Electromagnetic wave propagation in Josephson junction arrays: 
low voltage resonances and microwave induced synchronization.

Mikhail V. Fistul

Max Planck Institute for the Physics of Complex Systems
Noethnitzer Str., 38, Dresden D-01187 Germany

We present a theory of the electromagnetic waves propagation in a 
Josephson junction array embedded in a superconducting transmission 
line. The wave dispersion relation for such system is derived and we 
obtain that it displays a 
gap in the region of small wave vectors. This peculiar spectrum is shown to 
manifest itself by low voltage resonant steps in the 
current-voltage characteristics. Moreover, a strong microwave induced 
interaction between Josephson junctions occurs when the Josephson junction 
array biased on the resonant steps. The strength and the radius of the 
microwave coupling are found and by making use of a mapping to the theory of
Anderson localization, 
the synchronization of a large array 
in the presence of disorder is analyzed. The developed theory provides a 
natural explanation of experimentally 
observed resonances and the microwave radiation in underdamped
Josephson junction arrays with a ground plane  (P. Barbara et al., 
Phys. Rev. Lett., 82, 1963 (1999)).