Spectral densities and partition functions of modular quantum systems as derived from a central limit theorem

TL;DR

This paper derives analytical formulas for the spectral densities and partition functions of large modular quantum systems using a central limit theorem, showing good agreement with known results even for small systems.

Contribution

It introduces a central limit theorem approach to analytically approximate spectral densities and partition functions in modular quantum systems.

Findings

Analytical expressions valid for infinite subsystems

Good agreement with exact results for small systems

Provides a new theoretical tool for quantum statistical analysis

Abstract

Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite number of subsystems. Even for only small numbers of subsystems we find good accordance with some known, exact results.