A (p,q)-deformed Landau problem in a spherical harmonic well: spectrum and noncommuting coordinates

TL;DR

This paper explores a (p,q)-deformation of the Landau problem within a spherical harmonic well, revealing new noncommutative geometries and spectra that extend traditional quantum Hall models.

Contribution

It introduces a novel (p,q)-deformed algebra for space coordinates in the Landau problem, generalizing known noncommutative geometries and potentially impacting condensed matter physics.

Findings

Quantum spectrum derived for the (p,q)-deformed Landau problem

Recovery of standard noncommutative geometry at p,q=1

Discovery of a new noncommutative algebra for space coordinates

Abstract

A (p,q)-deformation of the Landau problem in a spherically symmetric harmonic potential is considered. The quantum spectrum as well as space noncommutativity are established, whether for the full Landau problem or its quantum Hall projections. The well known noncommutative geometry in each Landau level is recovered in the appropriate limit p,q=1. However, a novel noncommutative algebra for space coordinates is obtained in the (p,q)-deformed case, which could also be of interest to collective phenomena in condensed matter systems.