Anomalous Diffusion in Aperiodic Environments

Дата и время публикации : 1998-09-07T15:16:41Z

Авторы публикации и институты :
F. Igloi (Research Institute for Solid State Physics, Budapest, University of Szeged, Henri Poincare University, Nancy)
L. Turban (Henri Poincare University, Nancy)
H. Rieger (HLRZ, Forschungszentrum Juelich)

Ссылка на журнал-издание: Phys. Rev. E, 59 (1999) 1465
Коментарии к cтатье: 11 pages, RevTex
Первичная категория: cond-mat.stat-mech

Все категории : cond-mat.stat-mech

Краткий обзор статьи: We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the transverse-field Ising model with inhomogeneous couplings we obtain many new analytical results for the random walk problem. In the absence of global bias the qualitative behavior of the diffusive motion of the particle and the corresponding persistence probability strongly depend on the fluctuation properties of the environment. In environments with bounded fluctuations the particle shows normal diffusive motion and the diffusion constant is simply related to the persistence probability. On the other hand in a medium with unbounded fluctuations the diffusion is ultra-slow, the displacement of the particle grows on logarithmic time scales. For the borderline situation with marginal fluctuations both the diffusion exponent and the persistence exponent are continuously varying functions of the aperiodicity. Extensions of the results to disordered media and to higher dimensions are also discussed.

Category: Physics