Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Statistical Physics (General) I

DY 17.1: Talk

Tuesday, April 2, 2019, 10:00–10:15, H19

Fluctuations and correlation functions of occupation measures in single-file diffusion — •Alessio Lapolla and Aljaz Godec — Mathematical Biophysics Group, Max Planck Institute for Biophysical Chemistry, Goettingen, Germany

Dynamical processes in statistical physics are predominantly Markovian, at least within a sufficiently high-dimensional setting. However, single-particle experiments in fact probe functionals of lower-dimensional projected dynamics, which typically turns out to be non-Markovian. While the statistical behavior of functionals of trajectories of Markov processes is meanwhile rather well understood, much less is known about the respective behavior in non-Markovian systems. We will present rigorous results for fluctuations and two-tag correlations of bounded additive functionals of ergodic Markov processes having a diagonalizable propagator. Our results relate the statistics of functionals on arbitrary time-scales to the relaxation eigenspectrum. As an application, we will present exact results for one- and two-tag local times in single-file diffusion (SFD), which is central to several phenomena, i.e. the transport in biological channels. In SFD individual particles diffuse in a narrow, effectively one-dimensional channel, which prevents their crossing. Tagging the trajectory of a particular particle corresponds to a projection to a one-dimensional system and introduces a persistent memory. Our analytical results unveil the intricate meaning of such a projection-induced memory on a trajectory level and allow for a detailed analysis of related experiments.
[1] Alessio Lapolla and Aljaž Godec New J. Phys. 20 113021, 2018