Level spacing and Poisson statistics for continuum random Schrödinger operators

DOI10.4171/JEMS/1033zbMath1467.82037OpenAlexW3115844419MaRDI QIDQ2031668

Yanyan Li

Publication date: 10 June 2021

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jems/1033

zbMATH Keywords

Anderson localizationlevel statisticsMinami estimatePoisson statistics of eigenvalues

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) Random linear operators (47B80)

Related Items (5)

Eigenvalue fluctuations for random elliptic operators in homogenization regime ⋮ On the spatial extent of localized eigenfunctions for random Schrödinger operators ⋮ Local eigenvalue statistics for higher-rank Anderson models after Dietlein–Elgart ⋮ Derivation of Kubo's formula for disordered systems at zero temperature ⋮ A lower Wegner estimate and bounds on the spectral shift function for continuum random Schrödinger operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Level spacing for non-monotone Anderson models
• An eigensystem approach to Anderson localization
• Unique continuation principle for spectral projections of Schrödinger operators and optimal Wegner estimates for non-ergodic random Schrödinger operators
• Erratum to: ``Poisson statistics for eigenvalues of continuum random Schrödinger operators
• Eigenvalue statistics for random Schrödinger operators with non rank one perturbations
• Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method
• A remark on the estimate of a determinant by Minami
• An approach to Wegner's estimate using subharmonicity
• Localization near fluctuation boundaries via fractional moments and applications
• Absence of diffusion in the Anderson tight binding model for large disorder or low energy
• The local structure of the spectrum of the one-dimensional Schrödinger operator
• Localization at large disorder and at extreme energies: an elementary derivation
• Localization for some continuous, random Hamiltonians in \(d\)-dimensions
• Explicit finite volume criteria for localization in continuous random media and applications
• Perturbation theory for linear operators.
• Local fluctuation of the spectrum of a multidimensional Anderson tight binding model
• Simplicity of eigenvalues in Anderson-type models
• Metal--insulator transition in a weakly interacting many-electron system with localized single-particle states
• Scale-free unique continuation estimates and applications to random Schrödinger operators
• Minami's estimate: beyond rank one perturbation and monotonicity
• Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line
• Localization for Schrödinger operators with Poisson random potential
• Correlation estimates in the Anderson model
• On localization in the continuous Anderson-Bernoulli model in higher dimension
• Simplicity of eigenvalues in the Anderson model
• Simplicity of singular spectrum in Anderson-type Hamiltonians
• Local Wegner and Lifshitz tails estimates for the density of states for continuous random Schrödinger operators
• CYCLIC VECTORS IN THE ANDERSON MODEL
• On the Local Eigenvalue Spacings for Certain Anderson-Bernoulli Hamiltonians
• A Dynamical Approach to Random Matrix Theory
• The \(L^p\)-theory of the spectral shift function, the Wegner estimate, and the integrated density of states for some random operators.

This page was built for publication: Level spacing and Poisson statistics for continuum random Schrödinger operators