Quantum Transport in a Crystal with Short-Range Interactions: The Boltzmann

Quantum Transport in a Crystal with Short-Range Interactions: The Boltzmann–Grad Limit

Published:2021-07-26 Issue:2 Volume:184 Page:
ISSN:0022-4715
Container-title:Journal of Statistical Physics
language:en
Short-container-title:J Stat Phys

Author:

Griffin Jory^ORCID,Marklof Jens

Abstract

AbstractWe 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.

Funder

Engineering and Physical Sciences Research Council

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://link.springer.com/content/pdf/10.1007/s10955-021-02797-z.pdf

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