Quantum dynamics in two- and three-dimensional quasiperiodic tilings

We investigate the properties of electronic states in two- and three-dimensional quasiperiodic structures: the generalized Rauzy tilings. Exact diagonalizations, limited to clusters with a few thousands sites, suggest that eigenstates are critical and more extended at the band edges than at the band center. These trends are clearly confirmed when we compute the spreading of energy-filtered wave packets, using an algorithm that allows us to treat systems of about 10 6 sites. The present approach to quantum dynamics, which gives also access to the low-frequency conductivity, opens interesting perspectives in the analyzis of two- and three-dimensional models.