Kinetic model for q-deformed bosons and fermions

TL;DR

This paper develops a semiclassical kinetic model for $q$-deformed bosons and fermions, deriving a non-linear Fokker-Planck equation that captures their non-equilibrium dynamics and reproduces their equilibrium statistics.

Contribution

It introduces a novel kinetic framework linking $q$-deformed quantum statistics with a generalized exclusion-inclusion principle and derives a corresponding non-linear Fokker-Planck equation.

Findings

Derived a non-linear Fokker-Planck equation for $q$-deformed particles

Reproduces $q$-oscillator equilibrium statistics in steady state

Provides a tool for studying non-equilibrium behavior of $q$-deformed systems

Abstract

We have studied the kinetics of $q$-deformed bosons and fermions, within a semiclassical approach. This investigation is realized by introducing a generalized exclusion-inclusion principle, intrinsically connected with the quantum $q$-algebra by means of the creation and annihilation operators matrix elements. In this framework, we have derived a non-linear Fokker-Planck equation for $q$-deformed bosons and fermions which can be seen as a time evolution equation, appropriate to consider non-equilibrium or near-equilibrium systems in a semiclassical approximation. The steady state of this equation reproduces in a simple mode the $q$-oscillators equilibrium statistics.