NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2012, 3 (3), P. 23–30
SPECTRAL PROBLEM FOR THE CHAINS OF WEAKLY COUPLED CONGLOBATE RESONATORS
A.S. Anikevich – Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, Saint Petersburg, Russia, student, email@example.com
In this paper we consider the spectral problem for two kinds of chains of weakly coupled conglobate resonators: a direct one with a kink. Equations for spectrum of these chains are derived by using of the theory of self-adjoint extensions of symmetric operators, Bloch’s theory and approach of the transfer-matrices. The paper shows that the system of direct type chain of weakly coupled conglobate resonators has a continious energy spectrum with a band structure. And for the chain with a kink we prove the existence of point spectrum.
Keywords: spectrum, theory of extenctions, self-adjoint, transfer-matrices, existence theorem.