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Computing quantum dynamics in the semiclassical regime

Published online by Cambridge University Press:  30 November 2020

Caroline Lasser  and
Christian Lubich
Caroline Lasser
Affiliation:
Fakultät für Mathematik, Technische Universität München, 85748Garching bei München, Germany E-mail: classer@ma.tum.de
Christian Lubich
Affiliation:
Mathematisches Institut, Universität Tübingen, 72076Tübingen, Germany E-mail: lubich@na.uni-tuebingen.de
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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.

Type
Research Article
Information
Acta Numerica , Volume 29 , May 2020 , pp. 229 - 401
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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