Regensburg 2025 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 4: Focus Session: Nonlinear Dynamics and Stochastic Processes – Advances in Theory and Applications I

DY 4.2: Invited Talk

Monday, March 17, 2025, 09:45–10:15, H43

Physical application of infinite ergodic theory — •Eli Barkai — Phys. Dept. Bar-Ilan University, Ramat-Gan, Israel

Norm conserving dynamical mappings, for example the Pomeau Manneville scenario for intermittency, exhibit either a normalized invariant density or an infinite (non-normalized) state, depending on the non-linearity of the map. In the latter case infinite ergodic theory plays a key role in the description of time averages. We will present physical applications of infinite ergodic theory in the context of stochastic Langevin dynamics [1] where the normalizing partition function diverges, and for a gas of laser cooled atoms [2]. This allows for the construction of thermodynamical relations in a non-equilibrium setting, provided that the dynamics is recurrent.

[1.] E. Aghion, D. A. Kessler, and E. Barkai Phys. Rev. Lett. 122, 010601 (2019).

[2.] E. Barkai, G. Radons, and T. Akimoto Transitions in the ergodicity of subrecoil-laser-cooled gases Phys. Rev. Lett. 127, 140605 (2021).

Keywords: infinite ergodic theory; Langevin dynamics; stochastic theory