Thermal properties of a two-dimensional Duffin-Kemmer-Petiau oscillator under an external magnetic field in the presence of a minimal length

TL;DR

This paper explores the effects of a minimal length scale on the two-dimensional DKP oscillator under a magnetic field, deriving energy spectra and thermodynamic properties within a generalized uncertainty principle framework.

Contribution

It provides the first analysis of the DKP oscillator incorporating a minimal length, extending quantum mechanics to include quantum gravity effects.

Findings

Energy eigenvalues are modified by the minimal length correction.

Eigenfunctions reduce to standard quantum solutions when minimal length effects vanish.

Thermodynamic functions are derived at high temperatures considering minimal length effects.

Abstract

Generalized uncertainty principle puts forward the existence of the shortest distances and/or maximum momentum at the Planck scale for consideration. In this article, we investigate the solutions of a two-dimensional Duffin-Kemmer-Petiau (DKP) oscillator within an external magnetic field in a minimal length (ML) scale. First, we obtain the eigensolutions in ordinary quantum mechanics. Then, we examine the DKP oscillator in the presence of an ML for the spin-zero and spin-one sectors. We determine an energy eigenvalue equation in both cases with the corresponding eigenfunctions in the non-relativistic limit. We show that in the ordinary quantum mechanic limit, where the ML correction vanishes, the energy eigenvalue equations become identical with the habitual quantum mechanical ones. Finally, we employ the Euler-Mclaurin summation formula and obtain the thermodynamic functions of the DKP oscillator in the high-temperature scale.