INHOMOGENEOUS EIGENMODE LOCALIZATION, CHAOS, AND CORRELATIONS IN LARGE DISORDERED CLUSTERS

Statistical and localization properties of dipole eigenmodes (plasmons ) of fractal and random nonfractal clusters are investigated. The prob lem is mathematically equivalent to the quantum-mechanical eigenproble m for vector (spin-1) particles with a dipolar hopping amplitude in th e same cluster. In fractal clusters, individual eigenmodes are singula r on the small scale and their intensity strongly fluctuates in space. They possess neither strong nor weak localization properties. Instead , an inhomogeneous localization pattern takes place, where eigenmodes of very different coherence radii coexist at the same frequency. Chaot ic behavior of the eigenmodes is found for fractal clusters in the reg ion of small eigenvalues, i.e., in-the vicinity of the plasmon resonan ce. The observed chaos is ''stronger'' than for quantum-mechanical pro blems on regular sets in the sense that the present problem is charact erized by (deterministically) chaotic behavior of the amplitude correl ation function (dynamic form factor). This-chaotic behavior consists o f rapid changes of the phase of the amplitude correlation in Spatial a nd frequency domains, while its magnitude is a very smooth function. A transition between the chaotic and scaling behavior with increase of eigenvalue is observed. In contrast to fractal clusters, random cluste rs with nonfractal geometry do not exhibit chaotic behavior, but rathe r a mesoscopic delocalization transition of the eigenmodes with decrea se of eigenvalue.