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Table of Contents - - Volume - Issue
Ram V. Iyer, Raymond Holsapple and David Doman
© EDP Sciences, SMAI, 2006
Published online by Cambridge University Press: 22 February 2011
DOI: http://dx.doi.org/10.1051/cocv:2005026 (About DOI)
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Jun-Min Wang, Bao-Zhu Guo and Boumediène Chentouf
DOI: http://dx.doi.org/10.1051/cocv:2005030 (About DOI)
Omar Anza Hafsa, Jean-Philippe Mandallena and Gérard Michaille
DOI: http://dx.doi.org/10.1051/cocv:2005031 (About DOI)
Matthias Kurzke
DOI: http://dx.doi.org/10.1051/cocv:2005037 (About DOI)
Krzysztof Chełmiński and Agnieszka Kałamajska
DOI: http://dx.doi.org/10.1051/cocv:2005034 (About DOI)
Fredi Tröltzsch and Daniel Wachsmuth
DOI: http://dx.doi.org/10.1051/cocv:2005029 (About DOI)
Chadi Nour
DOI: http://dx.doi.org/10.1051/cocv:2005032 (About DOI)
Yacine Chitour
DOI: http://dx.doi.org/10.1051/cocv:2005035 (About DOI)
Piotr Grabowski and Frank M. Callier
DOI: http://dx.doi.org/10.1051/cocv:2005027 (About DOI)
Boris Kapitonov, Bernadette Miara and Gustavo Perla Menzala
DOI: http://dx.doi.org/10.1051/cocv:2005028 (About DOI)
Pierpaolo Soravia
DOI: http://dx.doi.org/10.1051/cocv:2005033 (About DOI)
Alexander Y. Khapalov
DOI: http://dx.doi.org/10.1051/cocv:2006001 (About DOI)
Carl-Friedrich Kreiner and Johannes Zimmer
DOI: http://dx.doi.org/10.1051/cocv:2005036 (About DOI)
Fabián Flores-Bazán and Rubén López
DOI: http://dx.doi.org/10.1051/cocv:2006005 (About DOI)
Joseph Gergaud and Thomas Haberkorn
DOI: http://dx.doi.org/10.1051/cocv:2006003 (About DOI)
Sophie Gombao and Jean-Pierre Raymond
DOI: http://dx.doi.org/10.1051/cocv:2006004 (About DOI)
Piermarco Cannarsa and Hélène Frankowska
DOI: http://dx.doi.org/10.1051/cocv:2006002 (About DOI)
Augusto Visintin
DOI: http://dx.doi.org/10.1051/cocv:2006012 (About DOI)
Ginés López and Juan-Aurelio Montero-Sánchez
DOI: http://dx.doi.org/10.1051/cocv:2006009 (About DOI)
Andrei Agrachev and Thomas Chambrion
Nowadays, quantum control appears to be one of the most challenging applications of control theory.
Indeed in many processes in modern technology it is necessary to induce a transition between energy levels of a quantum mechanical system, that usually is a molecule (in photochemistry or in laser spectroscopy) or a spin system (e.g. in nuclear magnetic resonance). In the experiments, excitation and ionization are induced by means of a sequence of external pulses (e.g. lasers or magnetic fields). Usually the transfer should be as fast as possible in order to minimize the effects of relaxation and decoherence that are always present. In most of the cases, the description of such processes translates into a multilinear control system on the unitary group SU(n) or on the group of unitary transformations on a complex infinite dimensional Hilbert space. One of the most promising application is in quantum information processing for the realization of quantum gates (namely the quantum counterpart of the elementary operations AND, OR, NOT).
This paper contains a crucial estimate for the minimum time necessary to induce a transition in a quantum mechanical system. More precisely, for a generic single-input control system on a compact semi-simple Lie group (and in particular on SU(n)), an upper and a lower bound on the minimum time necessary to steer (with unbounded controls) the identity to any other point of the group are provided. The most important byproduct of this paper is that the ideas presented generalize to infinite dimension, allowing to get controllability results for the bilinear Schroedinger equation (as a PDE) by means of Galerkin approximations, as obtained in a recent paper by one of the authors et al.
DOI: http://dx.doi.org/10.1051/cocv:2006007 (About DOI)
Enrique Fernández-Cara, Manuel González-Burgos, Sergio Guerrero and Jean-Pierre Puel
DOI: http://dx.doi.org/10.1051/cocv:2006010 (About DOI)
DOI: http://dx.doi.org/10.1051/cocv:2006011 (About DOI)
Sergio Guerrero
DOI: http://dx.doi.org/10.1051/cocv:2006006 (About DOI)
Emmanuelle Crépeau and Christophe Prieur
DOI: http://dx.doi.org/10.1051/cocv:2006008 (About DOI)
Riccarda Rossi and Giuseppe Savaré
DOI: http://dx.doi.org/10.1051/cocv:2006013 (About DOI)
Reinhard Illner, Horst Lange and Holger Teismann
DOI: http://dx.doi.org/10.1051/cocv:2006014 (About DOI)
Pascal Hébrard and Emmanuel Humbert
DOI: http://dx.doi.org/10.1051/cocv:2006015 (About DOI)
Martin V. Day
DOI: http://dx.doi.org/10.1051/cocv:2006016 (About DOI)
José Carlos Bellido
DOI: http://dx.doi.org/10.1051/cocv:2006018 (About DOI)
Nung Kwan Yip
DOI: http://dx.doi.org/10.1051/cocv:2006019 (About DOI)
Giuseppe Buttazzo, Filippo Santambrogio and Nicolas Varchon
DOI: http://dx.doi.org/10.1051/cocv:2006020 (About DOI)
Gen Qi Xu, Siu Pang Yung and Leong Kwan Li
DOI: http://dx.doi.org/10.1051/cocv:2006021 (About DOI)
Gregory S. Spradlin
DOI: http://dx.doi.org/10.1051/cocv:2006022 (About DOI)
David McCaffrey
DOI: http://dx.doi.org/10.1051/cocv:2006023 (About DOI)
