Long Time Tails in Quantum Brownian Motion of a charged particle in a magnetic field

TL;DR

This paper investigates the long-time decay behaviors of a charged quantum Brownian particle in a magnetic field, revealing a temperature-dependent crossover from power-law to exponential decay influenced by cyclotron frequency.

Contribution

It provides a detailed analysis of long time tails in quantum Brownian motion with magnetic fields, highlighting the effects of cyclotron frequency and bath coupling types.

Findings

Crossover from power-law to exponential decay at thermal time scale

Cyclotron frequency significantly affects long-time tail behavior

Differences observed between charged and neutral quantum Brownian particles

Abstract

We analyse the long time tails of a charged quantum Brownian particle in a harmonic potential in the presence of a magnetic field using the Quantum Langevin Equation as a starting point. We analyse the long time tails in the position autocorrelation function, position-velocity correlation function and velocity autocorrelation function. We study these correlations for a Brownian particle coupled to the Ohmic and Drude baths, via position coordinate coupling. At finite temperatures we notice a crossover from a power-law to an exponentially decaying behaviour around the thermal time scale \frac{\hbar}{K_B T} . We analyse how the appearance of the cyclotron frequency in our study of a charged quantum Brownian particle affects the behaviour of the long time tails and contrast it with the case of a neutral quantum Brownian particle.