Conférences plénières > Conférence 5

Professeur Popov, Igor Yurievich

Université nationale de recherche sur les technologies de l'information, la mécanique et l'optique de Saint-Pétersbourg, Russie

On the spectrum for domains with corrugated boundary or unusual coupling

Abstract : Scattering by a domain with semitransparent corrugated surface and inserted point-like potentials is studied. Asymptotics of the Green function and resonances are obtained. Application to the problem of ultrasound scattering by normal and cancer cells is discussed.

The spectrum and eigenfunctions for the Laplacian in the domain with the boundary composed of the Helmholtz resonators are investigated. The limiting case  when the number of the Helmholtz resonators tends to infinity is described.

The spectral problem for the Schrodinger operator with a magnetic field (the Landau operator) on the flat Mobius strip is considered as a model of the electron on this 2D manifold in a magnetic field. The model of the flat Mobius strip is based on gluing the rectangles. The spectrum and eigenfunctions for the model operator are described. The results are compared with the flat cylinder case. "Surgery" of the flat Mobius strip (by longitudinal cutting) is discussed.