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

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.

44 pages, 8 figures

Cited by in corpus (2)

• Derivation of the linear Boltzmann equation from the damped quantum Lorentz gas with a general scatterer configuration
• Efficient algorithm for simulating particles in real quasiperiodic environments