SPD

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.