Anomalous weakly nonergodic Brownian motions in non uniform temperatures

It is shown that ergodicity breaking and anomalous Brownian motion are not limited to composite and/or disordered systems, but can be generated also in simple fluids or solids with time-dependent and/or spatially nonuniform temperature T(t,r). A few examples of simple arrangements easy for experimental realization are discussed in detail. Proposed measurements will enable also the observation of transitions from ergodic to weakly nonergodic and from normal to anomalous diffusion. Similar behaviour can be expected in inflationary systems with time-dependent metric, and in expanding gases

Statistical properties of a dynamic process perturbed by a chaos-generator

We investigate the problem of discrete in time regular perturbations affecting a deterministic process with a generic relaxation time. The effect on the moments of a kinetic process caused by chaotic changes in the deterministic forcing is calculated. Our discussion is carried out in two stages. First, direct calculations determining statistical properties of the process driven by a chaotic motion are presented. Second, the long time predictions of the model are analyzed in a perspective of a properly taken limit of continuous-time idealization of a regular forcing. Some comparisons are made with the known properties of continuous time stochastic processes

Fractional Brownian motions

Properties of different models of fractional Brownian motions are discussed in detail. We shall collect here several possible ways of introducing and defining various possible fBms, discuss their properties, find how they are similar, and how they differ. In particular, we shall try to find what mechanisms or details in their definitions make these motions anomalous and whether can the various models be distinguished experimentally. To this aim, the main tool used here will be the autocorrelation function C(t,s), and related to it characteristics: nonmarkovian behaviour and so-called weak ergodicity breaking