arXiv:2303.09516

Quantum Brownian Motion in the Caldeira-Leggett Model with a Damped Environment

Lester Buxton, Marc-Thomas Russo, Jim Al-Khalili, Andrea Rocco

Published Mar 16, 2023• 0 citations

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.

DOI: 10.48550/arxiv.2303.09516

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