Computing quantum dynamics in the semiclassical regime

Abstract

The semiclassically scaled time-dependent multi-particle Schrödinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This paper reviews and studies numerical approaches that are robust to the small semiclassical parameter. We present and analyse variationally evolving Gaussian wave packets, Hagedorn's semiclassical wave packets, continuous superpositions of both thawed and frozen Gaussians, and Wigner function approaches to the direct computation of expectation values of observables. Making good use of classical mechanics is essential for all these approaches. The arising aspects of time integration and high-dimensional quadrature are also discussed.

166 pages. Prepared for Acta Numerica 2020. (Version 2: additional references and some corrections to Version 1.)

References in corpus (2)

• Nonadiabatic nuclear dynamics of the ammonia cation studied by surface hopping classical trajectory calculations
• Symmetry and Conservation Laws in Semiclassical Wave Packet Dynamics

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