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

TL;DR

This paper proposes an ansatz for exclusion statistics parameters in fractional exclusion statistics systems and tests it across various models, finding it generally applicable with some exceptions, and explores their properties in quantum systems.

Contribution

Introduces a new ansatz for FES parameters and validates it across multiple physical models, enhancing understanding of exclusion statistics in complex systems.

Findings

FES parameters satisfy the ansatz in Fermi liquids and 1D quantum systems.

FES parameters in fractional quantum Hall systems are close to the ansatz but show exceptions.

General properties of FES parameters are confirmed in FQH liquids.

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. Then, to check the applicability of the ansatz, I calculate the FES parameters in three well-known models: in a Fermi liquid type of system, a one-dimensional quantum systems described in the thermodynamic Bethe ansatz and quasiparticle excitations in the fractional quantum Hall (FQH) systems. 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. With this ocasion I also show that the general properties of the FES parameters, deduced elsewhere (EPL 87, 60009, 2009), are satisfied also by the parameters of the FQH liquid.