Tang Hui-yi, Ma Yong-li
State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 1):061135. doi: 10.1103/PhysRevE.83.061135. Epub 2011 Jun 23.
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.
在精确的微正则（MC）系综中，我们研究了捕获势中有限无相互作用玻色气体热力学函数研究中的非解析性。结果表明，作为系统总能量E的函数，MC热力学量存在丰富的振荡行为（例如，非单调温度、非解析和负比热以及微观相变）。这些非解析性的起源直接来自熵S(E)相对于E的反转曲率，并且在不同的捕获势几何形状、边界条件和能谱配置中行为不同。与通常的巨正则和正则结果相反，在具有不同捕获势的二维有限无相互作用玻色系统中存在玻色凝聚和非解析性。我们还讨论了不同系综、捕获势和边界条件下临界温度对粒子数N的依赖性。在足够大的N时，几乎所有热力学量的结果都变得平滑，这与通常的正则行为相似。我们强调了有限尺寸对MC熵变的影响，原则上，这在精心设计的小系统实验中应该是可观测的。
