Transmission Spectra of Third Sound in a Fibonacci Lattice

Kono, Kimitoshi; Nakada, Satoki; Narahara, Y.; Ootuka, Youiti

doi:10.1143/jpsj.60.368

Cited by 39 publications

(15 citation statements)

References 9 publications

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“…The reasons for this particular choice are twofold. In the first place, energy spectra corresponding to Fibonacci systems have been experimentally probed in a variety of situations, confirming that Fibonacci arrangements exhibit spectra with a hierarchy of splitting minibands displaying self-similar patterns [7][8][9][10], even when relativistic effects are taken into account [11]. In addition we have shown recently that this fractal structure of the energy spectrum has relevant consequences on the dc conductance of the system [12].…”

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confidence: 55%

Energy spectra of quasiperiodic systems via information entropy

1994

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We study the relationship between the electronic spectrum structure and the configurational order of one-dimensional quasiperiodic systems. We take the Fibonacci case as an specific example, but the ideas outlined here may be useful to accurately describe the energy spectra of general quasiperiodic systems of technological interest. Our main result concerns the {\em minimization} of the information entropy as a characteristic feature associated to quasiperiodic arrangements. This feature is shown to be related to the ability of quasiperiodic systems to encode more information, in the Shannon sense, than periodic ones. In the conclusion we comment on interesting implications of these results on further developments on the issue of quasiperiodic order.Comment: REVTeX 3.0, 8 pages, 3 figures available on request from FD-A (fimat02@emducms1.sis.ucm.es), Phys Rev E submitted, MA/UC3M/02/9

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confidence: 55%

Energy spectra of quasiperiodic systems via information entropy

1994

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“…21 A wealth of exotic properties, such as localized or critical wave functions and a Cantor-set spectrum, are theoretically predicted, 22,23,24 with varieties of experimental systems devoted for their exploration. 25,26,27,28,29,30,31,32,33,34,35,36,37,38,39 It is therefore of great interest to perceive how the magnetotransport phenomena observed in a periodic 1D-LSL are altered (or remain unaltered) in a quasiperiodic 1D-LSL, as well as to search for phenomena peculiar to the quasiperiodic systems. The Fibonacci sequence typifies quasiperiodic systems in one-dimension.…”

Section: Introductionmentioning

confidence: 99%

Fourier analyses of commensurability oscillations in Fibonacci lateral superlattices

Endo

Iye

2008

Phys. Rev. B

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Magnetotransport measurements have been performed on Fibonacci lateral superlattices (FLSLs) -two-dimensional electron gases subjected to a weak potential modulation arranged in the Fibonacci sequence, LSLLSLS..., with L/S=τ (the golden ratio). Complicated commensurability oscillation (CO) is observed, which can be accounted for as a superposition of a series of COs each arising from a sinusoidal modulation representing the characteristic length scale of one of the selfsimilar generations in the Fibonacci sequence. Individual CO components can be separated out from the magnetoresistance trace by performing a numerical Fourier band-pass filter. From the analysis of the amplitude of a single-component CO thus extracted, the magnitude of the corresponding Fourier component in the potential modulation can be evaluated. By examining all the Fourier contents observed in the magnetoresistance trace, the profile of the modulated potential seen by the electrons can be reconstructed with some remaining ambiguity about the interrelation of the phase between different components.

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“…Then, the study of classical waves propagating through a QP substrate offers a number of advantages over the study of quantum elementary excitations. Accordingly, a number of experimental studies dealing with the propagation of elastic waves, 15,16 third sound, 17 and ultrasonic waves 18 in Fibonacci systems have been reported, confirming that characteristic self-similar features in the transmission spectra are observable when the long-range aperiodic modulation is established at different scale lengths. Similarly, the introduction of the Fibonacci dielectric multilayer ͑FDM͒ by Kohmoto and collaborators 19 spurred the interest for both possible optical applications 20,21 and theoretical aspects of light transmission in aperiodic media.…”

Section: Introductionmentioning

confidence: 68%

Exploiting quasiperiodic order in the design of optical devices

Maciá

2001

Phys. Rev. B

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In this work we present a prospective study on the potential capabilities of optical devices based on Fibonacci dielectric multilayers. We perform a detailed analytical comparison of the linear optical response of periodic versus quasiperiodic multilayers. Based on this study we will suggest the use of hybrid-order devices, composed of both periodic and quasiperiodic subunits to design microcavities of practical interest, and we provide some illustrative examples. From our study we conclude that the inclusion of quasiperiodically ordered subunits substantially widens the possibilities of engineering modular optical structures.

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Transmission Spectra of Third Sound in a Fibonacci Lattice

Cited by 39 publications

References 9 publications

Energy spectra of quasiperiodic systems via information entropy

Energy spectra of quasiperiodic systems via information entropy

Fourier analyses of commensurability oscillations in Fibonacci lateral superlattices

Exploiting quasiperiodic order in the design of optical devices

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