Inhomogeneous eigenmode localization, chaos, and correlations in large disordered clusters

Abstract

Statistical and localization properties of dipole eigenmodes (plasmons) of fractal and random nonfractal clusters are investigated. The problem is mathematically equivalent to the quantum-mechanical eigenproblem for vector (spin-1) particles with a dipolar hopping amplitude in the same cluster. In fractal clusters, individual eigenmodes are singular 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. Chaotic behavior of the eigenmodes is found for fractal clusters in the region of small eigenvalues, i.e., in the vicinity of the plasmon resonance. The observed chaos is ``stronger'' than for quantum-mechanical problems on regular sets in the sense that the present problem is characterized by (deterministically) chaotic behavior of the amplitude correlation function (dynamic form factor). This chaotic behavior consists of rapid changes of the phase of the amplitude correlation in spatial and 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 clusters with nonfractal geometry do not exhibit chaotic behavior, but rather a mesoscopic delocalization transition of the eigenmodes with decrease of eigenvalue.