Magnetic Effects in Curved Quantum Waveguides

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 intens...

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Bibliographic Details
Published in:Annales Henri Poincaré 2014-10, Vol.15 (10), p.1993-2024
Main Authors: Krejčiřík, David, Raymond, Nicolas
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Dynamical Systems and Ergodic Theory
Elementary Particles
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical Physics
Mathematics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Theoretical
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Summary: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.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-013-0298-9