Quantum Smoluchowski equation: Escape from a metastable state
Dhruba Banerjee, Bidhan Chandra Bag, Suman Kumar Banik, Deb Shankar, Ray
TL;DR
This paper derives a quantum Smoluchowski equation to describe quantum Brownian motion in high friction regimes, providing a unified approach to calculate escape rates and tunneling at any temperature without using path integrals.
Contribution
It introduces a new quantum Smoluchowski equation based on canonical quantization, independent of path integral methods, for analyzing barrier crossing and tunneling.
Findings
Derived a quantum Smoluchowski equation for large friction
Unified treatment of thermal activation and tunneling processes
Applicable at arbitrary temperatures
Abstract
We develop a quantum Smoluchowski equation in terms of a true probability distribution function to describe quantum Brownian motion in configuration space in large friction limit at arbitrary temperature and derive the rate of barrier crossing and tunneling within an unified scheme. The present treatment is independent of path integral formalism and is based on canonical quantization procedure.
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