Extended States for the Schrödinger Operator with Quasi-periodic Potential in Dimension Two

DOI10.1090/memo/1239zbMath1442.35003arXiv1408.5660OpenAlexW2963482387MaRDI QIDQ5383913

Roman Shterenberg, Yulia E. Karpeshina

Publication date: 20 June 2019

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

Full work available at URL: https://arxiv.org/abs/1408.5660

zbMATH Keywords

absolutely continuous spectrumisoenergetic curves

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) General theory of partial differential operators (47F05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

Related Items (7)

Ballistic transport for the Schrödinger operator with limit-periodic or quasi-periodic potential in dimension two ⋮ Approximate normal forms via Floquet-Bloch theory: Nehorošev stability for linear waves in quasiperiodic media ⋮ Multidimensional Schrödinger operators whose spectrum features a half-line and a Cantor set ⋮ Mini-workshop: Reflectionless operators: the Deift and Simon conjectures. Abstracts from the mini-workshop held October 22--28, 2017 ⋮ Absence of eigenvalues of analytic quasi-periodic Schrödinger operators on \({\mathbb{R}}^d\) ⋮ On the spectrum of multi-frequency quasiperiodic Schrödinger operators with large coupling ⋮ Ballistic transport for Schrödinger operators with quasi-periodic potentials

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