Random walk in two-dimensional self-affine random potentials: strong-disorder renormalization approach.

We consider the continuous-time random walk of a particle in a two-dimensional self-affine quenched random potential of Hurst exponent H>0 . The corresponding master equation is studied via the strong disorder renormalization procedure introduced in Monthus and Garel [J. Phys. A: Math. Theor. 41, 255002 (2008)]. We present numerical results on the statistics of the equilibrium time t(eq) over the disordered samples of a given size L x L for 10 < or = L< or = 80. We find an "infinite disorder fixed point," where the equilibrium barrier Gamma(eq) identical with t(eq) scales as Gamma(eq)=L(H)u where u is a random variable of order O(1). This corresponds to a logarithmically slow diffusion |r(t)-r(0)| approximately (ln t)(1/H) for the position r(t) of the particle.