Contrôle et simulations numériques en chimie quantique

Abstract : An important part of simulations in computational quantum chemistry use nowadays very advanced scientific computing techniques. In reaction, this application field witnesses an increasing interest from the applied mathematicians community and provides research topics of high theoretical as well as practical complexity. Having entered this research field during my graduates studies, my researches in computational quantum chemistry have been confirmed in the sequel and are the central topic of this document. The presentation of my works has been divided in thematic chapters. After an introductory chapter on the SchrÄodinger equation and its approximations, the second chapter, dedicated to discretization methods, presents my theoretical contributions on the reduced basis method. The third chapter deals with a posteriori error analysis which, as is the case in real experiments where error bars are provided, allows to give quantitative information on the trust to put in the result of a numerical simulation. This method has been applied to two situations : the computation of the nuclear motion and the electronic structure. Another contribution that uses the same techniques and results in the design of Newton type algorithms for the Kohn-Sham equations is presented in Section 3.4. Switching to the time dependent equations, Chapter 4 introduces a parallel in time numerical scheme for the resolution of the evolution equations. The extension of this approach for the control setting is also given. At the heart of my research in quantum chemistry, the study of the control of quantum phenomena is described in Chapter 5. After a brief introduction I present in Sections 5.2 and 5.3 my studies on the controllability of the bilinear equations that appear in the mathematical description of the lasermatter interaction. These results continue in Section 5.4 with an application to the optimal discrimination of quantum systems. Then in Section 5.5 I give an overview of my contributions on the optimization algorithms used to find suitable laser fields in numerical control simulations. Finally, in Chapter 6 can be found a work on an epidemiological model. Chapter 7 assembles some ongoing or longer term research projects in the continuation of the contributions in the previous Chapters.
Keywords : numerical analysis
Document type :
Habilitation à diriger des recherches
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https://tel.archives-ouvertes.fr/tel-00377193
Contributor : Gabriel Turinici <>
Submitted on : Tuesday, April 21, 2009 - 10:48:44 AM
Last modification on : Thursday, February 7, 2019 - 1:32:09 AM
Long-term archiving on : Thursday, June 10, 2010 - 9:16:32 PM

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Gabriel Turinici. Contrôle et simulations numériques en chimie quantique. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2004. ⟨tel-00377193⟩

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