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arXiv · 2012.15312

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

Jory Griffin·Jens Marklof
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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.

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Jory Griffin, Jens Marklof. 2020-12-30. Quantum Transport in a Crystal With Short-Range Interactions: The Boltzmann-Grad Limit. https://doi.org/10.1007/s10955-021-02797-z

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