Aperiodic structures which are perfectly ordered, but lack translational symmetry, can be considered as intermediate between crystalline and amorphous systems. Their wave-functions and spectra exhibit unusual properties. A one-dimensional model, known as the Thue-Morse lattice, is here investigated; it is particularly interesting because ft is deterministic non-periodic, but not quasi-periodic. The propagation of both electrons and photons is considered and the corresponding spectra are characterized with a multifractal analysis. The multifractal scaling function tau(q) tends in both cases to a non-analytic limit that implies the presence of both extended and exponentially localized states, as confirmed by the behaviour of the wave functions.
DETERMINISTIC NONPERIODIC STRUCTURES
LA ROCCA, Giuseppe Carlo
1993
Abstract
Aperiodic structures which are perfectly ordered, but lack translational symmetry, can be considered as intermediate between crystalline and amorphous systems. Their wave-functions and spectra exhibit unusual properties. A one-dimensional model, known as the Thue-Morse lattice, is here investigated; it is particularly interesting because ft is deterministic non-periodic, but not quasi-periodic. The propagation of both electrons and photons is considered and the corresponding spectra are characterized with a multifractal analysis. The multifractal scaling function tau(q) tends in both cases to a non-analytic limit that implies the presence of both extended and exponentially localized states, as confirmed by the behaviour of the wave functions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
