Resonance theory for periodic Schrödinger operators

DOI10.24033/bsmf.2134zbMath0723.35059OpenAlexW1677880606MaRDI QIDQ3211714

Christian Gérard

Publication date: 1990

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=BSMF_1990__118_1_27_0

zbMATH Keywords

resolventperiodic Schrödinger operatorVan Hove singularities

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) PDEs in connection with quantum mechanics (35Q40) Schrödinger operator, Schrödinger equation (35J10) Many-body theory; quantum Hall effect (81V70)

Related Items (11)

Strong magnetic fields, Dirichlet boundaries, and spectral gaps ⋮ Finite-size effects in response functions of molecular systems ⋮ Efficient extraction of resonant states in systems with defects ⋮ Wave packets in honeycomb structures and two-dimensional Dirac equations ⋮ Virtual bound levels in a gap of the essential spectrum of the weakly perturbed periodic Schrödinger operator ⋮ Spectral theory for Borel sets in \(\mathbb{R}{}^ n\) of finite measure ⋮ An overview of periodic elliptic operators ⋮ Valeurs propres et résonances au voisinage d'un seuil ⋮ Defect modes for dislocated periodic media ⋮ Spectral shift function and resonances for slowly varying perturbations of periodic Schrödinger operators ⋮ A local trace formula for resonances of perturbed periodic Schrödinger operators.

Cites Work

• Fredholm resolvents of meromorphic kernels with complex parameters: A Landau singularity and the associated equations of type U in a non- holonomic case
• A local isotopy lemma
• On the singularities of the solution to the Cauchy problem with singular data in the complex domain
• Bimeromorphic smoothing of a complex-analytic space
• Theory of Bloch waves
• Resonance theory in atom-surface scattering
• Applications of an isotopy theorem
• Spectral properties of many-body Schrödinger operators with dilatation- analytic interactions
• The determinant theory in Banach spaces
• Singular Points of Complex Hypersurfaces. (AM-61)
• Le calcul différentiel et intégral sur une variété analytique complexe. (Problème de Cauchy. III.)
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