One-dimensional classical diffusion in a random force field with weakly concentrated absorbersC. Texier1, 2 and C. Hagendorf3
1 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
received 16 February 2009; accepted in final form 17 April 2009; published May 2009
published online 20 May 2009
A one-dimensional model of classical diffusion in a random force field with a weak concentration 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.
73.20.Fz - Weak or Anderson localization.
02.50.-r - Probability theory, stochastic processes, and statistics.
© EPLA 2009