1102.5624 (Agnieszka Werpachowska)

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

Agnieszka Werpachowska

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. NOTICE: This paper is an independent work of the author and is not related in any way to the author's PhD studies.

View original: http://arxiv.org/abs/1102.5624