4.4 Article

The thermodynamic limit of an ideal Bose gas by asymptotic expansions and spectral ζ-functions

期刊

JOURNAL OF MATHEMATICAL PHYSICS
卷 63, 期 12, 页码 -

出版社

AIP Publishing
DOI: 10.1063/5.0114640

关键词

-

资金

  1. Norbert Janssen Foundation

向作者/读者索取更多资源

By analyzing the thermodynamic limit, we can study the phase structure of a Bose gas and the phenomenon of Bose-Einstein condensation. The coefficients of the asymptotic expansion can be used to calculate thermodynamic observables.
We analyze the thermodynamic limit-modeled as the open-trap limit of an isotropic harmonic potential-of an ideal, non-relativistic Bose gas with a special emphasis on the phenomenon of Bose-Einstein condensation. This is accomplished by the use of an asymptotic expansion of the grand potential, which is derived by zeta-regularization techniques. Herewith, we can show that the singularity structure of this expansion is directly interwoven with the phase structure of the system: In the non-condensation phase, the expansion has a form that resembles usual heat kernel expansions. By this, thermodynamic observables are directly calculable. In contrast, the expansion exhibits a singularity of infinite order above a critical density, and a renormalization of the chemical potential is needed to ensure well-defined thermodynamic observables. Furthermore, the renormalization procedure forces the system to exhibit condensation. In addition, we show that characteristic features of the thermodynamic limit, such as the critical density or the internal energy, are entirely encoded in the coefficients of the asymptotic expansion.

作者

我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。

评论

主要评分

4.4
评分不足

次要评分

新颖性
-
重要性
-
科学严谨性
-
评价这篇论文

推荐

暂无数据
暂无数据