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DY: Fachverband Dynamik und Statistische Physik

DY 59: Brownian Motion and Anomalous Diffusion

DY 59.8: Talk

Friday, March 22, 2024, 11:30–11:45, BH-N 334

The Role of Cross-Correlations in the Fluctuation-Dissipation-Theorem of the Generalized Langevin Equation — •Niklas Wolf, Viktor Klippenstein, and Nico van der Vegt — TU Darmstadt, 64287 Darmstadt, Germany

In molecular dynamics, the development of dynamically consistent coarse-grained models revolves around modeling friction and random forces to reintroduce fluctuations in the force that are lost when choosing a more coarse description of a problem/system. Modeling these fluctuations with Markovian approaches like the Langevin equation or dissipative particle dynamics assumes time scale separation between the degrees of freedom in the atomistic and coarse model. Usually, this is not given in condensed matter systems but can be accounted for with non-Markovian models like the generalized Langevin equation (GLE), which we focused on in this work.

Recent works[1, 2] have demonstrated that for a GLE with position-independent friction, the usual second fluctuation-dissipation theorem connecting friction and random force should be modified with a cross-correlation term. We investigated these cross-correlations and their effect on dynamic properties in several model systems and found that discarding them does generally not lead to a correct description of the dynamics. To remedy this, we discuss different approaches to include cross-correlations in a GLE equation of motion.

[1] V. Klippenstein, N. F. A. van der Vegt, J. Chem. Phys. 154, 191102 (2021)

[2] H. Vroylandt, EPL 140, 62003 (2022)

Keywords: Generalized Langevin Equation; Stochastic Dynamics; Fluctuation-Dissipation-Theorem