Chaotic and ballistic dynamics in time-driven quasiperiodic lattices

Wulf, Thomas; Schmelcher, Peter

doi:10.1103/physreve.93.042215

Cited by 3 publications

(3 citation statements)

References 36 publications

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“…In this regard, it is worth noticing that a decomposition scheme based on the mirror reversed AB and AAB atomic clusters has been recently considered, in order to study the dynamics of classical particles in a time-driven Fibonacci lattice. [45] Alternatively, one may consider non-minimal blocking schemes allowing for an exact decomposition of the M N matrix string in terms of longer atomic clusters, in such a way that the resuting bloking schemes also preserve the characteristic aperiodic order of the structure. For instance, by introducing the block matricesR…”

Section: Local Transfer Matrices Classi…cationmentioning

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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Section: Local Transfer Matrices Classi…cationmentioning

confidence: 99%

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

Maciá

2017

Annalen der Physik

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“…four sequences are also examples of automatic sequences, which are sequences that can be generated by certain kinds of finite automata. The first three (FW, TM and RS) are known to have applications to condensed matter physics [15][16][17] The remaining two sequences are a random sequence with equal probabilities for +1 and -1, i.e., a fair coin tossing, and the periodic sequence (− + − + − + ...). Ignoring the cases where N is odd, for which its definition is ambiguous, the complexity of the periodic case is simply B = ln 2.…”

Section: Complexity Valuesmentioning

confidence: 99%

Average Symmetry and Complexity of Binary Sequences

Alamino

2017

Preprint

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The concept of complexity as average symmetry is here formalised by introducing a general expression dependent on the relevant symmetry and a related discrete set of transformations. This complexity has hybrid features of both statistical complexities and of those related to algorithmic complexity. Like the former, random objects are not the most complex while they still are more complex than the more symmetric ones (as in the latter). By applying this definition to the particular case of rotations of binary sequences, we are able to find a precise expression for it. In particular, we then analyse the behaviour of this measure in different well-known automatic sequences, where we find interesting new properties. A generalisation of the measure to statistical ensembles is also presented and applied to the case of i.i.d. random sequences and to the equilibrium configurations of the one-dimensional Ising model. In both cases, we find that the complexity is continuous and differentiable as a function of the relevant parameters and agrees with the intuitive requirements we were looking for.

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“…A rigorous mathematical framework for the description of symmetry breaking leading to local symmetries has been developed in [21][22][23], where nonlocal invariant currents have been identified as remnants of broken global symmetries. In [24] it was shown that the long-range order and complexity of lattice potentials generated by well-known binary aperiodic one-dimensional sequences can be encapsulated within their local symmetry structure, while in [25] the case of driven lattices was discussed. The scattering properties of quantum and photonic aperiodic structures were discussed in [26,27], answering the puzzling question about the existence of perfect transmission resonances in aperiodic systems and also providing a classification scheme with respect to their kind.…”

Section: Introductionmentioning

confidence: 99%

Duality of bounded and scattering wave systems with local symmetries

et al. 2019

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We investigate the spectral properties of a class of hard-wall bounded systems, described by potentials exhibiting domain-wise different local symmetries. Tuning the distance of the domains with locally symmetric potential from the hard wall boundaries leads to extrema of the eigenenergies. The underlying wavefunction becomes then an eigenstate of the local symmetry transform in each of the domains of local symmetry. These extrema accumulate towards eigenenergies which do not depend on the position of the potentials inside the walls. They correspond to perfect transmission resonances of the associated scattering setup, obtained by removing the hard walls. We argue that this property characterizes the duality between scattering and bounded systems in the presence of local symmetries. Our findings are illustrated at hand of a numerical example with a potential consisting of two domains of local symmetry, each one comprised of Dirac δ barriers. arXiv:1809.09139v1 [cond-mat.other]

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Chaotic and ballistic dynamics in time-driven quasiperiodic lattices

Cited by 3 publications

References 36 publications

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

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

Average Symmetry and Complexity of Binary Sequences

Duality of bounded and scattering wave systems with local symmetries

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