Constant magnetic field and 2d non-commutative inverted oscillator

TL;DR

This paper investigates a two-dimensional non-commutative inverted oscillator under a constant magnetic field, revealing conditions under which it exhibits a discrete energy spectrum, with implications for quantum systems in non-commutative geometry.

Contribution

It introduces a novel analysis of a non-commutative inverted oscillator coupled with a magnetic field, showing the emergence of discrete spectra under specific conditions.

Findings

Discrete energy spectrum exists at certain magnetic field values

Coupling methods influence spectral properties

Non-commutative geometry affects oscillator behavior

Abstract

We consider a two-dimensional non-commutative inverted oscillator in the presence of a constant magnetic field, coupled to the system in a ``symplectic'' and ``Poisson'' way. We show that it has a discrete energy spectrum for some value of the magnetic field.