Eigenstate structure in graphs and disordered lattices - art. no. 036225

We study wave function structure for quantum graphs in the chaotic and diso rdered regime, using measures such as the wave function intensity distribut ion and the inverse participation ratio. The result is much less ergodicity than expected from random matrix theory, even though the spectral statisti cs are in agreement with random matrix predictions. Instead, analytical cal culations based on short-time semiclassical behavior correctly describe the eigenstate structure.