Quantum Langevin equation of a charged oscillator in a magnetic field and coupled to a heat bath through momentum variables

TL;DR

This paper derives a quantum Langevin equation for a charged particle in a magnetic field coupled to a heat bath via momentum variables, revealing magnetic field-dependent memory effects and modified noise correlations.

Contribution

It presents a novel derivation of the quantum Langevin equation with momentum coupling, highlighting the influence of magnetic fields on the system's memory and noise characteristics.

Findings

Memory function depends explicitly on magnetic field

Random force correlation differs from coordinate coupling case

Coupling constants renormalize inertial and potential terms

Abstract

We obtain the quantum Langevin equation (QLE) of a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a quantum heat bath through momentum variables. The bath is modeled as a collection of independent quantum harmonic oscillators. The QLE involves a random force which does not depend on the magnetic field, and a quantum-generalized classical Lorentz force. These features are also present in the QLE for the case of particle-bath coupling through coordinate variables. However, significant differences are also observed. For example, the mean force in the QLE is characterized by a memory function that depends explicitly on the magnetic field. The random force has a modified form with correlation and commutator different from those in the case of coordinate-coordinate coupling. Moreover, the coupling constants, in addition to appearing in the random force and in the mean force, also renormalize the inertial term and the harmonic potential term in the QLE.