Magnetic-Dipole Spin Effects in Noncommutative Quantum Mechanics

TL;DR

This paper introduces a 3D noncommutative quantum model with spin, revealing a degenerate ground state and spontaneous symmetry breaking, with potential applications to dipolar Bose-Einstein condensates.

Contribution

It presents a novel noncommutative quantum framework incorporating spin and magnetic dipole effects, extending to many-particle systems.

Findings

Ground state is infinitely degenerate

Spontaneous symmetry breaking occurs

Model applicable to dipolar Bose-Einstein condensates

Abstract

A general three-dimensional noncommutative quantum mechanical system mixing spatial and spin degrees of freedom is proposed. The analogous of the harmonic oscillator in this description contains a magnetic dipole interaction and the ground state is explicitly computed and we show that it is infinitely degenerated and implying a spontaneous symmetry breaking. The model can be straightforwardly extended to many particles and the main above properties are retained. Possible applications to the Bose-Einstein condensation with dipole-dipole interactions are briefly discussed.