# Random walk in two-dimensional self-affine random potentials : strong disorder renormalization approach - Condensed Matter > Disordered Systems and Neural Networks

Random walk in two-dimensional self-affine random potentials : strong disorder renormalization approach - Condensed Matter > Disordered Systems and Neural Networks - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We consider the continuous-time random walk of a particle in atwo-dimensional self-affine quenched random potential of Hurst exponent $H>0$.The corresponding master equation is studied via the strong disorderrenormalization procedure introduced in Ref. C. Monthus and T. Garel, J. Phys.A: Math. Theor. 41 2008 255002. We present numerical results on thestatistics of the equilibrium time $t {eq}$ over the disordered samples of agiven size $L \times L$ for $10 \leq L \leq 80$. We find an -Infinite disorderfixed point-, where the equilibrium barrier $\Gamma {eq} \equiv \ln t {eq}$scales as $\Gamma {eq}=L^H u$ where $u$ is a random variable of order O1.This corresponds to a logarithmically-slow diffusion $| \vec rt - \vec r0| \sim \ln t^{1-H}$ for the position $\vec rt$ of the particle.

Autor: Cecile Monthus, Thomas Garel

Fuente: https://arxiv.org/