统计力学中的费米和玻色压力
Fermi and Bose pressures in statistical mechanics
摘要：
我展示了如何费米和玻色压力在量子系统中，确定在标准的讨论中，通过使用热力学类比，可以直接推导出的动量流通过使用量子力学应力张量的表面。在这种方法中，类似于经典的动力学理论，压力自然地被局部定义，这一点在应力张量方面是明显的，但在通常的热力学方法中是隐藏的。这两种方法是连接的一个有趣的应用边界微扰理论的量子系统。处理导致一个简单的解释费米和玻色系统中的压力编码的波函数的动量流。我适用于几个问题的方法，调查性质的准连续系统，费米和玻色压力的关系，形状相关的影响和各向异性，以及治疗的粒子在外部领域，并注意到几个有趣的问题，研究生课程在统计力学自然出现的背景下，这些例子。
英文摘要：
I show how the Fermi and Bose pressures in quantum systems, identified in standard discussions through the use of thermodynamic analogies, can be derived directly in terms of the flow of momentum across a surface by using the quantum mechanical stress tensor. In this approach, analogous to classical kinetic theory, pressure is naturally defined locally, a point which is obvious in terms of the stress-tensor but is hidden in the usual thermodynamic approach. The two approaches are connected by an interesting application of boundary perturbation theory for quantum systems. The treatment leads to a simple interpretation of the pressure in Fermi and Bose systems in terms of the momentum flow encoded in the wave functions. I apply the methods to several problems, investigating the properties of quasi continuous systems, relations for Fermi and Bose pressures, shape-dependent effects and anisotropies, and the treatment of particles in external fields, and note several interesting problems for graduate courses in statistical mechanics that arise naturally in the context of these examples.
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