Stochastic and deterministic molecular dynamics derived from the time-independent Schr\"odinger equation
Abstract
Ehrenfest, Born-Oppenheimer, Langevin and Smoluchowski dynamics are shown to be accurate approximations of time-independent Schr\"odinger observables for a molecular system avoiding caustics, in the limit of large ratio of nuclei and electron masses, without assuming that the nuclei are localized to vanishing domains. The derivation, based on a Hamiltonian system interpretation of the Schr\"odinger equation and stability of the corresponding Hamilton-Jacobi equation, bypasses the usual separation of nuclei and electron wave functions, includes crossing electron eigenvalues, and gives a different perspective on the Born-Oppenheimer approximation, Schr\"odinger Hamiltonian systems, stochastic electron equilibrium states and numerical simulation in molecular dynamics modeling.
Keywords
Cite
@article{arxiv.0812.4338,
title = {Stochastic and deterministic molecular dynamics derived from the time-independent Schr\"odinger equation},
author = {Anders Szepessy},
journal= {arXiv preprint arXiv:0812.4338},
year = {2010}
}
Comments
36 pages: improved convergence rates for Ehrenfest observables with crossing eigenvalues and corrected estimates for wave functions approximating electron eigenstates; stability proved for crossing electron eigenvalues, temperature dependent drift correction included