Comment on 'Semiclassical Klein-Kramers and Smoluchowski equations for the Brownian motion of a particle in an external potential'

TL;DR

This paper discusses the validity of a semiclassical Smoluchowski equation for Brownian motion, based on a quantum Smoluchowski equation, and introduces a quantum generalization of Einstein's law.

Contribution

It provides a critical analysis of the semiclassical Smoluchowski equation's validity and derives a quantum generalization of Einstein's law of Brownian motion.

Findings

Validity range of the semiclassical Smoluchowski equation is clarified

A quantum generalization of Einstein's law is proposed

The analysis is based on a previously derived quantum Smoluchowski equation

Abstract

The range of validity of the semiclassical Smoluchowski equation derived recently by Coffey et al is discussed. The analysis is based on the quantum Smoluchowski equation derived by the present author before. A quantum generalization of the Einstein law of Brownian motion is also obtained.