Fractional exclusion statistics in general systems with interaction

TL;DR

This paper demonstrates that fractional exclusion statistics (FES) naturally arises in general interacting systems and shows that mutual exclusion parameters are proportional to the Hilbert space dimension, ensuring consistency in the thermodynamic limit.

Contribution

The paper establishes a general connection between FES and interacting systems and derives a proportionality relation for mutual exclusion parameters, resolving previous inconsistencies.

Findings

Mutual exclusion parameters are proportional to Hilbert space dimension.

FES is manifested in general interacting systems.

Results are consistent with the thermodynamic limit and prior conjectures.

Abstract

I show that fractional exclusion statistics (FES) is manifested in general interacting systems and I calculate the exclusion statistics parameters. Most importantly, I show that the mutual exclusion statistics parameters--when the presence of particles in one Hilbert space influences the dimension of another Hilbert space--are proportional to the dimension of the Hilbert space on which they act. This result, although surprising and different from the usual way of understanding the FES, renders this statistics consistent and valid in the thermodynamic limit, in accordance with the conjucture introduced in J. Phys. A: Math. Theor. 40, F1013 (2007).