## I. INTRODUCTION 

A vast variety of physical, chemical, biological and other natural processes can be ad- equately described by random processes exhibiting anomalous diffusion behavior at long times. This behavior, which is characterized by a nonlinear dependence of the variance of these processes on time, can be observed in various systems. Anomalous diffusion actually occurs, for example, in turbulent fluids [1], amorphous solids [2], rotating flows [3], single molecules [4] and porous substrates [5], and has been predicted to occur in many other systems [6–10]. 

The existence of anomalous diffusion in systems with quenched, i.e., time-independent disorder has also been extensively studied [6, 7]. One of the most effective and simple ways to describe anomalous diffusion in these systems is based on the motion equations for diffusing objects (which we will call particles). In these equations, the influence of quenched disorder is usually modeled by a time-independent random potential producing the corresponding random force, and the influence of thermal fluctuations is accounted for by white noise. Specifically, this Langevin-type approach has been successfully applied to study a variety of phenomena, including biased diffusion, which occur when particles move under a constant external force in a one-dimensional potential [11]. 

If thermal fluctuations are absent then particles can be transported to an arbitrary large distance only if the distribution of the random force has bounded support. In this case, the directional transport of particles can be caused by either a periodic external force [12] or a constant one. In the latter case, particles move only in one direction and so the completely anisotropic case of biased diffusion, when the probability of motion along and against the external force equals 1 and 0, respectively, may exist. It has been shown for particular cases of the random force distribution that in the overdamped limit this diffusion is normal if the total force acting on a particle is strictly positive or strictly negative [13, 14]. In Ref. [13] it was also argued that the anomalous regimes of biased diffusion would exist if the lower (upper) bound of the total force at a fixed external force is equal to zero. However, none of the laws of anomalous diffusion was found in this case. 

The aim of this paper is to study the anomalous regimes of biased diffusion of particles moving under a constant force in a randomly layered medium which acts as a piecewise constant random force. The paper is organized as follows. In Sec. II, we describe the model, 

