Equation of State for Exclusion Statistics in a Harmonic Well

TL;DR

This paper derives equations of state for particles obeying exclusion statistics in harmonic potentials, linking them to models like Calogero particles and anyons in magnetic fields, enhancing understanding of fractional exclusion statistics.

Contribution

It establishes a connection between exclusion statistics in harmonic wells and well-known models like Calogero and anyons, providing new insights into their thermodynamic behavior.

Findings

Equations of state for exclusion statistics in harmonic wells derived.

Identifies equivalence with Calogero model and anyons in magnetic fields.

Provides a unified framework for fractional exclusion statistics in harmonic traps.

Abstract

We consider the equations of state for systems of particles with exclusion statistics in a harmonic well. Paradygmatic examples are noninteracting particles obeying ideal fractional exclusion statistics placed in (i) a harmonic well on a line, and (ii) a harmonic well in the Lowest Landau Level (LLL) of an exterior magnetic field. We show their identity with (i) the Calogero model and (ii) anyons in the LLL of an exterior magnetic field and in a harmonic well.