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

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.

13 pages, no figures, accepted on JPA

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• Correlation function intercepts for $\tilde{\mu },q$-deformed Bose gas model implying effective accounting for interaction and compositeness of particles
• Condensation of an ideal gas with intermediate statistics on the horizon
• Intercepts of the momentum correlation functions in μ-Bose gas model and their asymptotics
• A q-deformed logistic map and its implications
• Effective approach for taking into account interactions of quasiparticles from the low-temperature behavior of a deformed fermion-gas model
• Nonclassical properties of a particle in a finite range trap: the f-deformed quantum oscillator approach
• Exact expressions for the intercepts of r-particle momentum correlation functions in μ-Bose gas model
• Symmetric Tamm-Dancoff q-oscillator: representation, quasi-Fibonacci nature, accidental degeneracy and coherent states