IAS-2 Seminar: Nothing is local: Non-Gaussianity and varying scaling exponents in long-range dependent motion

Ralf Metzler

Theoretical Physics, Institute of Physics and Astromomy, University of Potsdam

Join us in person in Building 04.16, Room 2001

Abstract:

Nothing is local: Non-Gaussianity and varying scaling exponents in long-range dependent motion

Stochastic processes with long-range dependent correlations naturally emerge in many systems when degrees of freedom are integrated out, apart from the dynamics of the (tracer) particle of interest. In non-equilibrium situations, the resulting overdamped dynamics often corresponds to fractional Brownian motion (FBM).

Prime examples are crowded liquids such as the cytoplasm of biological cells or biological membranes. In disordered systems the observed displacement probability density is often non-Gaussian, and FBM-type processes display scaling exponents varying in time or space.

This talk introduces diffusion models with stochastically [1,2] and deterministically [3,4] varying diffusion coefficients and scaling exponents. Apart from the more traditional Mandelbrot-van Ness formulation of FBM, Levy’s non-equilibrium approach via a fractional integral will also be discussed. Various applications to experimental data will be introduced.

References:

[1] E. Barkai, Y. Garini, and R. Metzler, Strange kinetics of single molecules in Living Cells, Phys. Today 65(8), 29 (2012).

[2] D. Krapf and R. Metzler, Strange interfacial molecular dynamics, Phys. Today 72(9), 48 (2019).

[3] O. Vilk, E. Aghion, T. Avgar, C. Beta, O. Nagel, A. Sabri, R. Sarfati, D. K. Schwartz, M. Weiss, D. Krapf, R. Nathan, R. Metzler, and M. Assaf, Unravelling the origins of anomalous diffusion: from molecules to migrating storks, Phys. Rev. Res. 4, 033055 (2022).

[4] H. Seckler and R. Metzler, Bayesian deep learning for error estimation in the analysis of anomalous diffusion, Nature Comm. 13, 6717 (2022).