Volume 128, Number 4, November 2019
|Number of page(s)||7|
|Published online||21 January 2020|
Non-Markovian out-of-equilibrium dynamics: A general numerical procedure to construct time-dependent memory kernels for coarse-grained observables
1 Research Unit in Engineering Science, Université du Luxembourg - L-4364 Esch- sur-Alzette, Luxembourg
2 Physikalisches Institut, Albert-Ludwigs-Universität - D-79104 Freiburg, Germany
Received: 19 July 2019
Accepted: 26 November 2019
We present a numerical method to compute non-equilibrium memory kernels based on experimental data or molecular dynamics simulations. The procedure uses a recasting of the non-stationary generalized Langevin equation, in which we expand the memory kernel in a series that can be reconstructed iteratively. Each term in the series can be computed based solely on knowledge of the two-time auto-correlation function of the observable of interest. We discuss how to optimize this method in order to be the most numerically convenient. As a proof of principle, we test the method on the problem of crystallization from a super-cooled Lennard-Jones melt. We analyze the nucleation and growth dynamics of crystallites and observe that the memory kernel has a time extent that is about one order of magnitude larger than the typical timescale needed for a particle to be attached to the crystallite in the growth regime.
PACS: 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 02.70.-c – Computational techniques; simulations / 05.45.Tp – Time series analysis
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