Title :

Large time dynamics of a classical system subject to a fast varying force

Author(s) :

Castella, François [Auteur]
Institut de Recherche Mathématique de Rennes [IRMAR]
Degond, Pierre [Auteur]
Mathématiques pour l'Industrie et la Physique [MIP]
Goudon, Thierry [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
SImulations and Modeling for PArticles and Fluids [SIMPAF]

Journal title :

Communications in Mathematical Physics

Pages :

23-49

Publisher :

Springer Verlag

Publication date :

2007

ISSN :

0010-3616

English keyword(s) :

QUANTUM BOLTZMANN-EQUATION
VON-NEUMANN-EQUATION
TRANSPORT-EQUATIONS
DETERMINISTIC FRAMEWORK
KINETIC-EQUATIONS
RANDOM-MEDIA
BLOCH MODEL
HOMOGENIZATION
APPROXIMATION
CONVERGENCE

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

We investigate the asymptotic behavior of solutions to a kinetic equation describing the evolution of particles subject to the sum of a fixed, confining, Hamiltonian, and a small, time-oscillating, perturbation. The equation ...
Show more >We investigate the asymptotic behavior of solutions to a kinetic equation describing the evolution of particles subject to the sum of a fixed, confining, Hamiltonian, and a small, time-oscillating, perturbation. The equation also involves an interaction operator which acts as a relaxation in the energy variable. This paper aims at providing a classical counterpart to the derivation of rate equations from the atomic Bloch equations. In the present classical setting, the homogenization procedure leads to a diffusion equation in the energy variable, rather than a rate equation, and the presence of the relaxation operator regularizes the limit process, leading to finite diffusion coefficients. The key assumption is that the time-oscillatory perturbation should have well-defined long time averages: our procedure includes general "ergodic" behaviors, amongst which periodic, or quasi-periodic potentials only are a particular case.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL