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DY: Fachverband Dynamik und Statistische Physik

DY 12: Delay and Feedback Dynamics

DY 12.7: Vortrag

Montag, 20. März 2017, 17:00–17:15, ZEU 147

Approximating the non-Markovian dynamics of classical noisy systems with time-delay — •Sarah A. M. Loos and Sabine H. L. Klapp — Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, D-10623 Berlin, Germany

We investigate the probabilistic treatment of classical overdamped noisy systems with time-delayed forces (that depend on the system state at one earlier time t−τ) in the steady state. Due to the non-Markovianity, there is no standard Fokker-Planck (FP) equation that corresponds to the delayed Langevin equation for such systems. On the contrary, the FP approach yields an infinite hierarchy of coupled differential equations [1].

We investigate approaches to truncate this hierarchy by approximating the two-time probability density. An according first-order perturbation-theoretical approach was developed by Frank [2], starting from the corresponding system without delay force. Here we present a novel approach, starting from the corresponding linearized delayed system. We discuss the application of both approaches to a 1D system consisting of a Brownian particle in a static periodic potential subject to a time-delayed feedback force. Comparing with results from numerical simulations, we demonstrate advantages of the novel approach compared to the perturbation theory.

M. L. Rosinberg et al., Phys. Rev. E 91, 042114 (2015).
T. D. Frank, Phys. Rev. E 71, 031106 (2005).