Computing quantum dynamics in the semiclassical regime
Abstract
The semiclassically scaled time-dependent multi-particle Schr\"odinger 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.
Cite
@article{arxiv.2002.00624,
title = {Computing quantum dynamics in the semiclassical regime},
author = {Caroline Lasser and Christian Lubich},
journal= {arXiv preprint arXiv:2002.00624},
year = {2020}
}
Comments
166 pages. Prepared for Acta Numerica 2020. (Version 2: additional references and some corrections to Version 1.)