Pseudo generators for under-resolved molecular dynamics

• Published in: The European physical journal. ST, Special topics Vol. 224; no. 12; pp. 2463 - 2490
• Main Authors: Bittracher, A., Hartmann, C., Junge, O., Koltai, P.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2015
• Subjects: Atomic; Classical and Continuum Physics; Condensed Matter Physics; Discussion and Debate: Recurrent Problems in Scale Bridging Techniques in Molecular Simulation – What are the Current Options?; Materials Science; Measurement Science and Instrumentation; Molecular; Optical and Plasma Physics; Physics; Physics and Astronomy; Regular Article
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjst/e2015-02422-y

Many features of a molecule which are of physical interest (e.g. molecular conformations, reaction rates) are described in terms of its dynamics in configuration space. This article deals with the projection of molecular dynamics in phase space onto configuration space. Specifically, we study the situation that the phase space dynamics is governed by a stochastic Langevin equation and study its relation with the configurational Smoluchowski equation in the three different scaling regimes: Firstly, the Smoluchowski equations in non-Cartesian geometries are derived from the overdamped limit of the Langevin equation. Secondly, transfer operator methods are used to describe the metastable behaviour of the system at hand, and an explicit small-time asymptotics is derived on which the Smoluchowski equation turns out to govern the dynamics of the position coordinate (without any assumptions on the damping). By using an adequate reduction technique, these considerations are then extended to one-dimensional reaction coordinates. Thirdly, we sketch three different approaches to approximate the metastable dynamics based on time-local information only.