Popov I.Yu., Popova S.L.
Eigenvalues and bands imbedded in the continuous spectrum
for the system of resonators and waveguide: solvable model
(17K, LATeX)
ABSTRACT. Solvable model based on the operator extension theory is suggested
for the description of trapped modes imbedded in the continuous
spectrum. A system of resonators connected through small apertures
with a waveguide is considered as for the case of Neumann and
Dirichlet boundary conditions. That is, we study both acoustical
and quantum waveguides. The existence of such modes is shown
(corresponding sufficient condition is derived). An effective and
simple algorithm for its determination is suggested.
A system of acoustic (quantum) waveguide and periodic set of coupled
cavities
is studied in the framework of the model. The dispersion equation
is obtained in an explicit form. The existence of bands imbedded in
the continuous spectrum is proved, and an algorithm for its
determination is described.