SCATTERING IN TWISTED WAVEGUIDES
Résumé
We consider a twisted quantum waveguide, i.e., a domain of the form := r ! R where ! R2 is a bounded domain, and r = r (x3) is a rotation by the angle (x3) depending on the longitudinal variable x3. We investigate the nature of the essential spectrum of the Dirichlet Laplacian H , self-adjoint in L2( ), and consider related scattering problems. First, we show that if the derivative of the di erence 1 2 decays fast enough as jx3j ! 1, then the wave operators for the operator pair (H 1 ;H 2 ) exist and are complete. Further, we concentrate on appropriate perturbations of constant twisting, i.e. 0 = " with constant 2 R, and " which decays fast enough at in nity together with its rst derivative. In that case the unperturbed operator corresponding to " is an analytically bered Hamiltonian with purely absolutely continuous spectrum. Obtaining Mourre estimates with a suitable conjugate operator, we prove, in particular, that the singular continuous spectrum of H is empty.
Domaines
Théorie spectrale [math.SP]
Origine : Fichiers produits par l'(les) auteur(s)
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