An Efficient Time-splitting Method for the Ehrenfest Dynamics

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

Cited by in corpus (8)

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• On the Convergence of Time Splitting Methods for Quantum Dynamics in the Semiclassical Regime
• Evolution of hybrid quantum-classical wavefunctions
• Uniform error bounds of time-splitting methods for the nonlinear Dirac equation in the nonrelativistic regime without magnetic potential
• High-order geometric integrators for representation-free Ehrenfest dynamics
• Observable Error Bounds of the Time-splitting Scheme for Quantum-Classical Molecular Dynamics
• Complex fluid models of mixed quantum-classical dynamics
• Koopmon trajectories in nonadiabatic quantum-classical dynamics