Two-parameter spectral averaging and localization for non-monotonic random Schrödinger operators

DOI10.1090/S0002-9947-00-02674-XzbMath0978.81021OpenAlexW1626034296MaRDI QIDQ4517457

Günter Stolz, Dirk Buschmann

Publication date: 22 November 2000

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-00-02674-x

zbMATH Keywords

random Schrödinger operatorsone-dimensionalinverse spectral theoryPoisson modelrandom displacement modellocalization problem

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Random operators and equations (aspects of stochastic analysis) (60H25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Quantum stochastic calculus (81S25) Random linear operators (47B80)

Related Items (15)

$\mathbf {\operatorname {SL} _2({\mathbb {R}})}$, exponential Herglotz representations, and spectral averaging ⋮ Localization for the random displacement model ⋮ Localization for the random displacement model at weak disorder ⋮ Localization in asymmetric random displacements models with infinite range of interaction ⋮ Spectral averaging techniques for Jacobi matrices ⋮ Generic sets in spaces of measures and generic singular continuous spectrum for Delone Hamiltonians ⋮ Minimizing the ground state energy of an electron in a randomly deformed lattice ⋮ Understanding the Random Displacement Model: From Ground State Properties to Localization ⋮ Anderson localization in discrete random displacements models ⋮ An optimal result on localization in random displacements models ⋮ The Wegner estimate and the integrated density of states for some random operators ⋮ Wegner estimate for sparse and other generalized alloy type potentials ⋮ Strategies in localization proofs for one-dimensional random Schrödinger operators ⋮ The spectral minimum for random displacement models ⋮ On the Lipschitz continuity of the integrated density of states for sign-indefinite potentials

Cites Work

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