Fractional exclusion statistics in disordered interacting particle systems

TL;DR

This paper introduces a fractional exclusion statistics model for disordered, interacting particle systems, demonstrating its effectiveness through thermodynamic analysis and revealing effects like quasiparticle segregation and heat capacity variations.

Contribution

The paper develops a novel FES-based model for non-homogeneous systems with disorder and interactions, extending the applicability of FES to complex, localized states.

Findings

Quasiparticle population inversion observed in simple systems.

Maxima in heat capacity linked to FES parameters.

Disorder causes spatial segregation of quasiparticles.

Abstract

We develop a model based on the fractional exclusion statistics (FES) applicable to non-homogeneous interacting particle systems. Here the species represent elementary volumes in an (s+1)-dimensional space, formed by the direct product between the s-dimensional space of positions and the quasiparticle energy axis. The model is particularly suitable for systems with localized states. We prove the feasibility of our method by applying it to systems of different degrees of complexities. We first apply the formalism on simpler systems, formed of two sub-systems, and present numerical and analytical thermodynamic calculations, pointing out the quasiparticle population inversion and maxima in the heat capacity, in contrast to systems with only diagonal (direct) FES parameters. Further we investigate larger, non-homogeneous systems with repulsive screened Coulomb interactions, indicating accumulation and depletion effects at the interfaces. Finally, we consider systems with several degrees of disorder, which are prototypical for models with glassy behavior. We find that the disorder produces a spatial segregation of quasiparticles at low energies which significantly affects the heat capacity and the entropy of the system.