Pavel Exner: Geometrically induced discrete spectrum in soft quantum waveguides

Speaker
Pavel Exner, Doppler Institute, Prague

Abstract
The talk is concerned with properties of a quantum particle interacting with a potential having the form of potential ‘ditch’ of a fixed profile; we discuss how can be the geometry of the potential support reflected in the spectrum of the corresponding Schr oedinger operator. In particular, we provide sufficient conditions under which a bend of such a potential guide gives rise to a non- empty discrete spectrum. We also address the ground-state optimalisation in case of a loop-shaped configuration, and mention the situation then the ditch is replaced by an array of potential wells.