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On the equilibrium state of random walkers in random environments: analytical results

 
: Radons, G.

:

Journal of Physics. A, Mathematical and general 31 (1998), pp.4141-4148
ISSN: 0301-0015
ISSN: 0305-4470
ISSN: 0022-3689
German
Journal Article
Fraunhofer IPA ()
Chaos; Disordered Environment; Equilibrium; Equilibrium Distribution; Fraktale; Gleichgewichtsverteilung; Random; Random Walks; Rényi entropy; RWRE (Random Walks in Random Environments); Ungeordnete Umgebung; Unordnung; Zufallsbewegung

Abstract
We study equilibrium properties of random walkers in one-dimensional random environments of finite length L. From an exact expression for the quenched average of the free energy we derive analytical results for all cumulants and all Rényi entropies of the equilibrium distribution. In contrast to the finite variance of a typical non-equilibrium distribution in the unbiased situation, we find that in equilibrium the disorder averaged variance diverges with the size of the system as L3/2.

: http://publica.fraunhofer.de/documents/PX-27169.html