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

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.

Automated summary

The study reveals that in a crystal with short-range potentials, the macroscopic transport properties of the quantum Lorentz gas converge to a random flight process in the Boltzmann-Grad limit, which is not compatible with the linear Boltzmann equation. This derivation is based on a hypothesis about the statistical distribution of lattice points in thin domains, closely related to the Berry-Tabor conjecture in quantum chaos.