Wegner estimates and localization for Gaussian random potentials

DOI10.2977/prims/1145475966zbMath1134.60354OpenAlexW2034178466MaRDI QIDQ1884452

Naomasa Ueki

Publication date: 1 November 2004

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1145475966

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) PDEs in connection with quantum mechanics (35Q40) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (8)

Quantum Hamiltonians with weak random abstract perturbation. II: Localization in the expanded spectrum ⋮ Wegner estimate for discrete Schrödinger operators with Gaussian random potentials ⋮ Low lying spectrum of weak-disorder quantum waveguides ⋮ Low lying eigenvalues of randomly curved quantum waveguides ⋮ Inverse scattering problem for a two dimensional random potential ⋮ Wegner estimate for a nonsign definite generalized alloy type potential ⋮ Wegner estimate and localization for random magnetic fields ⋮ Discrete Schrödinger Operators with Random Alloy-type Potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Absence of diffusion in the Anderson tight binding model for large disorder or low energy
• Localization in general one-dimensional random systems. II: Continuum Schrödinger operators
• Anderson localization for random Schrödinger operators with long range interactions
• Localization for some continuous, random Hamiltonians in \(d\)-dimensions
• Local boundedness and continuity for weak solutions of \(-(\nabla-ib)^ 2u+Vu=0\)
• Existence of the density of states for multi-dimensional continuum Schrödinger operators with Gaussian random potentials
• Anderson localization for 2D discrete Schrödinger operators with random magnetic fields
• Explicit finite volume criteria for localization in continuous random media and applications
• The Wegner estimate and the integrated density of states for some random operators
• Wegner estimate for sparse and other generalized alloy type potentials
• The integrated density of states for some random operators with nonsign definite potentials
• A characterization of the Anderson metal-insulator transport transition
• Localization for some continuous random Schrödinger operators
• Wegner estimates and Anderson localization for alloy-type potentials
• CONTINUITY PROPERTIES OF SCHRÖDINGER SEMIGROUPS WITH MAGNETIC FIELDS
• Operator kernel estimates for functions of generalized Schrödinger operators
• Spectral localization by Gaussian random potentials in multi-dimensional continuous space.
• The \(L^p\)-theory of the spectral shift function, the Wegner estimate, and the integrated density of states for some random operators.
• Bootstrap multiscale analysis and localization in random media
• The absolute continuity of the integrated density of states for magnetic Schrödinger operators with certain unbounded random potentials

This page was built for publication: Wegner estimates and localization for Gaussian random potentials