Physics – Mathematical Physics
Scientific paper
2007-12-21
Physics
Mathematical Physics
39 pages: modeling and analysis in separate sections. Formulation of initial data simplified
Scientific paper
Stochastic Langevin molecular dynamics for nuclei is derived from the Ehrenfest Hamiltonian system (also called quantum classical molecular dynamics) in a Kac-Zwanzig 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 $\mathcal{O}(M^{-1/2})$ friction and $o(M^{-1/2})$ diffusion terms visible. The initial electron probability distribution is a Gibbs density at low temperture, derived by a stability and consistency argument: starting with any equilibrium measure of the Ehrenfest Hamiltonian system, the initial electron distribution is sampled from the equilibrium measure conditioned on the nuclei positions, which after long time leads to the nuclei positions in a Gibbs distribution (i.e. asymptotic stability); by consistency the original equilibrium measure is then a Gibbs measure.The diffusion and friction coefficients in the Langevin equation satisfy the Einstein's fluctuation-dissipation relation.
No associations
LandOfFree
Langevin molecular dynamics derived from Ehrenfest dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Langevin molecular dynamics derived from Ehrenfest dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Langevin molecular dynamics derived from Ehrenfest dynamics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-696613