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

Area of Science:

• Statistical Physics
• Condensed Matter Physics
• Complex Systems

Background:

• Continuous-time random walks (CTRW) are fundamental models for particle transport.
• Disordered systems, characterized by random potentials, exhibit complex transport behaviors.
• Self-affine quenched random potentials introduce spatial correlations affecting particle dynamics.

Purpose of the Study:

• To investigate the continuous-time random walk of a particle in a 2D self-affine quenched random potential.
• To analyze the behavior of the equilibrium time and barrier under strong disorder conditions.
• To determine the scaling properties and diffusion characteristics in such disordered environments.

Main Methods:

• Application of the strong disorder renormalization procedure.
• Numerical analysis of the master equation governing the random walk.
• Statistical evaluation of equilibrium time (t(eq)) over disordered samples of varying sizes (L x L).

Main Results:

• Identification of an "infinite disorder fixed point" in the system.
• The equilibrium barrier, Gamma(eq) (equivalent to t(eq)), scales as Gamma(eq) = L^H * u, where u is an order O(1) random variable.
• Observed logarithmically slow diffusion, with particle displacement |r(t)-r(0)| scaling as (ln t)^(1/H).

Conclusions:

• The study reveals a universal scaling behavior for the equilibrium barrier in 2D disordered potentials.
• The findings indicate a transition to anomalous diffusion governed by the Hurst exponent H.
• The identified infinite disorder fixed point provides insights into the long-time dynamics of particles in complex random environments.