From the quantum mechanical point of view, the electronic characteristics of
quasicrystals are determined by the nature of their eigenstates. A practicable
way to obtain information about the properties of these wave functions is
studying the scaling behavior of the generalized inverse participation numbers
Zq∼N−Dq(q−1) with the system size N. In particular, we
investigate d-dimensional quasiperiodic models based on different
metallic-mean quasiperiodic sequences. We obtain the eigenstates of the
one-dimensional metallic-mean chains by numerical calculations for a
tight-binding model. Higher dimensional solutions of the associated generalized
labyrinth tiling are then constructed by a product approach from the
one-dimensional solutions. Numerical results suggest that the relation
Dqdd=dDq1d holds for these models. Using the
product structure of the labyrinth tiling we prove that this relation is always
satisfied for the silver-mean model and that the scaling exponents approach
this relation for large system sizes also for the other metallic-mean systems.Comment: 7 pages, 3 figure