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
Tabla de Contenidos:
  • Frontmatter
  • Contents
  • Acknowledgment
  • Chapter 1. Introduction
  • Chapter 2. Transfer Matrix and Lyapounov Exponent
  • Chapter 3. Herman's Subharmonicity Method
  • Chapter 4. Estimates on Subharmonic Functions
  • Chapter 5. LDT for Shift Model
  • Chapter 6. Avalanche Principle in SL
  • Chapter 7. Consequences for Lyapounov Exponent, IDS, and Green's Function
  • Chapter 8. Refinements
  • Chapter 9. Some Facts about Semialgebraic Sets
  • Chapter 10. Localization
  • Chapter 11. Generalization to Certain Long-Range Models
  • Chapter 12. Lyapounov Exponent and Spectrum
  • Chapter 13. Point Spectrum in Multifrequency Models at Small Disorder
  • Chapter 14. A Matrix-Valued Cartan-Type Theorem
  • Chapter 15. Application to Jacobi Matrices Associated with Skew Shifts
  • Chapter 16. Application to the Kicked Rotor Problem
  • Chapter 17. Quasi-Periodic Localization on the Z
  • Chapter 18. An Approach to Melnikov's Theorem on Persistency of Nonresonant Lower Dimension Tori
  • Chapter 19. Application to the Construction of Quasi-Periodic Solutions of Nonlinear Schrödinger Equations
  • Chapter 20. Construction of Quasi-Periodic Solutions of Nonlinear Wave Equations
  • Appendix.

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