Periodic-orbit theory of anderson localization on graphs
We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an aperiodic Kronig-Penney model in one dimension. The exact expression for the probability to return to an initially localized state is computed in terms of classical trajectories. It saturates to a finite value due to localization, while the diagonal approximation decays diffusively. Our theory is based on the identification of families of isometric orbits. The coherent periodic-orbit sums within these families, and the summation over all families, are performed analytically using advanced combinatorial methods.
Schanz
H
Max-Planck-Institut fur Stromungsforschung, Bunsenstrasse 10, 37073 Gottingen, Germany.
Smilansky
U