Hiérarchie de modèles en optique quantique : de Maxwell-Bloch à Schrodinger non-linéaire / Brigitte Bidégaray-Fesquet

Auteur principal : Bidégaray-Fesquet, Brigitte, 1969-, AuteurType de document : MonographieCollection : Mathématiques et applications, 49Langue : français.Pays: Allemagne.Éditeur : Berlin : Springer-Verlag, 2006Description : 1 vol. (XIII-171 p.) : ill. ; 24 cmISBN: 3540272380.ISSN: 1154-483X.Bibliographie : Notes bibliogr. Index.Sujet MSC : 81V80, Applications of quantum theory to specific physical systems, Quantum optics
35L45, PDEs - Hyperbolic equations and hyperbolic systems, Initial value problems for first-order hyperbolic systems
35Q55, PDEs of mathematical physics and other areas of application, NLS equations (nonlinear Schrödinger equations)
35Q60, PDEs of mathematical physics and other areas of application, PDEs in connection with optics and electromagnetic theory
65M06, Numerical analysis, Finite difference methods for initial value and initial-boundary value problems involving PDEs
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Notes bibliogr. Index

... The book appears to be relevant in this respect since it cross-fertilizes such a fundamental field of research in physics in two important ways. Firstly, it is addressed to a public well educated in mathematics. Secondly, it gives a good description of numerical methods and their justification and solves fundamental sets of equations of quantum optics, such as the Maxwell-Bloch equations. This kind of book, when written well like this one, is always welcome. As a physicist the hope is to see this kind of achievement also for other aspects of physics that are not so well known to mathematicians but nevertheless worth studying.
The book is divided into three parts. In Part I the full Maxwell-Bloch model is introduced. In this part the Cauchy problem for these equations is discussed. The presentation is satisfactory both for physicists and for mathematicians. Asymptotic methods and a hierarchy of models are presented in Part II. Finally, in Part III, considerations about numerical solutions of Maxwell-Bloch equations are given. This is a quite recent field of analysis in quantum optics (the author refers to works of Ziolkowski in Physical Review A published in 1995 and after). Such an approach is invaluable, as we learn also from other fields of physics, as the possibility of analyzing real systems often overcomes our ability to solve such equations.
My overall impression is that the author achieves her aim and the book can be used, satisfactorily, in courses for graduate students, but also for researchers, both mathematicians and physicists, aiming to enter into this exciting field of research. (MathSciNet)

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