Quantum Brownian Motion in the Caldeira-Leggett Model with a Damped Environment
Abstract
We model a quantum system coupled to an environment of damped harmonic oscillators by following the approach of Caldeira-Leggett and adopting the Caldirola-Kanai Lagrangian for the bath oscillators. In deriving the master equation of the quantum system of interest (a particle in a general potential), we show that the potential is modified non-trivially by a new inverted harmonic oscillator term, induced by the damping of the bath oscillators. We analyze numerically the case of a particle in a double-well potential, and find that this modification changes both the rate of decoherence at short times and the well-transfer probability at longer times. We also identify a simple rescaling condition that keeps the potential fixed despite changes in the environmental damping. Here, the increase of environmental damping leads to a slowing of decoherence.
Keywords
Cite
@article{arxiv.2303.09516,
title = {Quantum Brownian Motion in the Caldeira-Leggett Model with a Damped Environment},
author = {Lester Buxton and Marc-Thomas Russo and Jim Al-Khalili and Andrea Rocco},
journal= {arXiv preprint arXiv:2303.09516},
year = {2023}
}