Quantum transport in a crystal with short-range interactions: The Boltzmann-Grad limit

Jory Griffin, Jens Marklof

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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
Original languageEnglish
Article number16
Number of pages46
JournalJournal of Statistical Physics
Volume184
Issue number2
DOIs
Publication statusPublished - 26 Jul 2021

Bibliographical note

Funding Information:
Research supported by EPSRC Grant EP/S024948/1.

Publisher Copyright:
© 2021, The Author(s).

Keywords

  • kinetic transport
  • Lorentz gas
  • Boltzmann equation
  • Floquet-Bloch theory
  • Berry-Tabor conjecture

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