Anderson Localization for Time Periodic Random Schrödinger Operators

DOI10.1081/PDE-120019385zbMath1028.81018arXivmath/0209091MaRDI QIDQ4805326

Wei-Min Wang, Avy Soffer

Publication date: 12 May 2003

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0209091

zbMATH Keywords

random Schrödinger operatorFloquet operatorlarge disordertime periodic perturbationsQuasi-energy operatorstability of Anderson localization

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Random linear operators (47B80)

Related Items

Anderson localization for periodically driven systems ⋮ Derivation of Kubo's formula for disordered systems at zero temperature ⋮ Diffusion bound and reducibility for discrete Schrödinger equations with tangent potential ⋮ On the problem of dynamical localization in the nonlinear Schrödinger equation with a random potential ⋮ A rigorous theory of many-body prethermalization for periodically driven and closed quantum systems ⋮ Anderson localization for time quasi-periodic random Schrödinger and wave equations

Cites Work

• Unnamed Item
• Unnamed Item
• Resonances for the AC-Stark effect
• A new proof of localization in the Anderson tight binding model
• Absence of diffusion in the Anderson tight binding model for large disorder or low energy
• Constructive proof of localization in the Anderson tight binding model
• Polynomially decaying transmission for the nonlinear Schrödinger equation in a random medium
• Localization in disordered, nonlinear dynamical systems
• A pure point spectrum of the stochastic one-dimensional Schrödinger operator
• Microlocalization, percolation, and Anderson localization for the magnetic Schrödinger operator with a random potential
• Spectral behavior of quasi periodic potentials
• Schrödinger semigroups
• On the stability of dense point spectrum for self-adjoint operators
• Scattering theory for Hamiltonians periodic in time
• Spectral and stability aspects of quantum chaos