Resonances under rank-one perturbations

DOI10.1063/1.4989882zbMath1372.81037arXiv1707.01597OpenAlexW3099804836MaRDI QIDQ5366985

Olivier Bourget, Claudio Fernandez, Rafael René del Río Castillo, Víctor Cortés

Publication date: 10 October 2017

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.01597

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sturm-Liouville theory (34B24) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) General spectral theory of ordinary differential operators (34L05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) (2)-body potential quantum scattering theory (81U05) Nonlocal and multipoint boundary value problems for ordinary differential equations (34B10)

Related Items (4)

Singular rank one perturbations ⋮ Inverse eigenvalue problems for rank one perturbations of the Sturm-Liouville operator ⋮ Asymptotics of the Schrödinger operator levels for a crystal film with a nonlocal potential ⋮ Inverse eigenvalue problems for singular rank one perturbations of a Sturm-Liouville operator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Energy-time uncertainty principle and lower bounds on sojourn time
• On a theorem of Kac and Gilbert
• On the lifetime of quasi-stationary states in non-relativistic QED
• Spectral theory of ordinary differential operators
• Exponential decay near resonance, without analyticity
• Resonances, spectral concentration and exponential decay
• The Livsic matrix in perturbation theory
• Renormalization group analysis of spectral problems in quantum field theory
• Quantum electrodynamics of confined nonrelativistic particles
• Scattering theory: some old and new problems
• Perturbation theory for linear operators.
• Introduction to spectral theory. With applications to Schrödinger operators
• Metastable states when the Fermi golden rule constant vanishes
• A general resonance theory based on Mourre's inequality
• Spectral concentration near embedded eigenvalues
• Smooth Spectral Calculus
• SPECTRAL RENORMALIZATION GROUP AND LOCAL DECAY IN THE STANDARD MODEL OF NON-RELATIVISTIC QUANTUM ELECTRODYNAMICS
• A UNIFIED APPROACH TO RESOLVENT EXPANSIONS AT THRESHOLDS
• SCATTERING THEORY FOR LATTICE OPERATORS IN DIMENSION d ≥ 3
• Behavior of the survival probability in some one-dimensional problems
• On the perturbation of spectra

This page was built for publication: Resonances under rank-one perturbations