Quantum Transport in a Crystal With Short-Range Interactions: The Boltzmann-Grad Limit
arXiv:2012.15312 · doi:10.1007/s10955-021-02797-z
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.
arXiv comment44 pages, 8 figures
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