Bose Einstein condensation in a gas of the Fibonacci oscillators

TL;DR

This paper explores a generalized boson gas with Fibonacci-based spectra, analyzing how two deformation parameters influence its thermodynamics and Bose-Einstein condensation, extending q-calculus to Fibonacci calculus.

Contribution

It introduces a two-parameter deformed boson model with Fibonacci spectrum and develops Fibonacci calculus to study its thermodynamics and condensation behavior.

Findings

Deformation parameters affect the thermodynamic properties.

Conditions for Bose-Einstein condensation are identified.

Classical boson results recovered at q1=q2=1.

Abstract

We consider a system of the two-parameter deformed boson oscillators whose spectrum is given by a generalized Fibonacci sequence. In order to obtain the role of the deformation parameters (q1,q2) on the thermostatistics of the system, we calculate several thermostatistical functions in the thermodynamical limit and investigate the low-temperature behavior of the system. In this framework, we show that the thermostatistics of the (q1,q2)-bosons can be studied by the formalism of Fibonacci calculus which generalizes the recently proposed formalism of q-calculus. We also discuss the conditions under which the Bose-Einstein condensation would occur in the present two-parameter generalized boson gas. However, the ordinary boson gas results can be obtained by applying the limit q1=q2=1.