Quantum Langevin Equation of a spin in a magnetic field : an analysis

TL;DR

This paper derives a quantum Langevin equation for a spin in a magnetic field, analyzing its dynamics with different bath models, and predicts observable effects relevant for ultracold atom experiments.

Contribution

It introduces a quantum Langevin framework for spin dynamics in magnetic fields, extending analysis to non-Markovian baths, and connects theoretical predictions with experimental setups.

Findings

Spin auto-correlation functions show damped oscillations.

Damping rate and memory time influence spin randomization.

Results align with cold atom experimental observations.

Abstract

We derive a quantum Langevin equation for a quantum spin in the presence of a magnetic field and study its dynamics in the Markovian limit using the Ohmic bath model. We extend our analysis to the Drude bath with a finite memory. We study the time evolution of the expectation values of the magnetic moments. The spin auto-correlation functions exhibit a damped oscillatory behaviour with the randomization time being determined by the damping rate and also the memory time for the Drude bath model. We also analyse the spin response function of the system for the Ohmic bath model. Our results are consistent with findings in cold atom experiments. In addition we make predictions which can be tested in future ultra cold atom experiments.