Magnetic Effects in Curved Quantum Waveguides
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- Krejčiřík, D. & Raymond, N. Ann. Henri Poincaré (2014) 15: 1993. doi:10.1007/s00023-013-0298-9
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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.