Scattering on the system of the sparse bumps: multidimensional case

DOI10.1080/00036819908840711zbMath1022.47510OpenAlexW2045542573MaRDI QIDQ4487767

Boris Vainberg, Stanislav Alekseevich Molchanov

Publication date: 25 June 2000

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036819908840711

zbMATH Keywords

Schrödinger operatorspectrumcoupling constantmultiscatteringsparse potentialspectral bifurcationrandom amplitudesAnderson conjecture

Mathematics Subject Classification ID

Related Items (15)

Large Time Behavior of Solutions to Difference Wave Operators ⋮ Schrödinger operators with complex sparse potentials ⋮ On the spectral estimates for the Schrödinger operator on \(\mathbb Z^d\), \(d \geqslant 3\) ⋮ Anderson-like transition for a class of random sparse models in \(d\geq 2\) dimensions ⋮ Extremal theory for spectrum of random discrete Schrödinger operator. II. Distributions with heavy tails ⋮ Bands of pure absolutely continuous spectrum for lattice Schrödinger operators with a more general long range condition ⋮ Essential spectrum of a periodic waveguide with non-periodic perturbation ⋮ Completeness for sparse potential scattering ⋮ Spectral estimates for Schrödinger operators with sparse potentials on graphs ⋮ Wave Propagation through sparse potential barriers ⋮ Waves in a plane rectangular lattice of thin elastic waveguides ⋮ Imperfectly grown periodic medium: absence of localized states ⋮ Absence of \(l^1\) eigenfunctions for lattice operators with fast local periodic approximation ⋮ Boris Rufimovich Vainberg ⋮ The Molchanov--Vainberg Laplacian

Cites Work

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• Singular continuous measures in scattering theory
• Localization at large disorder and at extreme energies: an elementary derivation
• Extended states in the Anderson model on the Bethe lattice
• Singular continuous spectrum under rank one perturbations and localization for random hamiltonians

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