The magnetic Laplacian in shrinking tubular neighborhoods of hypersurfaces

DOI10.1007/s12220-014-9525-yzbMath1337.35042arXiv1303.4753OpenAlexW2117624832MaRDI QIDQ253823

Nicolas Raymond, David Krejčiřík, Matěj Tušek

Publication date: 8 March 2016

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.4753

zbMATH Keywords

eigenvalue asymptoticseffective potentialcurvature of hypersurfaces

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for second-order elliptic equations (35J25) PDEs in connection with optics and electromagnetic theory (35Q60) Singular perturbations in context of PDEs (35B25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (12)

REDUCTION OF DIMENSION AS A CONSEQUENCE OF NORM‐RESOLVENT CONVERGENCE AND APPLICATIONS ⋮ Asymptotic spectral analysis in colliding leaky quantum layers ⋮ Quantum dynamics of a particle constrained to lie on a surface ⋮ Optimisation of the lowest Robin eigenvalue in the exterior of a compact set. II: Non-convex domains and higher dimensions ⋮ Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions ⋮ A geometric Iwatsuka type effect in quantum layers ⋮ Tunnel effect in a shrinking shell enlacing a magnetic field ⋮ Nodal sets of thin curved layers ⋮ Quantum waveguides with magnetic fields ⋮ On an extension of the Iwatsuka model ⋮ The adiabatic limit of the connection Laplacian ⋮ Effective quantum dynamics on the Möbius strip

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