https://doi.org/10.1140/epjs/s11734-023-00924-3
Regular Article
Coping with the node problem in resonant scattering simulations using quantum trajectories: an efficient and accurate combined analytical-numerical scheme
1
Laboratoire Univers et Particules de Montpellier, UMR-CNRS 5299, Université de Montpellier, Place Eugène Bataillon, 34095, Montpellier, France
2
Department of Physics, Rutgers University, 07102, Newark, NJ, USA
b
yohann.scribano@umontpellier.fr
Received:
30
January
2023
Accepted:
2
July
2023
Published online:
4
August
2023
We report an efficient approach to accurately and efficiently compute transmission probabilities in resonant deep tunneling regime. Dynamical systems subjects to this phenomenon prove hard to simulate numerically even with exact methods, which motivates new methodological developments owing to the impact resonant phenomena have in several processes such as chemical reactions and electronic transport. Our approach is based on the original reformulation of stationary quantum scattering as the propagation of a quantum trajectory in extended phase space. The present paper discusses in detail the node problem occurring to the time-independent quantum trajectory method in this very challenging situation, and introduces an efficient semi-analytical node-skipping scheme to circumvent expensive numerical integration in their vicinity. We illustrate how this numerical extension allows to treat all regimes of quantum tunneling with great versatility by comparison to existing approaches of the litterature. The quantum trajectory, thus, represents a very promising tool for the study of complex chemical reactions characterized by resonant tunneling effect.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
