On the adiabatic theorem when eigenvalues dive into the continuum

DOI10.1142/S0129055X18500113zbMath1392.81123arXiv1612.02354MaRDI QIDQ4569653

Hans Konrad Knörr, Arne Jensen, Gheorghe Nenciu, Horia D. Cornean

Publication date: 27 June 2018

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

Full work available at URL: https://arxiv.org/abs/1612.02354

zbMATH Keywords

adiabatic limitresolvent expansionpropagation estimatesFeshbach methodmesoscopic transportadiabatic pair creationgapless adiabatic theorem

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Atomic physics (81V45) Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics (70H11) Inelastic and multichannel quantum scattering (81U35) Quantum dots, waveguides, ratchets, etc. (81Q37)

Related Items (3)

The adiabatic Wigner-Weisskopf model ⋮ A solvable model of the breakdown of the adiabatic approximation ⋮ Adiabatic theorems for general linear operators with time-independent domains

Cites Work

• Unnamed Item
• Memory effects in non-interacting mesoscopic transport
• The Fermi golden rule and its form at thresholds in odd dimensions
• On adiabatic pair creation
• Existence of the spontaneous pair creation in the external field approximation of Q.E.D
• Spectral properties of Schrödinger operators and time-decay of the wave functions
• Adiabatic theorem without a gap condition
• Adiabatic perturbation theory in quantum dynamics
• A note on the adiabatic theorem without gap condition.
• A geometric approach to the Landauer-Büttiker formula
• Generalized eigenfunctions for Dirac operators near criticality
• On coupling constant thresholds and related eigenvalue properties of Dirac operators.
• A UNIFIED APPROACH TO RESOLVENT EXPANSIONS AT THRESHOLDS

This page was built for publication: On the adiabatic theorem when eigenvalues dive into the continuum