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arXiv · 1303.6844

Magnetic effects in curved quantum waveguides

David Krejcirik·Nicolas Raymond
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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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David Krejcirik, Nicolas Raymond. 2013-03-27. Magnetic effects in curved quantum waveguides. https://doi.org/10.1007/s00023-013-0298-9

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