eFTC-140801

Statistical Distributions and Particle-Hole Canonical Transformations in Small (Finite) Systems
3 August 2014
(Updated september 14, 2014)

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Abstract

In a previous paper we successfully identified the fermionic tilde degrees of freedom in Thermo Field Dynamics (TFD) as ordinary many-body physical fermion holes. In this paper we analyze the more general problem of statistical distributions and particle-hole canonical transformations in small (finite) systems, both for bosons and fermions. Unlike the fermion distribution case which is well-behaved, singularities and lack of single-valuedness plague the traditional Bose-Einstein distribution. Such a distribution cannot describe the Bose-Einstein condensed state. A microcanonical approach on the other hand reveals a well-behaved distribution over the entire energy spectrum (positive and negative) and so allows for the existence of physical bosonic holes which are necessary in TFD. The traditional Bose-Einstein distribution is recovered in the thermodynamic limit for positive energies. Bosonic holes are found in many physical problems of condensed matter as well as nuclear physics.

Copyright © 2014 Yvan Leblanc. All rights reserved

PACS: 05.30.Ch, 03.70.+k, 11.10.Gh

Cite as: Leblanc, Y., "Statistical Distributions and Particle-Hole Canonical Transformations in Small (Finite) Systems", manuscript no. eFTC-140801 (2014). http://www.efieldtheory.com/abs/?eFTC-140801; doi:10.13140/RG.2.1.1261.2960.