Quantum Transport in a Crystal With Short-Range Interactions: The Boltzmann-Grad Limit
Mathematical Physics
2021-08-18 v2 math.MP
Abstract
We study the macroscopic transport properties of the quantum Lorentz gas in a crystal with short-range potentials, and show that in the Boltzmann-Grad limit the quantum dynamics converges to a random flight process which is not compatible with the linear Boltzmann equation. Our derivation relies on a hypothesis concerning the statistical distribution of lattice points in thin domains, which is closely related to the Berry-Tabor conjecture in quantum chaos.
Keywords
Cite
@article{arxiv.2012.15312,
title = {Quantum Transport in a Crystal With Short-Range Interactions: The Boltzmann-Grad Limit},
author = {Jory Griffin and Jens Marklof},
journal= {arXiv preprint arXiv:2012.15312},
year = {2021}
}
Comments
44 pages, 8 figures