Stochastic and deterministic molecular dynamics derived from the time-independent Schrödinger equation

Details Stochastic and deterministic molecular dynamics derived from the time-independent Schrödinger equation Stochastic and deterministic molecular dynamics derived from the time-independent Schrödinger equation

2008-12-23

arxiv.org/abs/0812.4338v5

Physics

Mathematical Physics

36 pages: improved convergence rates for Ehrenfest observables with crossing eigenvalues and corrected estimates for wave func

Scientific paper

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.

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