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DY: Fachverband Dynamik und Statistische Physik

DY 27: Transport and Anomalous Diffusion

DY 27.2: Talk

Thursday, March 29, 2012, 15:00–15:15, MA 004

Fluctuations of time averages for Langevin dynamics in a binding force field — •Andreas Dechant¹, Eric Lutz², David A. Kessler³, and Eli Barkai³ — ¹Department of Physics, Universität Augsburg, D-86356 Augsburg, Germany — ²Department of Physics, Freie Universität Berlin, D-14195 Berlin, Germany — ³Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat Gan 52900, Israel

We derive a simple formula for the fluctuations of the time average around the thermal mean for overdamped Brownian motion in a binding potential. Using a backward Fokker-Planck equation, introduced by Szabo et al. in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large non-ergodic fluctuations and show how they are related to a super-aging correlation function.