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Quantum hydrodynamics: Capturing a reactive scattering resonance

J. Chem. Phys. 123, 054107 (2005); doi:10.1063/1.1994854

Published 11 August 2005

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Sean W. Derrickson and Eric R. Bittner
Department of Chemistry, University of Houston, Houston, Texas 77204

Brian K. Kendrick
Theoretical Division, (T-12, MS-B268), Los Alamos National Laboratory, Los Alamos, New Mexico 87545
The hydrodynamic equations of motion associated with the de Broglie-Bohm formulation of quantum mechanics are solved using a meshless method based upon a moving least-squares approach. An arbitrary Lagrangian-Eulerian frame of reference and a regridding algorithm which adds and deletes computational points are used to maintain a uniform and nearly constant interparticle spacing. The methodology also uses averaged fields to maintain unitary time evolution. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. A new and more robust artificial viscosity algorithm is presented which gives accurate scattering results and is capable of capturing quantum resonances. The methodology is applied to a one-dimensional model chemical reaction that is known to exhibit a quantum resonance. The correlation function approach is used to compute the reactive scattering matrix, reaction probability, and time delay as a function of energy. Excellent agreement is obtained between the scattering results based upon the quantum hydrodynamic approach and those based upon standard quantum mechanics. This is the first clear demonstration of the ability of moving grid approaches to accurately and robustly reproduce resonance structures in a scattering system. ©2005 American Institute of Physics
History: Received 18 April 2005; accepted 14 June 2005; published 11 August 2005
Permalink: http://link.aip.org/link/?JCPSA6/123/054107/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Ta
    Foundations of quantum mechanics; measurement theory
  • 82.20.Ej
    Quantum theory of reaction cross section in chemical kinetics
  • 82.20.Xr
    Quantum effects in rate constants (chemical kinetics) including tunneling, resonances, etc
  • 82.30.-b
    Specific chemical reactions; reaction mechanisms
  • 02.70.Rr
    General statistical methods
  • YEAR: 2005

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PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
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