https://doi.org/10.1140/epjb/e2011-20323-7
Regular Article
Generalized inverse participation numbers in metallic-mean quasiperiodic systems
Institut für Physik, Technische Universität
Chemnitz, 09107
Chemnitz,
Germany
a e-mail: stefanie.thiem@physik.tu-chemnitz.de
Received:
27
April
2011
Received in final form:
5
September
2011
Published online:
10
October
2011
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
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.
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2011