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Modern Physics Letters B

GENERALIZATION OF STATISTICS FOR SEVERAL SPECIES OF IDENTICAL PARTICLES

SERGEI B. ISAKOV

Published Feb 28, 1994• 79 citations
Publisher

Abstract

We present a framework for treating the statistical mechanics of systems including several species of particles with a statistical interaction between particles of different species. The statistical interaction is assumed to occur only between particles with the same momentum. Generalization of fractional statistics in one dimension to the case of several species of particles is discussed.

DOI
10.1142/s0217984994000327

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arXiv:0906.4836•Jun 26, 2009•4 citations
We present a framework for treating the statistical mechanics of systems including several species of particles with a statistical interaction between particles of different species. The statistical interaction is assumed to occur only between particles with the same momentum. Generalization of fractional statistics in one dimension to the case of several species of particles is discussed.
We examine a new fractional statistics for arbitrary dimensions, based on an extension of Pauli’s exclusion principle, to allow for finite multi-occupancies of a single quantum state. By explicitly constructing the many-body Hilbert space, we obtain a new algebra of operators and a new thermodynamics. The new statistics is different from fractional exclusion statistics. For a single species of particles it is equivalent to parafermi statistics; but their algebras are very different for the case of multiple species.
After a very brief introduction to the concept of fractional exclusion statistics (FES), introduced by Haldane in Phys. Rev. Lett. 67, 937 (1991), I shall present some recent results regarding the basic properties of this statistics. These properties have been overlooked for almost two decades and because of that, the application of FES to concrete physical systems was, to a certain degree, arbitrary. Essentially, the FES is a generalization of the Pauli Exclusion Principle which allows one to describe systems of interacting particles (bosons or fermions) as systems of ideal particles, but which obey a more peculiar type of statistics. In the second part of the paper I shall present some application of FES by analyzing concrete systems of interacting particles.