I Is Brownian motion a purely classical phenomenon or is it also quantm?

[Aidyan]

A water molecule is as tiny as 0.3 Angstrom. I would expect that quantum effects play a role. I'm wondering if its Brownian motion in a fluid is determined only by classical thermodynamics or if its collisional processes must take into account also quantum scatterings or other effects like quantum uncertainty? I looked for this but couldn't find anyone considering this. Any suggestion?

 

[Coelum]

When Einstein explained the Brownian motion in one of his wonderful papers of 1905 (https://www.maths.usyd.edu.au/u/UG/SM/MATH3075/r/Einstein_1905.pdf), he used classical mechanics only. Quantum mechanics was not invented yet, though Einstein himself was concurrently working on it. Unless you have a case where the details of the interactions during the collisions become relevant, you are unlikely to need quantum mechanics. As long as the collisions are elastic, a classical model is accurate enough.

 

[vanhees71]

Of course there's also "quantum Brownian motion". Interstingly it always leads to non-Markovian descriptions. A nice paper, which should be understandable at the introductory quantum-statistics-lecture level (or even after the QM 1 lecture) is

G. W. Ford, J. T. Lewis and R. F. O’Connell, Quantum
Langevin equation, Phys. Rev. A 37, 4419 (1988),
https://doi.org/10.1103/PhysRevA.37.4419