are evident and at T larger than the Fermi energy (the fourth stage of the evolution) any system attains to the classic Boltzmann-Maxwell limit irrespective of the particle
Fluctuation statistics of mesoscopic Bose-Einstein condensate: reconciling the master equation with the partition function to revisit the Uhlenbeck-Einstein dilemma
从几个不同的角度研究了理想介观玻色-爱因斯坦凝聚体的原子涨落统计。通过推广巨正则分析（适用于正则系综问题），我们得到了一个自洽的平均凝聚粒子数方程，该方程与激光主方程方法计算的微观结果相吻合。对于一个谐波陷阱的情况下，我们得到一个解析表达式的凝聚粒子数是非常准确的，在所有温度下，与数值正则系综结果相比。应用类似的广义巨正则处理的方差，我们得到一个准确的结果，只有低于临界温度。采用随机路径积分的形式主义，具有很好的精度的波动分布的所有高阶矩的分析结果。我们进一步讨论了一种混合处理，它将主方程/随机路径积分分析与基于正则系综准粒子形式主义获得的结果结合在一起[V. V. Kocharovsky等人，Phys.Rev.A61，053606（2000）]，在所有温度下产生与数值模拟基本上完美的一致。
Description using equilibrium temperature in the canonical ensemble within the framework of the Tsallis statistics employing the conventional expectation value
Heat Capacity Anomalies and Thermal Crossovers in Finite Su-Schrieffer-Heeger Chains
Universidade Federal Fluminense（弗鲁米嫩塞联邦大学）；Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Faculty of Electric Engineering, Universidad Michoacana de San Nicolás de Hidalgo（圣尼古拉斯德伊达尔戈米却肯自治大学电气工程学院）；Centro de Ciencias Exactas, Universidad del Bío-Bío（比奥比奥大学精确科学中心）；Departamento de Ciencias Básicas de la Facultad de Ciencias, Universidad del Bío-Bío（比奥比奥大学理学院基础科学系）
