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    Green's Function Estimates for Lattice Schrödinger Operators and Applications
    Green's Function Estimates for Lattice Schrödinger Operators and Applications
    Green's Function Estimates for Lattice Schrödinger Operators and Applications
    Ebook160 pages3 hours

    Green's Function Estimates for Lattice Schrödinger Operators and Applications

    By Jean Bourgain

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    About this ebook

    This book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schrödinger operators and the theory of quasi-periodicity in Hamiltonian evolution equations. The physical motivation of these models extends back to the works of Rudolph Peierls and Douglas R. Hofstadter, and the models themselves have been a focus of mathematical research for two decades. Jean Bourgain here sets forth the results and techniques that have been discovered in the last few years. He puts special emphasis on so-called "non-perturbative" methods and the important role of subharmonic function theory and semi-algebraic set methods. He describes various applications to the theory of differential equations and dynamical systems, in particular to the quantum kicked rotor and KAM theory for nonlinear Hamiltonian evolution equations.


    Intended primarily for graduate students and researchers in the general area of dynamical systems and mathematical physics, the book provides a coherent account of a large body of work that is presently scattered in the literature. It does so in a refreshingly contained manner that seeks to convey the present technological "state of the art."

    LanguageEnglish
    PublisherPrinceton University Press
    Release dateNov 1, 2004
    ISBN9781400837144
    Green's Function Estimates for Lattice Schrödinger Operators and Applications
    Author

    Jean Bourgain

    Jean Bourgain is Professor of Mathematics at the Institute for Advanced Study and J. Doob Professor of Mathematics at the University of Illinois, Urbana-Champaign. He is the author of Global Solutions of Nonlinear Schrödinger Equations.

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