Low-rank numerical approximations for high-dimensional Lindblad equations

C. Le Bris and P. Rouchon
Phys. Rev. A 87, 022125 – Published 27 February 2013

Abstract

A systematic numerical approach to approximate high-dimensional Lindblad equations is described. It is based on a deterministic rank m approximation of the density operator, the rank m being the only parameter to adjust. From a known initial density operator, this rank m approximation gives at each time step an estimate of its largest m eigenvalues with their associated eigenvectors. A numerical integration scheme is also proposed. Its numerical efficiency in the case of a rank m=12 approximation is demonstrated for oscillation revivals of 50 atoms interacting resonantly with a slightly damped coherent quantized field of 200 photons.

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  • Received 14 November 2012

DOI:https://doi.org/10.1103/PhysRevA.87.022125

©2013 American Physical Society

Authors & Affiliations

C. Le Bris1,* and P. Rouchon2,†

  • 1École Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, France and INRIA Rocquencourt, MICMAC project-team, Domaine de Voluceau, Boîte Postale 105, 78153 Le Chesnay Cedex, France
  • 2Mines-ParisTech, Mathématiques et Systèmes, Centre Automatique et Systèmes, 60, bd Saint-Michel, 75006 Paris, France

  • *lebris@cermics.enpc.fr
  • pierre.rouchon@mines-paristech.fr

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Vol. 87, Iss. 2 — February 2013

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