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Derivation of the linear Boltzmann equation from the damped quantum Lorentz gas with a general scatterer configuration
Jory Griffin
It is a fundamental problem in mathematical physics to derive macroscopic transport equations from microscopic models. In this paper we derive the linear Boltzmann equation in the…
Quantum Transport in a Crystal With Short-Range Interactions: The Boltzmann-Grad Limit
Jory Griffin, Jens Marklof
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 co…
Quantum Transport in a Low-Density Periodic Potential: Homogenisation via Homogeneous Flows
Jory Griffin, Jens Marklof
We show that the time evolution of a quantum wavepacket in a periodic potential converges in a combined high-frequency/Boltzmann-Grad limit, up to second order in the coupling cons…
On the Phase-Space Distribution of Bloch Eigenmodes for Periodic Point Scatterers
Jory Griffin
Consider the 3-dimensional Laplacian with a potential described by point scatterers placed on the integer lattice. We prove that for Floquet-Bloch modes with fixed quasi-momentum s…