 
Summary: Europhys. Lett., 60 (6), pp. 889895 (2002)
EUROPHYSICS LETTERS 15 December 2002
Coupling sensitivity of localization length
in onedimensional disordered systems
R. Zillmer, V. Ahlers and A. Pikovsky
Department of Physics, University of Potsdam
Postfach 601553, D14415 Potsdam, Germany
(received 13 August 2002; accepted 7 October 2002)
PACS. 72.15.Rn Localization effects (Anderson or weak localization).
Abstract. We investigate Anderson localization in a quasionedimensional disordered
system consisting of weakly coupled statistically independent channels. The dependence of
the localization length on the coupling is shown to be singular: proportional to 1/ ln .
Numerical evidence is given for coupled random chains with different statistics of site potential.
An analytical approach is developed based on the FokkerPlanck treatment of the coupled
stationary Schr¨odinger equations with Gaussian deltacorrelated potentials.
Anderson localization, i.e. an exponential in average decay of the amplitude of the wave
function in space, is a fundamental phenomenon in disordered systems [14]. It results from
a combination of tunneling and interference effects at the motion of a particle in a random
potential. In terms of condensedmatter physics, the disorder relates to impurities, vacancies
and dislocations in the crystal lattice. The exponential localization of the wave function plays
