论文标题
微型典型集合中的扰动理论
Perturbation Theory in a Microcanonical Ensemble
论文作者
论文摘要
微型典型合奏是统计力学的自然起点。但是，当涉及统计力学中的扰动理论时，传统上，只有使用规范和宏伟的规范合奏。在本文中，我们展示了如何直接使用微域合奏来为非相互作用和相互作用系统进行扰动理论。我们为非谐振荡器的特定热量以及实际气体的病毒扩张获得了第一个非平凡秩序答案。它们与从规范合奏中获得的结果完全一致。此外，我们还展示了如何使用微观集合的集合以及如何获得病毒扩张的后续项来构建非谐振荡器的特定热量的交叉功能。但是，我们发现，如果我们考虑在一维延伸盒中考虑量子L的量子颗粒，那么这两个合奏为在高温极限下对特定热量的首次校正给出了明显不同的答案。
The microcanonical ensemble is a natural starting point of statistical mechanics. However, when it comes to perturbation theory in statistical mechanics, traditionally only the canonical and grand canonical ensembles have been used. In this article we show how the microcanonical ensemble can be directly used to carry out perturbation theory for both non-interacting and interacting systems. We obtain the first non-trivial order answers for the specific heat of anharmonic oscillators and for the virial expansion in real gases. They are in exact agreement with the results obtained from the canonical ensemble. In addition, we show how crossover functions for the specific heat of anharmonic oscillators can be constructed using a microcanonical ensemble and also how the subsequent terms of the virial expansion can be obtained. However, we find that if we consider quantum free particles in a one-dimensional box of extension L, then the two ensembles give strikingly different answers for the first correction to the specific heat in the high temperature limit.
