Magnetic effects in curved quantum waveguides

David Krejcirik (1) , Nicolas Raymond (2)

1 Nuclear Physics Institute ASCR
2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: magnetic field; effective Hamiltonian; magnetic Hardy inequality; quantum waveguides; tubes; Dirichlet Laplacian

Domaines: Physique mathématique [math-ph]

David Krejcirik, Nicolas Raymond. Magnetic effects in curved quantum waveguides. Annales Henri Poincaré, 2014, 15 (10), pp.1993-2024. ⟨10.1007/s00023-013-0298-9⟩. ⟨hal-00804628⟩