Perfect self-similarity of energy spectra and gap-labeling properties in one-dimensional Fibonacci-class quasilattices

Fu, Xiujun; Liu, Youyan; Zhou, Peiqin; Sritrakool, W.

doi:10.1103/physrevb.55.2882

Cited by 76 publications

(43 citation statements)

References 29 publications

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“…In particular, the behavior of a variety of particles and quasi-particles (electrons [5], phonons [6], and others [7]) in quasiperiodic structures has been and is currently being studied. A fractal energy spectrum is a common feature to such structures (e.g., [8]). As in general these spectra tend to be quite complex, simple models have been studied to enlighten the thermodynamical specificities that such systems may display.…”

Section: Introductionmentioning

confidence: 99%

Connection between energy spectrum, self-similarity, and specific heat log-periodicity

et al. 1998

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As a first step towards the understanding of the thermodynamical properties of quasiperiodic structures, we have performed both analytical and numerical calculations of the specific heats associated with successive hierarchical approximations to multiscale fractal energy spectra. We show that, in a certain range of temperatures, the specific heat displays logperiodic oscillations as a function of the temperature. We exhibit scaling arguments that allow for relating the mean value as well as the amplitude and the period of the oscillations to the characteristic scales of the spectrum. 61.43.Hv; 65.40.+g; 61.44.Br

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Section: Introductionmentioning

confidence: 99%

Connection between energy spectrum, self-similarity, and specific heat log-periodicity

et al. 1998

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“…This has developed into a cool topic [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56], which besides is underpinned by remarkable mathematical properties [57]. This confirms that the deterministic aperiodic nanostructures is a highly interdisciplinary and fascinating research field, conceptually rooted in several branches of mathematics.…”

Section: Introductionmentioning

confidence: 57%

Lempel-Ziv Complexity of Photonic Quasicrystals

Monzón¹,

Felipe²,

Sánchez-Soto

2017

Preprint

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The properties of photonic quasicrystals ultimate rely on their inherent long-range order, a hallmark that can be quantified in many ways depending on the specific aspects to be studied. We use the Lempel-Ziv measure, a basic tool for information theoretic problems, to characterize the complexity of the specific structure under consideration. Using the generalized Fibonacci quasicrystals as our thread, we adress the relation between the optical response and the associated complexity.

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“…Indeed, this substitution sequence was originally introduced in order to generalize the standard Fibonacci lattices, [48] and we note that by de…ning A 0 B n 1 A the proposed substitution rule reduces to the standard Fibonacci one for n 6 = 1 as well. By inspecting Table I one realizes that the FC(n) related substitution matrices share the same characteristic polynomial as the precious means related ones, and can thus be considered as formally equivalent as regarding the Pisot and unimodularity…”

Section: Fibonacci-class Quasicrystalsmentioning

confidence: 99%

Spectral Classification of One‐Dimensional Binary Aperiodic Crystals: An Algebraic Approach

Maciá

2017

Annalen der Physik

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A spectral classi…cation of general one-dimensional binary aperiodic crystals (BACs) based on both their di¤raction patterns and energy spectrum measures is introduced along with a systematic comparison of the zeroth-order energy spectrum main features for BACs belonging to di¤erent spectral classes, including Fibonacci-class, precious means, metallic means, mixed means and period doubling based representatives. These systems are described by means of mixed-type Hamiltonians which include both diagonal and o¤-diagonal terms aperiodically distributed. An algebraic approach highlighting chemical correlation e¤ects present in the underlying lattice is introduced.Close analytical expressions are obtained by exploiting some algebraic properties of suitable blocking schemes preserving the atomic order of the original lattice. The existence of a resonance energy which de…nes the basic anatomy of the zeroth-order energy spectra structure for the standard Fibonacci, the precious means and the Fibonacci-class quasicrystals is disclosed. This eigenstate is also found in the energy spectra of BACs belonging to other spectral classes, but for speci…c particular choices of the corresponding model parameters only. The transmission coe¢ cient of these resonant states is always bounded below, although their related Landauer conductance values may range from highly conductive to highly resistive ones, depending on the relative strength of the chemical bonds.

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Perfect self-similarity of energy spectra and gap-labeling properties in one-dimensional Fibonacci-class quasilattices

Cited by 76 publications

References 29 publications

Connection between energy spectrum, self-similarity, and specific heat log-periodicity

Connection between energy spectrum, self-similarity, and specific heat log-periodicity

Lempel-Ziv Complexity of Photonic Quasicrystals

Spectral Classification of One‐Dimensional Binary Aperiodic Crystals: An Algebraic Approach

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