Bosonic and fermionic single-particle states in the Haldane approach to statistics for identical particles

TL;DR

This paper introduces two formulations of exclusion statistics using variable single-particle states, discusses their application to various models like FQHE quasiparticles and Calogero-Sutherland, and derives integral equations for particle distributions.

Contribution

It presents new formulations of exclusion statistics with variable single-particle states and extends the framework to generalized ideal gases with momentum-dependent interactions.

Findings

Formulations applicable to FQHE quasiparticles and anyons

Integral equations for momentum distribution derived

Single-family solutions sufficient for Calogero-Sutherland model

Abstract

We give two formulations of exclusion statistics (ES) using a variable number of bosonic or fermionic single-particle states which depend on the number of particles in the system. Associated bosonic and fermionic ES parameters are introduced and are discussed for FQHE quasiparticles, anyons in the lowest Landau level and for the Calogero-Sutherland model. In the latter case, only one family of solutions is emphasized to be sufficient to recover ES; appropriate families are specified for a number of formulations of the Calogero-Sutherland model. We extend the picture of variable number of single-particle states to generalized ideal gases with statistical interaction between particles of different momenta. Integral equations are derived which determine the momentum distribution for single-particle states and distribution of particles over the single-particle states in the thermal equilibrium.