# T:A:L:K:S

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 title: Stochastic molecular dynamics name: Szepessy first name: Anders location/conference: SPDE09 PRESENTATION-link: http://www.dfg-spp1324.de/download/spde09/material/szepessy.pdf abstract: Starting from the Schrödinger equation for nuclei-electron systems I will show two stochastic molecular dynamics effects derived from a Gibbs distribution: \begin{itemize} \item When the ground state has a large spectral gap a precise Langevin equation for molecular dynamics approximates observables from the Schrödinger equation. \item If the gap is smaller in some sense, the temperature also gives a precise correction to the ab initio ground state potential energy. \end{itemize} The two approximation results holds with a rate depending on the spectral gap and the ration of nuclei and electron mass. \\ I will also give an example of course-graining this stochastic Langevin molecular dynamics equation to obtain a continuum stochastic partial differential equation for phase transitions.