Quantum dynamics by the constrained adiabatic trajectory method

A. Leclerc, S. Guérin, G. Jolicard, and J. P. Killingbeck
Phys. Rev. A 83, 032113 – Published 16 March 2011

Abstract

We develop the constrained adiabatic trajectory method (CATM), which allows one to solve the time-dependent Schrödinger equation constraining the dynamics to a single Floquet eigenstate, as if it were adiabatic. This constrained Floquet state (CFS) is determined from the Hamiltonian modified by an artificial time-dependent absorbing potential whose forms are derived according to the initial conditions. The main advantage of this technique for practical implementation is that the CFS is easy to determine even for large systems since its corresponding eigenvalue is well isolated from the others through its imaginary part. The properties and limitations of the CATM are explored through simple examples.

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  • Received 1 December 2010

DOI:https://doi.org/10.1103/PhysRevA.83.032113

©2011 American Physical Society

Authors & Affiliations

A. Leclerc1,*, S. Guérin2, G. Jolicard1, and J. P. Killingbeck3

  • 1Institut UTINAM, CNRS UMR 6213, Université de Franche-Comté, Observatoire de Besançon, 41 bis Avenue de l’Observatoire, Boîte Postale 1615, F-25010 Besançon cedex, France
  • 2Laboratoire Interdisciplinaire Carnot de Bourgogne (CNRS UMR 5209, Université de Bourgogne), Boîte Postale 47870, F-21078 Dijon, France
  • 3Centre for Mathematics, University of Hull, Hull HU6 7RX, United Kingdom

  • *Arnaud.Leclerc@utinam.cnrs.fr

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Vol. 83, Iss. 3 — March 2011

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