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

C. Texier; C. Hagendorf

doi:10.1209/0295-5075/86/37011

All issues

Volume 86 / No 3 (May 2009)

EPL, 86 3 (2009) 37011

Abstract

Issue		EPL Volume 86, Number 3, May 2009


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

EPL, 86 (2009) 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

Corresponding authors: christophe.texier@u-psud.fr hagendor@lpt.ens.fr

Received: 16 February 2009
Accepted: 17 April 2009

Abstract

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 $\langle \phi (x)\rangle =0$ 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.

PACS: 73.20.Fz – Weak or Anderson localization / 02.50.-r – Probability theory, stochastic processes, and statistics

© EPLA, 2009

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