Volume 86, Number 3, May 2009
|Number of page(s)||6|
|Section||Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties|
|Published online||20 May 2009|
One-dimensional classical diffusion in a random force field with weakly concentrated absorbers
Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, CNRS, UMR 8626 F-91405 Orsay cedex, France, EU
2 Laboratoire de Physique des Solides, Université Paris-Sud, CNRS, UMR 8502 - F-91405 Orsay cedex, France, EU
3 Laboratoire de Physique Théorique de l'École Normale Supérieure, CNRS, UMR 8549 - 24, rue Lhomond, F-75230 Paris cedex 05, France, EU
Accepted: 17 April 2009
A one-dimensional model of classical diffusion in a random force field with a weak concentration ρ of absorbers is studied. The force field is taken as a Gaussian white noise with and . Our analysis relies on the relation between the Fokker-Planck operator and a quantum Hamiltonian in which absorption leads to breaking of supersymmetry. Using a Lifshits argument, it is shown that the average return probability is a power law (to be compared with the usual Lifshits exponential decay in the absence of the random force field). The localisation properties of the underlying quantum Hamiltonian are discussed as well.
PACS: 73.20.Fz – Weak or Anderson localization / 02.50.-r – Probability theory, stochastic processes, and statistics
© EPLA, 2009
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