A simple semiclassical approach to Kramers' problem
Jyotipratim Ray Chaudhuri, Bidhan Chandra Bag, Deb Shankar Ray
TL;DR
This paper presents a semiclassical method based on the Wigner-Leggett-Caldeira equation to compute quantum corrections to Kramers' escape rate in high-temperature, Ohmic environments.
Contribution
It introduces a semiclassical approach by expanding in powers of to solve the Wigner-Leggett-Caldeira equation, linking quantum Brownian motion to Kramers' problem.
Findings
Derived semiclassical correction to Kramers' rate.
Established the Wigner-Leggett-Caldeira equation as a semiclassical Kramers' equation.
Provided a method to compute quantum effects in classical escape problems.
Abstract
We show that Wigner-Leggett-Caldeira equation for Wigner phase space distribution function which describes the quantum Brownian motion of a particle in a force field in a high temerature, Ohmic environment can be identified as a semiclassical version of Kramers' equation. Based on an expansion in powers of we solve this equation to calculate the semiclassical correction to Kramers' rate.
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