Quantum Dynamics of a Dissipative and Confined Cyclotron Motion

TL;DR

This paper investigates the quantum dissipative dynamics of a charged particle in a magnetic field, deriving autocorrelation functions and analyzing equilibrium dispersions across various conditions, revealing classical and quantum behaviors.

Contribution

It provides a comprehensive derivation of autocorrelation functions and equilibrium dispersions for a dissipative charged oscillator in a magnetic field, including low and high temperature regimes.

Findings

Derived autocorrelation functions for position and momentum.

Analyzed equilibrium dispersions at different temperatures and magnetic fields.

Connected reduced partition function with equilibrium dispersions.

Abstract

We study the dissipative dynamics of a charged oscillator in a magnetic field by coupling (a la Caldeira and Leggett) it to a heat bath consisting of non-interacting harmonic oscillators. We derive here the auto-correlation functions of the position and momentum and study its behavior at various limiting situations. The equilibrium (steady state) dispersions of position and momentum are obtained from their respective autocorrelation functions. We analyse the equilibrium position and momentum dispersions at low and high temperatures for both low and high magnetic field strengths. We obtain the classical diffusive behavior (at long times) as well as the equilibrium momentum dispersion of the free quantum charged particle in a magnetic field, in the limit of vanishing oscillator potential {\omega}_0 . We establish the relations between the reduced partition function and the equilibrium dispersions of the dissipative and confined cyclotron problem.