Effective approach for taking into account interactions of quasiparticles from the low-temperature behavior of a deformed fermion-gas model

TL;DR

This paper introduces a deformed fermion gas model using Fibonacci oscillators to better understand quasiparticle interactions at low temperatures, with implications for nanomaterials and material properties.

Contribution

It presents a novel fermion gas model based on Fibonacci calculus that incorporates quasiparticle interactions and deformations, extending traditional Fermi theory.

Findings

The model accurately describes low-temperature thermodynamic properties.

The p,q-deformed Sommerfeld parameter aligns with experimental data.

The approach offers insights into quasiparticle interactions and material behavior.

Abstract

A deformed fermion gas model aimed at taking into account thermal and electronic properties of quasiparticle systems is devised. The model is constructed by the fermionic Fibonacci oscillators whose spectrum is given by a generalized Fibonacci sequence. We first introduce some new properties concerning the Fibonacci calculus. We then investigate the low-temperature thermostatistical properties of the model, and derive many of the deformed thermostatistical functions such as the chemical potential and the entropy in terms of the model deformation parameters p and q. We specifically focus on the p,q-deformed Sommerfeld parameter for the heat capacity of the model, and its behavior is compared with those of both the free-electron Fermi theory and the experimental data for some materials. The results obtained in this study reveal that the present deformed fermion model leads to an effective approach accounting for interaction and compositeness of quasiparticles, which have remarkable implications in many technological applications such as in nanomaterials.