Article (Scientific journals)
On the non-stationary generalized Langevin Equation
Meyer, Hugues; Voigtmann, Thomas; Schilling, Tanja
2017In Journal of Chemical Physics, 147 (21), p. 214110
Peer reviewed
 

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Abstract :
[en] In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble (“bundle”) of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. By contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows us to relate the Taylor expansion of the memory kernel to data that are accessible in MD simulations and experiments, thus allowing us to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions and is shown to be consistent with direct measurements from simulations.
Disciplines :
Physics
Author, co-author :
Meyer, Hugues ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Physics and Materials Science Research Unit ; Albert-Ludwigs-Universität Freiburg > Physikalisches Institut
Voigtmann, Thomas;  Deutsches Zentrum für Luft- und Raumfahrt - DLR > Institut für Materialphysik im Weltraum ; Heinrich-Heine-Universität > Department of Physics
Schilling, Tanja;  Albert-Ludwigs-Universität Freiburg > Physikalisches Institut
External co-authors :
yes
Language :
English
Title :
On the non-stationary generalized Langevin Equation
Publication date :
07 December 2017
Journal title :
Journal of Chemical Physics
Volume :
147
Issue :
21
Pages :
214110
Peer reviewed :
Peer reviewed
Focus Area :
Physics and Materials Science
Funders :
FNR - Fonds National de la Recherche [LU]
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