$1+1$-dimensional Dirac oscillator with deformed algebra with minimal uncertainty in position and maximal in momentum

TL;DR

This paper studies a 1+1-dimensional Dirac oscillator with deformed algebra incorporating minimal position uncertainty and maximal momentum, revealing a finite energy spectrum and deriving thermodynamic properties.

Contribution

It introduces a novel analysis of the Dirac oscillator under deformed algebra with minimal and maximal uncertainties, identifying two spectral branches and their thermodynamic implications.

Findings

Two spectral branches identified, one matching standard spectrum as deformation vanishes.

Maximal momentum imposes an upper energy bound, resulting in a finite spectrum.

Thermodynamic functions derived numerically from the partition function.

Abstract

$1+1$-dimensional Dirac oscillator with minimal uncertainty in position and maximal in momentum is investigated. To obtain energy spectrum SUSY QM technique is applied. It is shown that the Dirac oscillator has two branches of spectrum, the first one gives the standard spectrum of the Dirac oscillator when the parameter of deformation goes to zero and the second branch does not have nondeformed limit. Maximal momentum brings an upper bound for the energy and it gives rise to the conclusion that the energy spectrum contains a finite number of eigenvalues. We also calculate partition function for the spectrum of the first type. The partition function allows us to derive thermodynamic functions of the oscillator which are obtained numerically.