We investigate the thermodynamical properties of plasmon-polaritons that propagate in multiple semiconductor layers arranged in a quasi-periodical fashion of Fibonacci and Thue-Morse types. We have chosen these two types of quasi-periodic structures for the following reasons: (i) both were realized experimentally, so they are not mere academic examples of a quasi-crystal; (ii) it is believed that the Thue-Morse chain is more disordered than the Fibonacci one, i.e., it has a degree of aperiodicity intermediate between the Fibonacci chain and the random systems. More precisely, the Fourier amplitude spectrum of the Thue-Morse sequence is singular continuous, while for the Fibonacci case we found δ-function peaks not arranged periodically. Both analytical and numerical studies on the temperature dependence of the excitation's specific heat associated with the generation number n=1,2,3,⋯ for their multiscale fractal energy spectra are presented. We show that when T tends to zero, the specific heat displays oscillations and when T tends to infinity, the specific heat goes to zero as T-2, because the energy spectrum considered is bounded. © 2004 Elsevier B.V. All rights reserved.
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