Localization in general one-dimensional random systems. II: Continuum Schrödinger operators
From MaRDI portal
Publication:1098495
DOI10.1007/BF01217682zbMath0637.60080OpenAlexW2914320231MaRDI QIDQ1098495
Publication date: 1987
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01217682
localizationpure point spectrumLyapunov exponentexponential decay of the Green functionSchrödinger equation with random potential
Random operators and equations (aspects of stochastic analysis) (60H25) Weyl theory and its generalizations for ordinary differential equations (34B20) PDEs with randomness, stochastic partial differential equations (35R60)
Related Items (46)
Efficient localization bounds in a continuous \(N\)-particle Anderson model with long-range interaction ⋮ Moment analysis for localization in random Schrödinger operators ⋮ THE DENSITY OF STATES AND THE SPECTRAL SHIFT DENSITY OF RANDOM SCHRÖDINGER OPERATORS ⋮ Localization in general one dimensional random systems. I: Jacobi matrices ⋮ Localization in single Landau bands ⋮ Wegner estimates and localization for Gaussian random potentials ⋮ Continuity of the integrated density of states on random length metric graphs ⋮ Localization for some continuous random Schrödinger operators ⋮ Unnamed Item ⋮ Twelve tales in mathematical physics: An expanded Heineman prize lecture ⋮ Localization for off-diagonal disorder and for continuous Schrödinger operators ⋮ Bounds on the spectral shift function and the density of states ⋮ Local Wegner and Lifshitz tails estimates for the density of states for continuous random Schrödinger operators ⋮ Unnamed Item ⋮ Localization for Schrödinger operators with effective barriers ⋮ Sturm-Liouville operators in the half axis with local perturbations ⋮ $\mathbf {\operatorname {SL} _2({\mathbb {R}})}$, exponential Herglotz representations, and spectral averaging ⋮ Landau Hamiltonians with random potentials: Localization and the density of states ⋮ Singular continuous spectrum is generic ⋮ Anderson localization for the 1-d Schrödinger operator with white noise potential ⋮ Localization properties of the Chalker-Coddington model ⋮ Wegner estimates for sign-changing single site potentials ⋮ Localization for random unitary operators ⋮ Spectral averaging, perturbation of singular spectra, and localization ⋮ Inverse scattering problem for a two dimensional random potential ⋮ Wegner estimate for a nonsign definite generalized alloy type potential ⋮ Supersymmetric quantum mechanics with Lévy disorder in one dimension ⋮ Exponential Localization for Multi-Dimensional Schrödinger Operator with Random Point Potential ⋮ An optimal Wegner estimate and its application to the global continuity of the integrated density of states for random Schrödinger operators ⋮ Widths of the Hall conductance plateaus ⋮ Unnamed Item ⋮ Generalized eigenvalue-counting estimates for some random acoustic operators ⋮ Half-line Schrödinger operators with no bound states ⋮ Regularity of the surface density of states ⋮ Sturm–Liouville operators in the half axis with shifted potentials ⋮ Singular continuous spectrum in a class of random Schrödinger operators ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Finite Trotter approximation to the averaged mean square distance in the Anderson model ⋮ Non-monotonic random Schrödinger operators: The Anderson model ⋮ Localization for random Schrödinger operators on \(L^ 2 (\mathbb{R}^ d)\): a semiclassical model ⋮ The Wegner estimate and the integrated density of states for some random operators ⋮ Strategies in localization proofs for one-dimensional random Schrödinger operators ⋮ The integrated density of states for some random operators with nonsign definite potentials ⋮ On the Lipschitz continuity of the integrated density of states for sign-indefinite potentials ⋮ Two-parameter spectral averaging and localization for non-monotonic random Schrödinger operators
Cites Work
- On absence of diffusion near the bottom of the spectrum for a random Schrödinger operator on \(L^ 2({\mathbb{R}}^ v)^+\)
- One-dimensional Schrödinger operators with random or deterministic potentials: New spectral types
- Constructive proof of localization in the Anderson tight binding model
- Support theorems for random Schrödinger operators
- Anderson localization for multi-dimensional systems at large disorder or large energy
- Remark on the absence of absolutely continuous spectrum for d-dimensional Schrödinger operators with random potential for large disorder or low energy
- Localization in general one dimensional random systems. I: Jacobi matrices
- Localization for off-diagonal disorder and for continuous Schrödinger operators
- Sur le spectre des opérateurs aux différences finies aléatoires
- Exponential localization in one dimensional disordered systems
- A pure point spectrum of the stochastic one-dimensional Schrödinger operator
- Schrödinger semigroups
- Singular continuous spectrum under rank one perturbations and localization for random hamiltonians
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Localization in general one-dimensional random systems. II: Continuum Schrödinger operators
