Localization properties of acoustic waves in the random-dimer media

Esmailpour, Ayoub; Esmailpour, Mohammad; Sheikhan, Ameneh; Elahi, Mohammad; Tabar, M. Reza Rahimi; Sahimi, Muhammad

doi:10.1103/physrevb.78.134206

Cited by 27 publications

(43 citation statements)

References 39 publications

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“…The evidence of delocalized electronic states was experimentally demonstrated in a random-dimer GaAs-AlGaAs superlattice [7], while for photons, a RDM dielectric system was used [8]. Recently, a RDM setup has been proposed to demonstrate the delocalization of acoustic waves [9]. For polymers, semiconductor lattices, photonic crystals and elastic chains, the dimer resonant energies cannot be modified without changing the sample itself.…”

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Localization-delocalization transition in the random dimer model

2010

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The random-dimer model is probably the most popular model for a one-dimensional disordered system where correlations are responsible for delocalization of the wave functions. This is the primary model used to justify the insulator-metal transition in conducting polymers and in DNA. However, for such systems, the localization-delocalization regimes have only been observed by deeply modifying the system itself, including the correlation function of the disordered potential. In this article, we propose to use an ultracold atomic mixture to cross the transition simply by externally tuning the interspecies interactions, and without modifying the impurity correlations.PACS numbers: 64.60. Cn,67.60.Bc In a one-dimensional disordered system, Anderson localization is known to occur at any energy when the disorder is δ correlated [1,2]. Nevertheless, if one introduces particular short-range correlations, delocalization of a significant subset of the eigenstates can appear. This happens in the random-dimer model (RDM) [3], in which the sites of a lattice are assigned energies ǫ a or ǫ b at random, with the additional constraint that sites of energy ǫ b always appear in pairs, or dimers. The same occurs in its dual counterpart (DRDM) [3], in which lattice sites with energy ǫ b never appear as neighbors. In these models, extended states arise from resonant modes of the (dual)dimers which present vanishing backscattering at energy E res . In the thermodynamic limit, the ratio √ N /N between the number of delocalized states and the total number of states vanishes, and there is no mobility edge separating extended and localized energy eigenstates. Nevertheless in finite size systems, thus in real systems, a localization-delocalization transition can be induced by driving E res inside the spectrum.This model was proposed to be the possible mechanism which leads to the insulator-metal transition in a wide class of conducting polymers such as polyaniline and heavily doped polyacetylene (see, for instance, [4]) and in some biopolymers such as DNA [5,6]. The evidence of delocalized electronic states was experimentally demonstrated in a random-dimer GaAs-AlGaAs superlattice [7], while for photons, a RDM dielectric system was used [8]. Recently, a RDM setup has been proposed to demonstrate the delocalization of acoustic waves [9]. For polymers, semiconductor lattices, photonic crystals and elastic chains, the dimer resonant energies cannot be modified without changing the sample itself. Thus the localization-delocalization transition for a (D)RDM chain as a function of the relative position of the resonant modes with respect to the band modes cannot easily be studied using these physical systems.In this article, we propose an experimental procedure to realize a DRDM experiment with a one-dimensional (1D) two-component ultracold atomic mixture in an optical lattice, and we demonstrate that the localizationdelocalization transition can be explored by tuning the interparticle interactions.To introduce disorder, a component (B d ) has ...

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Localization-delocalization transition in the random dimer model

2010

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“…However, the studies on the properties of the phonon system with LRC, as compared with those in the electron system, are rather scare [20,21,22,23,24]. In particular, there are many unclear points as to phonon dynamics of the disordered harmonic chains with LRC [25,26,27,28,29,30,31,32,33,34,35,36].…”

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confidence: 99%

Localization of disordered harmonic chain with long-range correlation

Yamada¹

2018

Chaos, Solitons & Fractals

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In the previous paper [Yamada, Chaos, Solitons & Fractals, 109,99(2018)], we investigated localization properties of onedimensional disordered electronic system with long-range correlation generated by modified Bernoulli (MB) map. In the present paper, we report localization properties of phonon in disordered harmonic chains generated by the MB map. Here we show that Lyapunov exponent becomes positive definite for almost all frequencies ω except ω = 0, and the B−dependence changes to exponential decrease for B > 2, where B is a correlation parameter of the MB map. The distribution of the Lyapunov exponent of the phonon amplitude has a slow convergence, different from that of uncorrelated disordered systems obeying a normal central-limit theorem. Moreover, we calculate the phonon dynamics in the MB chains. We show that the time-dependence of spread in the phonon amplitude and energy wave packet changes from that in the disordered chain to that in the periodic one, as the correlation parameter B increases.

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“…Finally, we note that our results may also be relevant to acoustic waves in layered media owing to the fact that acoustic and optical waves obey similar propagation equations [71][72][73][74]. To this extent, the realization of a coherently tunable and periodically modulated acoustic response may turn out to be an attractive prospect for acoustic metamaterials [75][76][77][78][79].…”

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confidence: 99%

Perfect absorption and no reflection in disordered photonic crystals

Artoni

Rocca

2017

Phys. Rev. A

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Understanding the effects of disorder on the light propagation in photonic devices is of major importance from both fundamental and applied points of view. Unidirectional reflectionless and coherent perfect absorption of optical signals are unusual yet fascinating phenomena that have recently sparked an extensive research effort in photonics. These two phenomena, which arise from topological deformations of the scattering matrix S parameters space, behave differently in the presence of different types of disorder, as we show here for a lossy photonic crystal prototype with a parity-time antisymmetric susceptibility or a more general non-Hermitian one.

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Localization properties of acoustic waves in the random-dimer media

Cited by 27 publications

References 39 publications

Localization-delocalization transition in the random dimer model

Localization-delocalization transition in the random dimer model

Localization of disordered harmonic chain with long-range correlation

Perfect absorption and no reflection in disordered photonic crystals

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