An interacting ensemble of particles in the context of quantum algebra

Abstract

In the framework of the q-deformed oscillator algebra we investigate the nature of the interaction among the particles of a freeq-boson gas with a view to interpreting the interaction in terms of the general properties of theq-deformation. It is shown that many thermodynamic quantities characterizing theq-boson system can be expressed as power series in the number of particles operator or as a series in the deformation parameterq, implyingthat the q-deformation can originate from the interaction among the particles ofthe ensemble. As an example, we derive the virial expansion of theq-boson gas, showing that the lowest order coefficient reduces to the standard virialcoefficient of an undeformed boson gas, while the higher order coefficients contain effectsarising from interaction.