The kinetic description of a collisionless system of particles in an external stochastic field possessing helicity is examined. The kinetic equation which contains an additional term proportional to the helicity is obtained. The solution describing evolution of the distribution function for...

We demonstrate that the Fokker–Planck equation can be generalized into a ‘fractional Fokker–Planck’ equation, i.e., an equation which includes fractional space differentiations, in order to encompass the wide class of anomalous diffusions due to a Lévy stable stochastic forcing. A...

The role of Lévy flights on fluctuation-driven transport in time independent periodic potentials with broken spatial symmetry is studied. Two complementary approaches are followed. The first one is based on a generalized Langevin model describing overdamped dynamics in a ratchet type external...

The concept of multifractality is applied in the analysis of molecular spectra. A scaling relationship is established between moments of the spectral intensities and the experimental resolution. The obtained scaling exponents are shown to support a non-random distribution of intensities. Using...

We consider the linear response of systems modelled by continuous-time random walks (CTRW) and by fractional Fokker–Planck equations under the influence of time-dependent external fields. We calculate the corresponding response functions explicitly. The CTRW curve exhibits aging, i.e., it is...

We investigate the influence of a weak uniform bias on chaotic diffusion generated by iterated one-dimensional maps which, in the absence of the bias, lead to subdiffusion.

The basic characteristics of molecular systems under shear are briefly reviewed and methods to control friction are proposed. These control methods allow to eliminate chaotic stick–slip motion, and modify frictional forces. The possibilities to control friction are demonstrated using a model...

We investigate anomalous diffusion generated by iterated maps and analyze the motion in terms of the probabilistic Lévy walks. We present expressions for the mean-squared displacement and for the propagator, which deviate from those for Brownian motion. The theoretical results are corroborated...

We investigate a model system which consists of a chain of particles that interact with two periodic potentials representing two confining plates, one of which is externally driven. The model leads to a spectrum of rich behaviors in the motion of the top driven plate: stick–slip, intermittent...

The transport properties of Lévy walks are discussed in the framework of continuous time random walks (CTRW) with coupled memories. This type of walks may lead to anomalous diffusion where the mean squared displacement 〈r2(t)〉∼tα with α≠1. We focus on the enhanced diffusion limit,...