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

Christophe Texier (1) , Christian Hagendorf (2)

1 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
2 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

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 $\mean{\phi(x)}=0$ and $\mean{\phi(x)\phi(x')}=g \delta(x-x')$. 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 $\smean{P(x,t|x,0)}\sim{}t^{-\sqrt{2\rho/g}}$ (to be compared with the usual Lifshits exponential decay $\exp{-(\rho^2t)^{1/3}}$ in the absence of the random force field). The localisation properties of the underlying quantum Hamiltonian are discussed as well.

Domaines: Autre [cond-mat.other]

Christophe Texier, Christian Hagendorf. One-dimensional classical diffusion in a random force field with weakly concentrated absorbers. EPL - Europhysics Letters, 2009, 86, pp.37011. ⟨hal-00397813⟩