IMPACT OF LOCALIZATION ON DYSONS CIRCULAR ENSEMBLE

A wide variety of complex physical systems described by unitary matric es have been shown numerically to satisfy level statistics predicted b y Dyson's circular ensemble. We argue that the impact of localization in such systems is to impose certain restrictions on the eigenvalues. We consider a solvable model which takes into account such restriction s qualitatively and find that within the model a gap is created in the spectrum, and there is a transition from the universal Wigner distrib ution towards a Poisson distribution with increasing localization.