Green's function estimates for lattice Schrödinger operators and applications /

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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Bourgain, Jean, 1954-2018
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, N.J. : Princeton University Press, ©2005.
©2005
Colección:Annals of mathematics studies ; no. 158.
Temas:
Schrödinger operator.
Green's functions.
Hamiltonian systems.
Evolution equations.
Fonctions de Green.
Systèmes hamiltoniens.
Équations d'évolution.
Opérateur de Schrödinger.
MATHEMATICS > Differential Equations > General.
Evolution equations
Green's functions
Hamiltonian systems
Schrödinger operator
Mathematische fysica.
Green-functies.
Hamiltonianen.
Schrödingervergelijking.
Almost Mathieu operator.
Analytic function.
Anderson localization.
Betti number.
Cartan's theorem.
Chaos theory.
Density of states.
Dimension (vector space).
Diophantine equation.
Dynamical system.
Equation.
Existential quantification.
Fundamental matrix (linear differential equation).
Green's function.
Hamiltonian system.
Hermitian adjoint.
Infimum and supremum.
Iterative method.
Jacobi operator.
Linear equation.
Linear map.
Linearization.
Monodromy matrix.
Non-perturbative.
Nonlinear system.
Normal mode.
Parameter space.
Parameter.
Parametrization.
Partial differential equation.
Periodic boundary conditions.
Phase space.
Phase transition.
Polynomial.
Renormalization.
Self-adjoint.
Semialgebraic set.
Special case.
Statistical significance.
Subharmonic function.
Summation.
Theorem.
Theory.
Transfer matrix.
Transversality (mathematics).
Trigonometric functions.
Trigonometric polynomial.
Uniformization theorem.
Acceso en línea:Texto completo
Descripción
Sumario: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."
Descripción Física:1 online resource : illustrations
Bibliografía:Includes bibliographical references.
ISBN:9780691120980
0691120986
9781400837144
1400837146
1322075719
9781322075716

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