Volume 86, Number 3, May 2009
Article Number 37011
Number of page(s) 6
Section Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties
Published online 20 May 2009
EPL, 86 (2009) 37011
DOI: 10.1209/0295-5075/86/37011

One-dimensional classical diffusion in a random force field with weakly concentrated absorbers

C. 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 $\rho $ of absorbers is studied. The force field is taken as a Gaussian white noise with $\langle \phi (x)\rangle =0$ and $\langle \phi (x)\phi (x^\prime )\rangle =g\,\delta (x-
x^\prime)$. 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 $\langle {P(x,t\vert x,0)} \rangle \sim t^{-\sqrt{2\rho/g}} $ (to be compared with the usual Lifshits exponential decay ${\rm exp}-(\rho ^{2}t)^{1/3}$ 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