Statistics of Q-Oscillators, Quons and Relation to Fractional Satistics

TL;DR

This paper explores the statistical properties of q-oscillators, quons, and anyons, deriving their distribution functions, equations of state, and analyzing phenomena like Bose-Einstein condensation within these deformed quantum systems.

Contribution

It provides explicit distribution functions, equations of state, and virial coefficient corrections for q-oscillators and related particles, linking fractional statistics to deformed quantum algebra.

Findings

Derived q-deformed distribution functions for bosonic and fermionic oscillators.

Established equations of state for q-gases in various dimensions.

Analyzed Bose-Einstein condensation in q-deformed gases.

Abstract

The statistics of $q$-oscillators, quons and to some extent, of anyons are studied and the basic differences among these objects are pointed out. In particular, the statistical distributions for different bosonic and fermionic $q$-oscillators are found for their corresponding Fock space representations in the case when the hamiltonian is identified with the number operator. In this case and for nonrelativistic particles, the single-particle temperature Green function is defined with $q$-deformed periodicity conditions. The equations of state for nonrelativistic and ultrarelativistic bosonic $q$-gases in an arbitrary space dimension are found near Bose statistics, as well as the one for an anyonic gas near Bose and Fermi statistics. The first corrections to the second virial coefficients are also evaluated. The phenomenon of Bose-Einstein condensation in the $q$-deformed gases is also discussed.