Langevin molecular dynamics derived from Ehrenfest dynamics
type: Item
instance of: scholarly article
zbMATH Open document ID: 1246.82074
DOI: 10.1142/S0218202511005751
author: Anders Szepessy
publication date: 2012-05-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/0712.3656
Mathematics Subject Classification ID: 82C31
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 82C10
zbMATH DE Number: 6032266
zbMATH Keywords: Langevin equation
zbMATH Keywords: Ehrenfest dynamics
zbMATH Keywords: quantum classical molecular dynamics
zbMATH Keywords: Gibbs distribution
zbMATH Keywords: heat bath
zbMATH Keywords: Brownian particle
zbMATH Keywords: ab initio molecular dynamics
zbMATH Keywords: Mori-Zwanzig theory
MaRDI profile type: Publication
arXiv ID: 0712.3656
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OpenAlex ID: W2964168344
published in: M\(^3\)AS. Mathematical Models \& Methods in Applied Sciences
title: Langevin molecular dynamics derived from Ehrenfest dynamics
review text: The author presents investigations in which the stochastic Langevin molecular dynamics for nuclei is derived from the Ehrenfest Hamiltonian system in a Kac-Zwanzig setting, with initial data for the electrons stochastically perturbed from the ground state and the ratio \(M\) of nuclei and electron mass tending to infinity.NEWLINENEWLINEThe paper is divided into five sections. In the introduction, the author gives preliminaries to ab initio molecular dynamics and also the motivation for this paper which is related to stochastic models proposed in [\textit{G. W. Ford} and \textit{M. Kac}, J. Stat. Phys. 46, No. 5--6, 803--810 (1987; Zbl 0682.60069); \textit{G. Ford, M. Kac} and \textit{P. Mazur}, J. Math. Phys. 6, 504--515 (1965; Zbl 0127.21605)] and by \textit{R. Zwanzig} [``Nonlinear generalized Langevin equations'', J. Statist. Phys. 9, No. 3, 215--220 (1973; \url{doi:10.1007/BF01008729})] who derived a Langevin equation for a heavy particle from a Hamiltonian system with the heavy particle coupled through a harmonic interaction potential to a heat bath particle system. In Section 2, the author showed that Zwanzig's model is closely related to the Ehrenfest Hamiltonian system and extends in Sections 4 and 5 ideas presented by Zwanzig [loc. cit.]. Section 3 is related to stability and a consistency argument used to answer the following question: why should the electron initial data be Gibbs distributed? In Section 5, proofs for two theorems given in Section 4 are presented. These theorems contribute to the central problem in statistical mechanics of showing that Hamiltonian dynamics of heavy particles, coupled to a heat bath of many lighter particles with random initial data, can be approximately described by Langevin's equation.NEWLINENEWLINEConsidering this problem at least four new issues are indicated.NEWLINENEWLINE(i) The slow nuclei dynamics compared to the fast electron dynamics is exploited to find a proper Langevin equation without using explicit heat bath …
reviewed by: Dominik Strzałka
description: scientific article; zbMATH DE number 6032266