Quantum canonical ensemble: A projection operator approach

Wim Magnus, Lucien Lemmens and Fons Brosens

Physica A: Statistical Mechanics and its Applications, 2017, vol. 482, issue C, 1-13

Abstract: Knowing the exact number of particles N, and taking this knowledge into account, the quantum canonical ensemble imposes a constraint on the occupation number operators. The constraint particularly hampers the systematic calculation of the partition function and any relevant thermodynamic expectation value for arbitrary but fixed N. On the other hand, fixing only the average number of particles, one may remove the above constraint and simply factorize the traces in Fock space into traces over single-particle states. As is well known, that would be the strategy of the grand-canonical ensemble which, however, comes with an additional Lagrange multiplier to impose the average number of particles. The appearance of this multiplier can be avoided by invoking a projection operator that enables a constraint-free computation of the partition function and its derived quantities in the canonical ensemble, at the price of an angular or contour integration.

Keywords: Quantum statistics; Canonical ensemble; Fermions; Bosons (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:482:y:2017:i:c:p:1-13

DOI: 10.1016/j.physa.2017.04.069

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