# The spectrum of discrete periodic operators with defects

Anton Kuchenko
(Universite de Lorraine)
Analyseseminar
Fredag, 30 januar, 2015, at 13:15-14:00, in Koll. G (1532-214)
Abstrakt:
Defects significantly complicate the spectrum of purely periodic operators because along with the standard undamped waves we can observe the waves which propagate along the defects only and exponentially decrease in other directions. These properties of the structures with broken periodicity are actively used in various fields of Mechanics and Optics.

During the talk, we define the algebra of periodic operators with defects  and construct vector-valued determinants and traces of these operators  which help us to determine the spectrum and isospectral sets. As an example we consider the uniform lattice with simple guide and single inclusion. In particular, our explicit methods of determining the spectrum
allow to obtain the probability of isolated eigenvalues. This probability is
exactly $3/4-1/(2\pi)$.
Kontaktperson: Jacob Schach Møller