Stochastic molecular dynamics
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
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.