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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.17053 |
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Table of Contents:
- This paper is devoted to the construction of approximations of the propagator associated with a semi-classical matrix-valued Schrödinger operator with symbol presenting smooth eigenvalues crossings. Inspired by the approach of the theoretical chemists Herman and Kluk who propagated continuous superpositions of Gaussian wave-packets for scalar equations, we consider frozen and thawed Gaussian initial value representations that incorporate classical transport and branching processes along a hopping hypersurface. Based on the Gaussian wave-packet framework, our result relies on an accurate analysis of the solutions of the associated Schrödinger equation for data that are vector-valued wave-packets. We prove that these solutions are asymptotic to wavepackets at any order in terms of the semi-classical parameter.