A Generalization of Quantum Statistics

TL;DR

This paper introduces a novel fractional quantum statistics extending Pauli's exclusion principle to arbitrary dimensions, allowing finite multi-occupancies, with new algebraic structures and thermodynamics, differing from existing fractional exclusion statistics.

Contribution

It presents a new fractional quantum statistics framework based on an extended exclusion principle, with explicit Hilbert space construction and thermodynamic formulation.

Findings

Defines a new algebra of operators for the statistics

Constructs the many-body Hilbert space explicitly

Shows reduction to parafermi statistics in a certain limit

Abstract

We propose a new fractional statistics for arbitrary dimensions, based on an extension of Pauli's exclusion principle, to allow for finite multi-occupancies of a single quantum state. By explicitly constructing the many-body Hilbert space, we obtain a new algebra of operators and a new thermodynamics. The new statistics is different from fractional exclusion statistics; and in a certain limit, it reduces to the case of parafermi statistics.