Berlin 2018 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 60: Anomalous Diffusion (joint session DY/BP)

DY 60.6: Vortrag

Donnerstag, 15. März 2018, 11:15–11:30, BH-N 334

Infinite invariant densities in intermittent systems — •Philipp Meyer¹, Eli Barkai², and Holger Kantz¹ — ¹Max Planck Institute for the Physics of Complex Systems, Noethnitzer Str. 38, D 01187, Dresden, Germany — ²Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel

Dynamical intermittency is known to generate anomalous statistical behaviour of dynamical systems, a prominent example being the Pomeau-Manneville map. The system exhibits waiting times and chaotic bursts. For a wide range of parameters no physical invariant density exists. We show how this regime can be characterised quantitatively using the techniques of infinite invariant densities and the Thaler-Dynchin limit theorem.

We obtain pseudo Brownian motion by summing up the increments created by the map. The output corresponds to stochastic processes like continuous time random walks. We are able to relate infinite ergodic theory with scale invariant transport. Here time average diffusivities are especially interesting, because they depend not only on the joint probability density function but also on the exact definition of the paths during waiting periods.

We also present a nonlinear oscillator, i.e., a physical model in continuous time, whose properties in terms of weak ergodity breaking and ageing have a one-to-one correspondence to the properties of the Pomeau-Manneville map. We see how expectation values exhibit ageing in terms of scaling in time.