Our previous results [V.N. Kuzovkov, W. von Niessen, V. Kashcheyevs, O. Hein, J. Phys. Condens. Matter 14 (2002) 13777] dealing with the analytical solution of the two-dimensional (2-D) Anderson localization problem due to disorder is generalized for anisotropic systems (two different hopping...

We discuss here in detail a new analytical random walk approach to calculating the phase diagram for spatially extended systems with multiplicative noise. We use the Anderson localization problem as an example. The transition from delocalized to localized states is treated as a generalized...

The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J. Phys.: Condens. Matter <Emphasis Type="Bold">14, 13777 (2002)] is generalized for higher spatial dimensions D. In this way the generalized Lyapunov exponents for diagonal correlators of the wave...</emphasis>

In this paper we introduce a stochastic ansatz which can be used to model surface reaction systems. The systems may include mono- and bimolecular steps (i.e. adsorption, desorption, reaction and diffusion steps). We take advantage of the Markovian behaviour of these systems by using master...