Nonanalyticities of thermodynamic functions in finite noninteracting Bose gases within an exact microcanonical ensemble.
Nonanalyticities of thermodynamic functions in finite noninteracting Bose gases within an exact microcanonical ensemble.
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DOI：
10.1103/physreve.83.061135
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发表时间：
2011-06
期刊：
影响因子：
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通讯作者：
Hui-yi Tang;Yongli Ma
中科院分区：
文献类型：
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作者：
Hui-yi Tang;Yongli Ma
在严格的微正则系综下，我们研究了囚禁中有限非相互作用玻色气体热力学函数的非解析性。结果表明，MC热力学量作为系统总能量E(如非单调温度、非解析比热和负比热以及微观相变)的函数存在丰富的振荡行为。这些非解析性的起源直接来自于S(E)相对于E的倒曲率熵，并且在不同的陷阱几何、边界条件和能谱组态下，其行为是不同的。与通常的超正则和正则结果相反，具有不同陷阱的二维有限非相互作用玻色系统存在玻色凝聚和非解析性。我们还讨论了在不同系综、陷阱和边界条件下，临界温度对粒子数N的依赖关系。在足够大的N中，几乎所有的热力学结果都变得光滑，这类似于通常的正则行为。我们强调了有限尺寸效应对MC熵变的影响，原则上，这种效应在适当设计的小系统实验中应该是可观察到的。
Within an exact microcanonical (MC) ensemble, we study the nonanalyticities of thermodynamic functions research in finite noninteracting Bose gases in traps. The results show that there exists a rich oscillatory behavior of MC thermodynamical quantities as a function of a system's total energy E (e.g., nonmonotonous temperature, nonanalytic and negative specific heats, and microscopic phase transitions). The origin of these nonanalyticities comes directly from the inverted curvature entropy S(E) with respect to E and the behaviors are different in different trap geometries, boundary conditions, and energy spectrum configurations. Contrary to the usual grandcanonical and canonical results, there exists Bose condensation and the nonanalyticities in the two-dimensional finite noninteracting Bose systems with different traps. We also discuss the critical temperature dependence on the particle number N with different ensembles, traps, and boundary conditions. In large enough N, almost all the results of the thermodynamical quantities become smooth, which are similar to the usual canonical behaviors. We emphasize the finite-size effects on the MC entropy change, which should, in principle, be observable in suitably designed experiments of the small systems.