Many-Anyons Wavefunction, State Capacity and Gentile Statistics

TL;DR

This paper introduces a new wavefunction for many-anyons, revealing a finite state capacity that interpolates between fermions and bosons, and distinguishes Gentile statistics from fractional exclusion statistics.

Contribution

It constructs a many-anyons wavefunction based on permutation superpositions and explores its unique interchange properties, defining a finite state capacity linked to Gentile statistics.

Findings

Interchange phase yields finite state capacity between fermions and bosons

Mutual exchange phase does not affect statistics

Finite capacity is characterized by Gentile statistics, distinct from fractional exclusion statistics

Abstract

The many-anyons wavefunction is constructed via the superposition of all the permutations on the direct product of single anyon states and its interchange properties are examined. The phase of permutation is not a representation but the word metric of the permutation group . Amazingly the interchange phase yields a finite capacity of one quantum state interpolating between Fermion and Boson and the mutual exchange phase has no explicit effect on statistics. Finite capacity of quantum state is defined as Gentile statistics and it is different from the fractional exclusion statistics. Some discussion on the general model is also given.