Mi. Stockman, INHOMOGENEOUS EIGENMODE LOCALIZATION, CHAOS, AND CORRELATIONS IN LARGE DISORDERED CLUSTERS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 56(6), 1997, pp. 6494-6507
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.