Generalized statistics in one dimension

TL;DR

This paper reviews various quantum statistical approaches in one-dimensional systems, analyzing permutation, scattering, and exclusion statistics through models like Calogero, matrix, and spin chains.

Contribution

It provides a comprehensive exposition of different quantum statistics definitions and their realizations in one-dimensional models, highlighting their interrelations.

Findings

Permutation, scattering, and exclusion statistics are systematically analyzed.

Specific models like Calogero, matrix, and spin chains are used to realize these statistics.

The paper clarifies the connections between different statistical approaches in 1D quantum systems.

Abstract

An exposition of the different definitions and approaches to quantum statistics is given, with emphasis in one-dimensional situations. Permutation statistics, scattering statistics and exclusion statistics are analyzed. The Calogero model, matrix model and spin chain models constitute specific realizations.