Application of Fibonacci oscillators in the Debye model

TL;DR

This paper explores how Fibonacci oscillators, deformed by two parameters, can model the thermodynamics of crystals and their impurity-induced changes in thermal conductivity.

Contribution

It introduces a (q1, q2)-deformed Hamiltonian using Fibonacci oscillators to describe crystal thermodynamics and impurity effects.

Findings

Deformation parameters modify crystal characteristics.

Fibonacci oscillators can model impurity effects.

Adjustable parameters describe thermal conductivity changes.

Abstract

In this paper we study the thermodynamics of a crystalline solid by applying q-deformed algebra of Fibonacci oscillators through the generalized Fibonacci sequence of two real and independent deformation parameters q1 and q2. We find a (q1, q2)-deformed Hamiltonian and consequently the q-deformed thermodynamic quantities. The results led us to interpret the deformation parameters acting as disturbance or impurities factors modifying the characteristics of a crystal structure. More specifically, we found the possibility of adjusting the Fibonacci oscillators to describe the change of thermal conductivity of a given element as one inserts impurities.