Inclusion Statistics

TL;DR

This paper reviews the development of inclusion statistics, highlighting its differences from exclusion statistics, its duality relation, and its realization in the Calogero model, emphasizing its role in quantum many-body systems.

Contribution

It introduces inclusion statistics, explores its duality with exclusion statistics, and discusses its realization in the Calogero model, expanding the understanding of quantum statistical behaviors.

Findings

Inclusion statistics particles tend to form condensates more readily than bosons.

A duality transformation relates inclusion and exclusion statistics.

The Calogero model is extended to realize inclusion statistics.

Abstract

We present a historical review of anyon and exclusion statistics, introduced in the 1980s and 1990s respectively, and then turn to developments in the recently introduced inclusion statistics. In contrast to exclusion statistics, where particles tend to be more exclusive than usual fermions, inclusion statistics particles tend to be more gregarious than usual bosons and manifest an enhanced propensity to form condensates. Inclusion and exclusion statistics are related through a duality transformation, generalizing the well-known Bose-Fermi duality. We conclude with a review of the Calogero model realization of exclusion statistics and its extension to inclusion statistics.