Interacting particles system revisited in the framework of the q-deformed algebra

TL;DR

This paper explores how q-deformed algebra can model interactions in particle systems, showing that q-deformation effectively incorporates interaction effects through virial expansion and momentum transformations.

Contribution

It demonstrates that q-deformed algebra can represent interactions in particle systems, linking classical and quantum frameworks via virial expansion and momentum transformations.

Findings

q-deformed virial coefficients encode interaction effects

q-deformed momentum series expansion relates to interactions

q-deformed quantization emerges from classical interaction models

Abstract

We discuss the possibility of interpreting a q-deformed non-interacting system as incorporating the effects of interactions among its particles. This can be accomplished, for instance, in an ensemble of $q$-Bosons by means of the virial expansion of a real gas in powers of the deformed parameter. The lowest order virial coefficient reduces to the case of the standard, non-interacting Bose gas, while the higher order virial coefficients contain effects arising from the interaction. The same picture can be drawn in a quantum mechanical system where it is shown that the q-deformed momentum can be expanded in a series contains high-order powers of the standard quantum phase-space variables. Motivated by this result, we introduce, in the classical framework, a transformation relating the momentum of a free system with the momentum of an interacting system. It is shown that the canonical quantization applied to the interacting system imply a q-deformed quantization for the free system.