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Partition asymptotics from one-dimensional quantum entropy and energy currents

Miles P. Blencowe·Nicholas C. Koshnick
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Abstract

We give an alternative method to that of Hardy-Ramanujan-Rademacher to derive the leading exponential term in the asymptotic approximation to the partition function p(n,a), defined as the number of decompositions of a positive integer 'n' into integer summands, with each summand appearing at most 'a' times in a given decomposition. The derivation involves mapping to an equivalent physical problem concerning the quantum entropy and energy currents of particles flowing in a one-dimensional channel connecting thermal reservoirs, and which obey Gentile's intermediate statistics with statistical parameter 'a'. The method is also applied to partitions associated with Haldane's fractional exclusion statistics.

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Miles P. Blencowe, Nicholas C. Koshnick. 2001-12-11. Partition asymptotics from one-dimensional quantum entropy and energy currents. https://doi.org/10.1063/1.1416195

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