Annales Henri Poincaré

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

Magnetic Effects in Curved Quantum Waveguides

  • David Krejčiřík
  • Nicolas Raymond


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.


Discrete Spectrum Essential Spectrum Tubular Neighbourhood Hardy Inequality Spectral Theorem 
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© 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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