Magnetic Effects in Curved Quantum Waveguides

0433717 - ÚJF 2015 RIV CH eng J - Článek v odborném periodiku
Krejčiřík, David - Raymond, N.
Magnetic Effects in Curved Quantum Waveguides.
Annales Henri Poincare. Roč. 15, č. 10 (2014), s. 1993-2024. ISSN 1424-0637. E-ISSN 1424-0661
Grant CEP: GA ČR GAP203/11/0701
Institucionální podpora: RVO:61389005
Klíčová slova: Schrödinger operator * cross section * asymptotic behavior
Kód oboru RIV: BE - Teoretická fyzika
Impakt faktor: 1.643, rok: 2014

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.
Trvalý link: http://hdl.handle.net/11104/0237907