RESUMO
We present a nonlinear model that allows exploration of the relationship between energy relaxation, thermal conductivity and the excess of low-frequency vibrational modes (LFVMs) that are present in glasses. The model is a chain of the Fermi-Pasta-Ulam (FPU) type, with nonlinear second neighbour springs added at random. We show that the time for relaxation is increased as LFVMs are removed, while the thermal conductivity diminishes. These results are important in order to understand the role of the cooling speed and thermal conductivity during glass transition. Also, the model provides evidence for the fundamental importance of LFVMs in the FPU problem.
RESUMO
In this paper we study the propagation of light through an asymmetric array of dielectric multilayers built by joining two porous silicon substructures in a Fibonacci sequence. Each Fibonacci substructure follows the well-known recursive rule but in the second substructure dielectric layers A and B are exchanged. Even without mirror symmetry, this array gives rise to multiple transparent states, which follow the scaling properties and self-similar spectra of a single Fibonacci multilayer. We apply the transfer matrix formalism to calculate the transmittance. By setting the transfer matrix of the array equal to ± I, the identity matrix, frequencies of perfect light transmission are reproduced in our theoretical calculations. Although the light absorption of porous silicon in the optical range limits our experimental study to low Fibonacci generations, the positions of the transparent states are well predicted by the above-mentioned condition. We conclude that mirror symmetry in arrays of Fibonacci multilayers is sufficient but not necessary to generate multiple transparent states, opening broader applications of quasiperiodic systems as filters and microcavities of multiple frequencies.
