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Langevin molecular dynamics derived from Ehrenfest dynamics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2011 (English)In: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 21, no 11, 2289-2334 p.Article in journal (Refereed) Published
Abstract [en]

Stochastic Langevin molecular dynamics for nuclei is derived from the Ehrenfest Hamiltonian system (also called quantum classical molecular dynamics) in a KacZwanzig setting, with the initial data for the electrons stochastically perturbed from the ground state and the ratio M of nuclei and electron mass tending to infinity. The Ehrenfest nuclei dynamics is approximated by the Langevin dynamics with accuracy o(M-1/2) on bounded time intervals and by o(1) on unbounded time intervals, which makes the small O(M -1/2) friction and o(M-1/2) diffusion terms visible. The initial electron probability distribution is a Gibbs density at low temperature, motivated by a stability and consistency argument. The diffusion and friction coefficients in the Langevin equation satisfy the Einstein's fluctuationdissipation relation.

Place, publisher, year, edition, pages
World Scientific, 2011. Vol. 21, no 11, 2289-2334 p.
Keyword [en]
ab initio molecular dynamics, Brownian particle, Ehrenfest dynamics, Gibbs distribution, heat bath, Langevin equation, MoriZwanzig theory, quantum classical molecular dynamics
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-46459DOI: 10.1142/S0218202511005751ISI: 000298499100006OAI: oai:DiVA.org:kth-46459DiVA: diva2:453722
Funder
Swedish Research Council, 621-2010-5647Swedish eā€Science Research Center
Note
QC 20111103Available from: 2011-11-03 Created: 2011-11-03 Last updated: 2017-12-08Bibliographically approved

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