Properties of Fractional Exclusion Statistics in Interacting Particle Systems

TL;DR

This paper demonstrates that fractional exclusion statistics naturally arises in interacting particle systems, linking it to the change from free-particle to quasi-particle descriptions and confirming a recent conjecture about mutual exclusion parameters.

Contribution

It provides concrete calculations and intuitive arguments showing the natural emergence of fractional exclusion statistics in interacting systems, confirming a specific conjecture about mutual exclusion parameters.

Findings

Fractional exclusion statistics is manifested in interacting systems.

Mutual exclusion parameters are proportional to the Hilbert space dimension.

Thermodynamic equivalence holds for systems with the same density of states.

Abstract

We show that fractional exclusion statistics is manifested in general in interacting systems and we discuss the conjecture recently introduced (J. Phys. A: Math. Theor. 40, F1013, 2007), according to which if in a thermodynamic system the mutual exclusion statistics parameters are not zero, then they have to be proportional to the dimension of the Hilbert space on which they act. By using simple, intuitive arguments, but also concrete calculations in interacting systems models, we show that this conjecture is not some abstract consequence of unphysical modeling, but is a natural--and for a long time overlooked--property of fractional exclusion statistics. We show also that the fractional exclusion statistics is the consequence of interaction between the particles of the system and it is due to the change from the description of the system in terms of free-particle energies, to the description in terms of the quasi-particle energies. From this result, the thermodynamic equivalence of systems of the same, constant density of states, but any exclusion statistics follows immediately.