Anomalous processes with general waiting times: Functionals, Multipoint Structure and a new perspective on their Langevin description

Date

Oct 19, 2015

Time

2:00 PM - 3:00 PM

Speaker

Andrea Cairoli

Affiliation

Queen Mary University of London

Language

en

Main Topic

Physik

Other Topics

Physik

Host

Advanced Study Group Klages

Description

Continuous Time Random Walks (CTRWs) have been successfully used to model subdiffusive biological processes characterized by a sublinear power-law scaling of the mean square displacement. However, many transport processes have recently been found in experiments exhibiting more complex anomalous diffusive behavior, where typically crossovers between different scaling regimes appear over time. In this talk we discuss a class of anomalous diffusion processes that is able to capture such complex dynamics by extending usual CTRWs to more general waiting time distributions. We obtain a complete characterization of their functionals and multipoint structure by using a representation in terms of a normal diffusive process plus a stochastic time change. In particular, we provide closed form expressions for their two-point correlation functions, which can be readily applied to experimental data. We also show that the free-force dynamics of these processes can be conveniently described with a single Langevin equation in physical time driven by a new additive non-Gaussian noise. We characterize it in terms of the full multipoint statistics and show that, in the presence of external forces, we generate a different class of processes with forces acting at all times.

Last modified: Oct 19, 2015, 9:54:43 AM