Magnetic effects in curved quantum waveguides

Abstract

The interplay among the spectrum, geometry and magnetic field in tubular neighbourhoods of curves in Euclidean spaces is investigated in the limit when the cross section shrinks to a point. Proving a norm resolvent convergence, we derive effective, lower-dimensional models which depend on the intensity of the magnetic field and curvatures. The results are used to establish complete asymptotic expansions for eigenvalues. Spectral stability properties based on Hardy-type inequalities induced by magnetic fields are also analysed.

28 pages

References in corpus (3)

• The effective Hamiltonian in curved quantum waveguides under mild regularity assumptions
• On the discrete spectrum of quantum layers
• Quantum Layers over Surfaces Ruled Outside a Compact Set

Cited by in corpus (5)

• Generalised Quantum Waveguides
• Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian
• On an extension of the Iwatsuka model
• Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions
• Quantum waveguides with magnetic fields