Exact and approximate methods of calculating the sum of states for noninteracting classical and quantum particles occupying a finite number of modes

Abstract

We present exact expressions for the sum of states of noninteracting classical and quantum particles occupying a finite number of modes with arbitrary spacings. Exploiting a probabilistic analogy, we derive an analytic fourth-order approximation to the density of states, which captures its variance and kurtosis, and is superior to the previous, commonly used methods for all three particle statistics. Our approach employs a simple exact method of calculating the moments of the microcanonical density of states for quantum particles, which requires less computational effort than the commonly used saddle-point approximation. We test our methods numerically and discuss their applicability to various physical systems.

8 pages, 6 figures

References in corpus (1)

• Microcanonical description of (micro) black holes

Cited by in corpus (2)

• Approximations of the Sum of States by Laplace's Method for a System of Particles with a Finite Number of Energy Levels and Application to Limit Theorems
• On the merit of a Central Limit Theorem-based approximation in statistical physics