Derivation of the Linear Landau Equation and Linear Boltzmann Equation from the Lorentz Model with Magnetic Field
| Autor: | Matteo Marcozzi, Alessia Nota |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Linear Landau equation
Lorentz gas FOS: Physical sciences 01 natural sciences Hyperboloid model Linear Boltzmann equation 0103 physical sciences Limit (mathematics) 0101 mathematics Mathematical Physics Physics Coupling Plane (geometry) 010102 general mathematics Statistical and Nonlinear Physics Mathematical Physics (math-ph) Low density limit Weak coupling limit Action (physics) Magnetic field Classical mechanics Distribution (mathematics) 010307 mathematical physics Test particle |
| Zdroj: | Journal of Statistical Physics. 162:1539-1565 |
| ISSN: | 1572-9613 0022-4715 |
| DOI: | 10.1007/s10955-016-1453-8 |
| Popis: | We consider a test particle moving in a random distribution of obstacles in the plane, under the action of a uniform magnetic field, orthogonal to the plane. We show that, in a weak coupling limit, the particle distribution behaves according to the linear Landau equation with a magnetic transport term. Moreover, we show that, in a low density regime, when each obstacle generates an inverse power law potential, the particle distribution behaves according to the linear Boltzmann equation with a magnetic transport term. We provide an explicit control of the error in the kinetic limit by estimating the contributions of the configurations which prevent the Markovianity. We compare these results with those ones obtained for a system of hard disks in \cite{BMHH}, which show instead that the memory effects are not negligible in the Boltzmann-Grad limit. Comment: 22 pages, 4 figures in Journal of Statistical Physics 2016 |
| Databáze: | OpenAIRE |
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