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arXiv · 1701.05941

An Efficient Time-splitting Method for the Ehrenfest Dynamics

Di Fang·Shi Jin·Christof Sparber
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Abstract

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 Schr\"odinger-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 - in addition to classical mesh sizes for the Liouville equation. Numerical examples illustrate the validity of our meshing strategy.

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BibTeXRIS

Di Fang, Shi Jin, Christof Sparber. 2017-01-20. An Efficient Time-splitting Method for the Ehrenfest Dynamics. https://doi.org/10.1137/17m1112789

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