Partition asymptotics from one-dimensional quantum entropy and energy currents

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.

Published version

References in corpus (2)

• Fractional Exclusion Statistics and the Universal Quantum of Thermal Conductance: A Unifying Approach
• Exclusion statistics: A resolution of the problem of negative weights

Cited by in corpus (6)

• Intermediate-statistics quantum bracket, coherent state, oscillator, and representation of angular momentum (su(2)) algebra
• Integer Partitions and Exclusion Statistics
• Factorising numbers with a Bose-Einstein condensate
• $Q$-deformed description of excitons and associated physical results
• Gentile statistics and restricted partitions
• The Euler-Riemann Gases, and Partition Identities