Modul:   MAT870  Zurich Colloquium in Applied and Computational Mathematics

Localized states in soft waveguides and quantum dot arrays

Vortrag von Dr. Pavel Exner

Datum: 02.04.25  Zeit: 16.30 - 18.00  Raum: ETH HG G 19.2

The talk discusses a class of Schrödinger operators the potentials of which are channels of a fixed profile, focusing on relations between the spectrum of such an operator and the channel geometry. We provide different sufficient conditions under which a non-straight but asymptotically straight channel gives rise to a non-empty discrete spectrum. We also address the groundstate optimalization problem in case of a loop-shaped configuration, and consider a modification of the model where the channel is replaced by an array of potential wells, each exhibiting a rotational symmetry.