# 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 - Download this document for free, or read online. Document in PDF available to download.

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.

Author: ** Cecile Monthus, Thomas Garel**

Source: https://arxiv.org/