Non-equilibrium Quantum Langevin dynamics of orbital diamagnetic moment

TL;DR

This paper models the time evolution of the orbital diamagnetic moment of a charged particle in a magnetic field within a viscous medium using Quantum Langevin dynamics, highlighting temperature-dependent quantum and classical behaviors.

Contribution

It introduces a detailed quantum Langevin framework to analyze orbital magnetic moments, including effects of confinement and bath interactions, applicable to cold atom experiments.

Findings

High temperature limit reproduces Bohr Van Leeuwen theorem.

Dynamics governed by interplay of cyclotron frequency and damping rate.

Predictions applicable to cold atom experimental setups.

Abstract

We investigate the time dependent orbital diamagnetic moment of a charged particle in a magnetic field in a viscous medium via the Quantum Langevin Equation. We study how the interplay between the cyclotron frequency and the viscous damping rate governs the dynamics of the orbital magnetic moment in the high temperature classical domain and the low temperature quantum domain for an Ohmic bath. These predictions can be tested via state of the art cold atom experiments with hybrid traps for ions and neutral atoms. We also study the effect of a confining potential on the dynamics of the magnetic moment. We obtain the expected Bohr Van Leeuwen limit in the high temperature, asymptotic time ($ \gamma t\longrightarrow \infty$, where $ \gamma $ is the viscous damping coefficient) limit.