### Stochastic molecular dynamics

Szepessy, A *(KTH NADA)*

Thursday 01 July 2010, 15:40-16.30

Seminar Room 1, Newton Institute

#### Abstract

Starting from the Schrödinger equation for nuclei-electron systems I will show two stochastic molecular dynamics effects derived from a Gibbs distribution:
- when the ground state has a large spectral gap a precise Langevin equation for molecular dynamics approximates observables from the Schrödinger equation
- if the gap is smaller in some sense, the temperature also gives a precise correction to the ab initio ground state potential energy.
The two approximation results holds with a rate depending on the spectral gap and the ratio of nuclei and electron mass.
I will also give an example of coarse-graining this stochastic Langevin molecular dynamics equation to obtain a continuum stochastic partial differential equation for phase transitions.

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