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

Lester BuxtonMarc-Thomas RussoJim Al-KhaliliAndrea Rocco
Mar 2023
摘要
We model a quantum system coupled to an environment of damped harmonicoscillators by following the approach of Caldeira-Leggett and adopting theCaldirola-Kanai Lagrangian for the bath oscillators. In deriving the masterequation 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 harmonicoscillator term, induced by the damping of the bath oscillators. We analyzenumerically the case of a particle in a double-well potential, and find thatthis modification changes both the rate of decoherence at short times and thewell-transfer probability at longer times. We also identify a simple rescalingcondition that keeps the potential fixed despite changes in the environmentaldamping. Here, the increase of environmental damping leads to a slowing ofdecoherence.
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