paper

Universal behaviour of ideal and interacting quantum gases in two dimensions

arXiv:cond-mat/0105089 · doi:10.1088/0305-4470/35/34/302

Abstract

I discuss ideal and interacting quantum gases obeying general fractional exclusion statistics. For systems with constant density of single-particle states, described in the mean field approximation, the entropy depends neither on the microscopic exclusion statistics, nor on the interaction. Such systems are called {\em thermodynamically equivalent} and I show that the microscopic reason for this equivalence is a one-to-one correspondence between the excited states of these systems. This provides a method, different from the bosonisation technique, to transform between systems of different exclusion statistics. In the last section the macroscopic aspects of this method are discussed. In Appendix A I calculate the fluctuation of the ground state population of a condensed Bose gas in grandcanonical ensemble and mean field approximation, while in Appendix B I show a situation where although the system exhibits fractional exclusion properties on microscopic energy intervals, a rigorous calculation of the population of single particle states reveals a condensation phenomenon. This also implies a malfunction of the usual and simplified calculation technique of the most probable statistical distributions.

About 14 journal pages, with 1 figure. Changes: Body of paper: same content, with slight rephrasing. Apendices are new. In the original submission I just mentioned the condensation, which is now detailed in Appendix B. They were intended for a separate paper. Reason for changes: rejection from Phys. Rev. Lett., resubmission to J. Phys. A: Math. Gen

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