Collisional Quantum Brownian Motion

TL;DR

This paper derives a first-principles quantum master equation for collisional Brownian motion, clarifying the physical nature of position diffusion and avoiding mathematical inconsistencies present in previous models.

Contribution

It introduces a novel derivation method using localized wave packets, eliminating the ill-defined square of the Dirac delta and clarifying the physical interpretation of position diffusion.

Findings

Position diffusion is an artifact, not a physical process.

The derivation avoids mathematical inconsistencies of previous models.

Provides a more accurate quantum description of collisional Brownian motion.

Abstract

We derive a quantum master equation from first principles to describe friction in one dimensional, collisional Brownian motion. We are the first to avoid an ill-defined square of the Dirac delta function by using localized wave packets rather than plane waves. Solving the Schr\"odinger equation for two colliding particles, we discover that the previously found position diffusion is not a physical process, but an artifact of the approximation of a coarse grained time scale, which in turn is needed to find Markkovian dynamics.