title: 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.
authors.affiliation: Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom. a.werpachowska@ucl.ac.uk
authors.forename: Agnieszka
authors.initials: A
authors.lastname: Werpachowska