Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-05-04
J. Phys. A: Math. Gen. 35, 7255 (2002)
Physics
Condensed Matter
Statistical Mechanics
About 14 journal pages, with 1 figure. Changes: Body of paper: same content, with slight rephrasing. Apendices are new. In the
Scientific paper
10.1088/0305-4470/35/34/302
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.
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