Chaos and Spatial Correlations for Dipolar Eigenproblems

Spatial-correlation properties of the wave functions (eigenvectors) of a spin-one eigenproblem for dipole interaction is studied for random geometries of the underlying system. This problem describes, in particular, polar excitations (“plasmons”) of large clusters. In contrast to Berry's conjecture of quantum chaos for massive particles, we have found long-range spatial correlations for wave functions (eigenvectors). For fractal systems, not only individual eigenvectors are chaotic, but also the amplitude-correlation function exhibits an unusual chaotic, “turbulent” behavior that is preserved by ensemble averaging. For disordered nonfractal systems, the eigenvectors show a mesoscopic delocalization transition different from the Anderson transition.