Fermion–boson transmutation and comparison of statistical ensembles in one dimension

1996/06/05 by K. Schoenhammer, K. Schönhammer, V. Meden · 6 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cold Atom Physics and Bose-Einstein Condensates #Theoretical and Computational Physics #cond-mat

paper · pdf · doi:10.1119/1.18339

10 pages, latex, 8 eps-figures, Am. J. Phys. in press. This is a pedagogical introduction to bosonization with a useful application for a Statistical Mechanics course

arxiv created 1996/06/05 · openalex publication_date 1996/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The theoretical description of interacting fermions in one spatial dimension is simplified by the fact that the low-energy excitations can be described in terms of bosonic degrees of freedom. This fermion–boson transmutation (FBT) which lies at the heart of the Luttinger liquid concept is presented in a way which does not require a knowledge of quantum field theoretical methods. As the basic facts can already be introduced for noninteracting fermions they are mainly discussed. As an application we use the FBT to present exact results for the low-temperature thermodynamics and the occupation numbers in the microcanonical and the canonical ensemble. They are compared with the standard grand canonical results.

Citations

• An Exactly Soluble Model of a Many-Fermion System

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