An ansatz for the exclusion statistics parameters in macroscopic physical systems described by fractional exclusion statistics

Department of Theoretical Physics, National Institute for Physics and Nuclear Engineering “Horia Hulubei” Str. Atomistilor no. 407, P.O.BOX MG-6, Bucharest - Magurele, Romania, EU

Corresponding author: dragos@theory.nipne.ro

Received: 19 November 2009
Accepted: 21 March 2010

Abstract

I introduce an ansatz for the exclusion statistics parameters of fractional-exclusion-statistics (FES) systems and I apply it to calculate the statistical distribution of particles from both, bosonic and fermionic perspectives. To check the applicability of the ansatz, I calculate the FES parameters in three well-known models: a Fermi-liquid–type system, a one-dimensional quantum system described in the thermodynamic Bethe ansatz and quasi-particle excitations in a fractional quantum Hall (FQH) system. The FES parameters of the first two models satisfy the ansatz, whereas those of the third model, although close to the form given by the ansatz, represent an exception. In this case I also show that the general properties of the FES parameters, deduced elsewhere (EPL, 87 (2009) 60009), are satisfied also by the parameters of the FQH liquid.