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29 March 2024
 
  » arxiv » cond-mat/0105089

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Universal behaviour of ideal and interacting quantum gases in two dimensions
Dragos-Victor Anghel ;
Date 4 May 2001
Journal J. Phys. A: Math. Gen. 35, 7255 (2002)
Subject Statistical Mechanics | cond-mat.stat-mech
AbstractI 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.
Source arXiv, cond-mat/0105089
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