AN EFFICIENT TIME-SPLITTING METHOD FOR THE EHRENFEST DYNAMICS.

The Ehrenfest dynamics, representing a quantum-classical mean-field type coupling, is a widely used approximation in quantum molecular dynamics. In this paper, we propose a time-splitting method for an Ehrenfest dynamics, in the form of a nonlinearly coupled Schrödinger-Liouville system. We prove that our splitting scheme is stable uniformly with respect to the semiclassical parameter and, moreover, that it preserves a discrete semiclassical limit. Thus one can accurately compute physical observables using time steps induced only by the classical Liouville equation, i.e., independent of the small semiclassical parameter and, moreover, that it preserves a discrete semiclassical limit. Thus one can accurately compute physical observables using time steps induced only by the classical Liouville equation, i.e., independent of the small semiclassical parameter-in addition to classical mesh sizes for the Liouville equation. Numerical examples illustrate the validity of our meshing strategy. [ABSTRACT FROM AUTHOR]