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.

• Publication year

  2009

• Venue

  Physical review. E, Statistical, nonlinear, and soft matter physics

• Publication date

  2009-10-01

• Fields of study

  Mathematics, Physics, Medicine

• Identifiers
  DOI 10.1103/PhysRevE.81.011138arXiv 0910.0111PMID 20365354
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Coarse graining of master equations with fast and slow states.

  2008cited by this paper
• Partially asymmetric exclusion processes with sitewise disorder.

  2006cited by this paper
• Partially asymmetric zero-range process with quenched disorder.

  2005cited by this paper
• Partially asymmetric exclusion models with quenched disorder.

  2004cited by this paper
• Absorbing state phase transitions with quenched disorder.

  2004cited by this paper
• Anomalous diffusion, localization, aging, and subaging effects in trap models at very low temperature.

  2003cited by this paper
• Nonlinear response of the trap model in the aging regime: exact results in the strong-disorder limit.

  2003cited by this paper
• Strong disorder fixed point in absorbing-state phase transitions.

  2002cited by this paper
• Localization properties of the anomalous diffusion phase in the directed trap model and in the Sinai diffusion with a bias.

  2002cited by this paper
• Diffusion and Reactions in Fractals and Disordered Systems

  2002cited by this paper
• Random vibrational networks and the renormalization group.

  2002cited by this paper
• Nonequilibrium dynamics of random field Ising spin chains: exact results via real space renormalization group.

  2000cited by this paper
• Diffusion and Reactions in Fractals and Disordered Systems: References

  2000cited by this paper
• Reaction diffusion models in one dimension with disorder.

  1999cited by this paper
• Random walkers in one-dimensional random environments: exact renormalization group analysis.

  1998cited by this paper
• Critical behavior of random transverse-field Ising spin chains.

  1995cited by this paper
• Random antiferromagnetic quantum spin chains.

  1994cited by this paper
• Random transverse field Ising spin chains.

  1992cited by this paper
• Fractals in nature: from characterization to simulation

  1988cited by this paper
• Fractals: Form, Chance and Dimension

  1978cited by this paper

• Strong disorder RG approach – a short review of recent developments

  2018cites this paper
• Sub-diffusive scaling with power-law trapping times

  2014cites this paper
• Low-temperature dynamics of long-ranged spin-glasses: full hierarchy of relaxation times via real-space renormalization

  2014cites this paper
• Dynamical barriers for the random ferromagnetic Ising model on the Cayley tree: traveling-wave solution of the real space renormalization flow

  2013cites this paper
• Competition between quenched disorder and long-range connections: a numerical study of diffusion.

  2011cites this paper
• Random elastic networks: a strong disorder renormalization approach

  2010cites this paper
• Localization in fractal and multifractal media

  2010cites this paper
• Random walk in a two-dimensional self-affine random potential: Properties of the anomalous diffusion phase at small external force.

  2010cites this paper