Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-02-28
Phys. Rev. E 84, 041125 (2011)
Physics
Condensed Matter
Statistical Mechanics
8 pages, 6 figures
Scientific paper
10.1103/PhysRevE.84.041125
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.
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