Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function

DOI10.4171/JST/267zbMath1442.81027arXiv1701.02956MaRDI QIDQ2335834

Peter Müller, Adrian Dietlein, Martin Gebert

Publication date: 15 November 2019

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.02956

zbMATH Keywords

random Schrödinger operatorsspectral shift functionAnderson orthogonality

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

Stability of a Szegő-type asymptotics ⋮ Band edge localization beyond regular Floquet eigenvalues ⋮ 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
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The exponent in the orthogonality catastrophe for Fermi gases
• Sampling inequality for \(L^2\)-norms of eigenfunctions, spectral projectors, and Weyl sequences of Schrödinger operators
• Unique continuation principle for spectral projections of Schrödinger operators and optimal Wegner estimates for non-ergodic random Schrödinger operators
• Operator theoretic methods for the eigenvalue counting function in spectral gaps
• Anderson's orthogonality catastrophe for one-dimensional systems
• Moment analysis for localization in random Schrödinger operators
• Bounds on the spectral shift function and the density of states
• Scale-free uncertainty principles and Wegner estimates for random breather potentials
• Localization near fluctuation boundaries via fractional moments and applications
• The index of a pair of projections
• An optimal \(L^p\)-bound on the Krein spectral shift function.
• A constructive characterization of the Sobolev and Besov classes
• Anderson's orthogonality catastrophe
• An improved Combes-Thomas estimate of magnetic Schrödinger operators
• Trace class conditions for functions of Schrödinger operators
• Existence and regularity properties of the integrated density of states of random Schrödinger operators
• An optimal Wegner estimate and its application to the global continuity of the integrated density of states for random Schrödinger operators
• New characterizations of the region of complete localization for random Schrödinger operators
• \(c_ p\)
• Schrödinger semigroups
• Anderson’s orthogonality catastrophe in one dimension induced by a magnetic field
• The spectral shift function for compactly supported perturbations of Schrödinger operators on large bounded domains
• Small Perturbations and the Eigenvalues of the Laplacian on Large Bounded Domains
• CONTINUITY PROPERTIES OF SCHRÖDINGER SEMIGROUPS WITH MAGNETIC FIELDS
• A Bound on the Averaged Spectral Shift Function and a Lower Bound on the Density of States for Random Schrödinger Operators on ${\mathbb{R}}^{\boldsymbol{d}}$
• Operator kernel estimates for functions of generalized Schrödinger operators
• The asymptotics of an eigenfunction-correlation determinant for Dirac-δ perturbations
• Measure and integration theory
• Caught by disorder. Bound states in random media
• The \(L^p\)-theory of the spectral shift function, the Wegner estimate, and the integrated density of states for some random operators.
• Finite-volume fractional-moment criteria for Anderson localization