The adiabatic limit of Schrödinger operators on fibre bundles

DOI10.1007/s00208-016-1421-2zbMath1371.58010arXiv1402.0382OpenAlexW3105149944MaRDI QIDQ522643

Stefan Teufel, Jonas Lampart

Publication date: 18 April 2017

Published in: Mathematische Annalen, Microlocal Methods in Mathematical Physics and Global Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.0382

zbMATH Keywords

eigenvalueasymptoticsSchrödinger operatorRiemannian manifoldRiemannian submersiontime dependent Schrödinger equationadiabatic limitfibre bundlequantum waveguideseigenband

Mathematics Subject Classification ID

Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Spectral theory; eigenvalue problems on manifolds (58C40) Perturbations of PDEs on manifolds; asymptotics (58J37)

Related Items (15)

REDUCTION OF DIMENSION AS A CONSEQUENCE OF NORM‐RESOLVENT CONVERGENCE AND APPLICATIONS ⋮ Spectral asymptotics for the Schrödinger operator on the line with spreading and oscillating potentials ⋮ On the MIT bag model in the non-relativistic limit ⋮ Generalised quantum waveguides ⋮ Spectral analysis on ruled surfaces with combined Dirichlet and Neumann boundary conditions ⋮ Scales, blow-up and quasimode constructions ⋮ The adiabatic limit of Schrödinger operators on fibre bundles ⋮ Convergence of nodal sets in the adiabatic limit ⋮ Weyl formulae for the Robin Laplacian in the semiclassical limit ⋮ Ruled strips with asymptotically diverging twisting ⋮ The NLS limit for Bosons in a quantum waveguide ⋮ Quantum waveguides with magnetic fields ⋮ Quantum strips in higher dimensions ⋮ The adiabatic limit of the connection Laplacian ⋮ Spectral properties of relativistic quantum waveguides

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