Dispersionless states in random Cayley trees with multiple connectivity.

Abstract

Exponentially localized states appear at the center of the energy spectrum of Cayley trees characterized by two different connectivities randomly distributed within the tree. These states share with ``ultralocalized'' states (states located on a few sites of the lattice) found in dilute lattices and, more recently, in Penrose lattices the surprising feature of showing no dispersion. This random system illustrates the fact that disorder not always tends to round off the density-of-states curves or to broaden \ensuremath{\delta}-function peaks.