Brownian motion at absolute zero

TL;DR

This paper derives a universal quantum formula for the mean-square displacement of a diffusing particle at absolute zero, revealing a logarithmic behavior and significant deviations from classical diffusion at low temperatures and long times.

Contribution

It introduces a general, composition-independent quantum formula for diffusion at zero Kelvin, highlighting universal logarithmic behavior and potential experimental regimes.

Findings

Logarithmic mean-square displacement at near 0 K

Deviations from classical diffusion at larger times and temperatures

Independence from heat bath composition and coupling strength

Abstract

We derive a general quantum formula giving the mean-square displacement of a diffusing particle as a function of time. Near {\bf 0 K} we find a universal logarithmic behavior (valid for times longer than the relaxation time), and deviations from classical behavior can also be significant at larger values of time and temperature. Our derivation depends neither on the specific composition of the heat bath nor on the strength of the coupling between the bath and the particle. An experimental regime of microseconds and microdegrees Kelvin would elicit the pure logarithmic diffusion.