Theory of noninteracting fermions and bosons in the canonical ensemble
Theory of noninteracting fermions and bosons in the canonical ensemble
复制标题
DOI：
10.1103/physrevresearch.2.043206
复制
发表时间：
2020-11-09
影响因子：
4.2
通讯作者：
Del Maestro, Adrian
中科院分区：
文献类型：
--
作者：
Barghathi, Hatem;Yu, Jiangyong;Del Maestro, Adrian
我们提出了一个完备的理论，用于精确计算正则系综中非相互作用的不可分辨粒子的粒子计数统计。这个一般框架引入了辅助配分函数的概念，并代表了以前不同的方法与许多已知的结果出现的直接后果发达的数学结构的统一。此外，我们引入了一个一般的分解的占用数之间的相关性的个人能级的占用数，这是有效的非简并和简并光谱。为了证明该理论在简并存在下的适用性，我们计算了在磁场存在下玻色子环中四阶的能级关联。
We present a self-contained theory for the exact calculation of particle number counting statistics of noninteracting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary partition functions, and represents a unification of previous distinct approaches with many known results appearing as direct consequences of the developed mathematical structure. In addition, we introduce a general decomposition of the correlations between occupation numbers in terms of the occupation numbers of individual energy levels, that is valid for both nondegenerate and degenerate spectra. To demonstrate the applicability of the theory in the presence of degeneracy, we compute energy-level correlations up to fourth order in a bosonic ring in the presence of a magnetic field.