Annales Henri Poincaré

, Volume 15, Issue 10, pp 1993–2024 | Cite as

Magnetic Effects in Curved Quantum Waveguides

Article

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.

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsNuclear Physics Institute ASCRR̆ez̆Czech Republic
  2. 2.IRMAR, Université de Rennes 1Rennes CedexFrance

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