Dresden 2020 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 48: Statistical Physics far from Thermal Equilibrium

DY 48.9: Talk

Thursday, March 19, 2020, 11:45–12:00, ZEU 147

Analytical solutions for non-Markovian Brownian systems far from thermal equilibrium — •Timo Dörries, Sarah A.M. Loos, and Sabine H.L. Klapp — Institut für Theoretische Physik, Hardenbergstr. 36, TU Berlin, 10623 Berlin, Germany

Markovian Langevin equations are an established tool to describe stochastic motion. However, in many real-world systems, memory effects play a crucial role and e.g. complex environments can yield to stochastic motion characterized by different timescales. Analytical solutions are in general difficult to obtain here. We propose (linear) toy models where we non-reciprocally couple auxiliary variables to a Brownian particle, each auxiliary variable corresponding to one characteristic timescale. Projecting out the auxiliary variables, we obtain a non-Markovian Langevin equation with memory and colored noise.

By deriving closed expressions for up to three auxiliary variables, we can systematically study the connection between the coupling topology and the resulting autocorrelation functions. Further, by studying the connection between topology and thermodynamical properties, we demonstrate that models with non-reciprocal coupling automatically have a net heat production, i.e. describe nonequilibrium systems [1,2].

Finally, we show that a minimal model with two auxiliary variables yields correlation functions similar to those describing hydrodynamic backflow in an optical trap [3].

[1] S.A.M. Loos et al., arXiv:1910.08372 (submitted)

[2] S.A.M. Loos and H.L. Klapp, Scientific Reports 9, 2491 (2019)

[3] Franosch et al., Nature 478, 85-88 (2011)