On the Periodic Lorentz Gas and the Lorentz Kinetic Equation

Abstract

We prove that the Boltzmann-Grad limit of the Lorentz gas with periodic distribution of scatterers cannot be described with a linear Boltzmann equation. This is at variance with the case of a Poisson distribution of scatterers, for which the convergence to the linear Boltzmann equation has been proved by Gallavotti [Phys. Rev. (2) 185 (1969), p. 308].

References in corpus (1)

• On the distribution of free-path lengths for the periodic Lorentz gas III

Cited by in corpus (13)

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• Recent Results on the Periodic Lorentz Gas
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• The low-density limit of the Lorentz gas: periodic, aperiodic and random
• The Brownian motion as the limit of a deterministic system of hard-spheres
• The Lorentz Process with a Nearly Periodic Distribution of Scatterers
• Homogenization of the linear Boltzmann equation in a domain with a periodic distribution of holes
• Quantum Transport in a Low-Density Periodic Potential: Homogenisation via Homogeneous Flows
• Kinetic Theory for the Low-Density Lorentz Gas
• Convergence to the equilibrium for the kinetic transport equation in the two-dimensional periodic Lorentz Gas
• Generalized linear Boltzmann equations for particle transport in polycrystals
• Long Range Particle Dynamics and the Linear Boltzmann Equation