Magnetic Effects in Curved Quantum Waveguides |
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Authors: | David Krej?i?ík Nicolas Raymond |
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Institution: | 1. Department of Theoretical Physics, Nuclear Physics Institute ASCR, 25068, R?ez?, Czech Republic 2. IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042, Rennes Cedex, France
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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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