Thermostatistics of bosonic and fermionic Fibonacci oscillators

Abstract

In this work, we first introduce some new properties concerning the Fibonacci calculus. We then discuss the thermostatistics of gas models of two-parameter deformed oscillators, called bosonic and fermionic Fibonacci oscillators, in the thermodynamical limit. In this framework, we analyze the behavior of two-parameter deformed mean occupation numbers describing the Fibonacci-type bosonic and fermionic intermediate-statistics particles. A virial expansion of the equation of state for the bosonic Fibonacci oscillators’ gas model is obtained in both two and three dimensions, and the first five virial coefficients are derived in terms of the real independent deformation parameters [Formula: see text] and [Formula: see text]. The effect of bosonic and fermionic [Formula: see text], [Formula: see text]-deformation on the thermostatistical properties of Fibonacci-type [Formula: see text], [Formula: see text]-boson and [Formula: see text], [Formula: see text]-fermion gas models are also discussed. The results obtained in this work can be useful for investigating some exotic quasiparticle states encountered in condensed matter systems.