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

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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 Ref. [C. Monthus and T. Garel, J. Phys. A: Math. Theor. 41 (2008) 255002]. We present numerical results on the statistics of the equilibrium time teq over the disordered samples of a given size L × L for 10 ≤ L ≤ 80. We find an 'Infinite disorder fixed point', where the equilibrium barrier Γeq ≡ teq scales as Γeq=Lʰ u where u is a random variable of order O(1). This corresponds to a logarithmically-slow diffusion | r(t) - r(0) | (t)¹/ʰ for the position r(t) of the particle.