Pavel Exner and Semjon Vugalter
Bound states in bent soft waveguides
(535K, pdf)

ABSTRACT.  The aim of this paper is to show that a two-dimensional 
Schr dinger operator with the potential in the form of a `ditch' of 
a fixed profile can have a geometrically induced discrete spectrum; 
this happens if such a potential channel has a single or multiple 
bends being straight outside a compact. Moreover, under stronger 
geometric restrictions the claim remains true in the presence of a 
potential bias at one of the channel `banks'.