Position-dependent mass in strong quantum gravitational background fields

TL;DR

This paper investigates how quantum gravitational effects influence the dynamics of a position-dependent mass particle in a noncommutative space, revealing energy level deformations and potential for low-energy gravity particle detection.

Contribution

It introduces a model of a particle with position-dependent mass in a noncommutative quantum gravity space and analyzes how quantum gravitational effects deform energy levels.

Findings

Quantum gravitational effects increase the PDM of the particle.

Energy levels experience deformations with increasing quantum gravitational effects.

Particles can transition between states with high probability densities at low energies.

Abstract

More recently, we have proposed a set of noncommutative space that describes the quantum gravity at the Planck scale [J. Phys. A: Math. Theor. 53, 115303 (2020)]. The interesting significant result we found is that, the generalized uncertainty principle induces a maximal measurable length of quantum gravity. This measurement revealed strong quantum gravitational effects at this scale and predicted a detection of gravity particles with low energies. In the present paper, to make evidence this prediction, we study in this space, the dynamics of a particle with position-dependent mass (PDM) trapped in an infinite square well. We show that, by increasing the quantum gravitational effect, the PDM of the particle increases and induces deformations of the quantum energy levels. These deformations are more pronounced as one increases the quantum levels allowing, the particle to jump from one state to another with low energies and with high probability densities.