One-Dimensional Statistical Mechanics for Identical Particles : The Calogero and Anyon Cases

TL;DR

This paper explores the thermodynamics of one-dimensional particles with intermediate statistics, including anyons and Calogero models, providing a unified computational approach and linking to Haldane's generalized Pauli principle.

Contribution

It introduces a unified algorithm for the statistical mechanics of one-dimensional particles with intermediate statistics, encompassing anyon and Calogero models, and relates these to Haldane's Pauli principle.

Findings

Unified algorithm for statistical mechanics of these systems

Connection between anyon models and Haldane's Pauli principle

Analysis of thermodynamics in low-dimensional quantum systems

Abstract

The thermodynamic of particles with intermediate statistics interpolating between Bose and Fermi statistics is adressed in the simple case where there is one quantum number per particle. Such systems are essentially one-dimensional. As an illustration, one considers the anyon model restricted to the lowest Landau level of a strong magnetic field at low temperature, the generalization of this model to several particles species, and the one dimensional Calogero model. One reviews a unified algorithm to compute the statistical mechanics of these systems. It is pointed out that Haldane's generalization of the Pauli principle can be deduced from the anyon model in a strong magnetic field at low temperature.