Intermediate statistics as a consequence of deformed algebra

TL;DR

This paper introduces a deformed algebra framework that models intermediate quantum statistics, bridging Bose-Einstein and Fermi-Dirac distributions, and provides a new expression for occupation numbers.

Contribution

It develops a generalized algebra and permutation symmetry leading to intermediate statistics, with a novel continued fraction expression for occupation numbers.

Findings

Derived mean occupation number for intermediate statistics

Established connection between permutation symmetry and deformed algebra

Provided an infinite continued fraction representation for occupation numbers

Abstract

We present a formulation of the deformed oscillator algebra which leads to intermediate statistics as a continuous interpolation between the Bose-Einstein and Fermi-Dirac statistics. It is deduced that a generalized permutation or exchange symmetry leads to the introduction of the basic number and it is then established that this in turn leads to the deformed algebra of oscillators. We obtain the mean occupation number describing the particles obeying intermediate statistics which thus establishes the interpolating statistics and describe boson like and fermion like particles obeying intermediate statistics. We also obtain an expression for the mean occupation number in terms of an infinite continued fraction, thus clarifying successive approximations.