arXiv:1001.1142v1 [cond-mat.stat-mech] 7 Jan 2010 Anomalous biased diffusion in a randomly layered medium ∗ Electronic address: stdenis@pks.mpg.de 1 S. I. Denisov 1 , 2 ∗ and H. Kantz 1 $^{1}$Max-Planck-Institut f¨ ur Physik komplexer Systeme, N¨ othnitzer Straße 38, D-01187 Dresden, Germany $^{2}$Sumy State University, 2 Rimsky-Korsakov Street, UA-40007 Sumy, Ukraine We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The long-time behavior of the particle position is studied in the frame of a continuous-time random walk on a semi-infinite one-dimensional lattice. We formulate the conditions for anomalous diffusion, derive the diffusion laws and analyze their dependence on the particle mass and the distribution of the random force. PACS numbers: 05.40.Fb, 02.50.Ey Abstract