Quantum waveguides with magnetic fields

Abstract

We study generalised quantum waveguides in the presence of moderate and strong external magnetic fields. Applying recent results on the adiabatic limit of the connection Laplacian we show how to construct and compute effective Hamiltonians that allow, in particular, for a detailed spectral analysis of magnetic waveguide Hamiltonians. We apply our general construction to a number of explicit examples, most of which are not covered by previous results.

On Duclos–Exner’s conjecture about waveguides in strong uniform magnetic fields

“…1 Let us also mention that, in [14], the spectrum is also analyzed (by means of resolvent convergence) in the shrinking limit with a possibly -dependent magnetic field. Deriving effective operators in such regimes can actually be done in a quite general framework; see [10]. …”

On Duclos-Exner's conjecture about waveguides in strong uniform magnetic fields

“…Let us also mention that, in[13], the spectrum is also analyzed (by means of resolvent convergence) in the shrinking limit δ → 0 with a possibly δ-dependent magnetic field. Deriving effective operators in such regimes can actually be done in a quite general framework, see[9].…”