Extended acoustic modes in random systems withn-mer short range correlations

Abstract

In this paper we study the propagation of acoustic waves in a one-dimensional medium with a short range correlated elasticity distribution. In order to generate local correlations we consider a disordered binary distribution in which the effective elastic constants can take on only two values, η(A) and η(B). We add an additional constraint that the η(A) values appear only in finite segments of length n. This is a generalization of the well-known random-dimer model. By using an analytical procedure we demonstrate that the system displays n - 1 resonances with frequencies ω(r). Furthermore, we apply a numerical transfer matrix formalism and a second-order finite-difference method to study in detail the waves that propagate in the chain. Our results indicate that all the modes with ω ≠ ω(r) decay and the medium transmits only the frequencies ω(r).

Extended states in disordered one-dimensional systems in the presence of the generalizedN-mer correlations

“…Although, it is possible to create this kind of correlations by careful setup of an experiment, as described in [35] for the case of random dimers or in [9] for the similar case of dual random dimers (frozen particles are always separated by at least one empty site), generating longer chains using such methods is cumbersome. The analytical expression for the positions of delocalized modes in Nmer is well known and can be found using several methods [8,[36][37][38][39]. It is, however, worth checking how our method works with it and what additional information we can obtain.…”

Entropic analysis of the localization–delocalization transition in a one-dimensional correlated lattice

“…Currently, Anderson localization transition is well-understood in one-dimensional (1D) random media [1][2][3][4][5]. According to the scaling theory of localization [1], in 1D systems, any weak white noise disorder will localize all the (electron) states [6].…”

“…They numerically showed that for a binary chain exhibiting long-range correlations (LRC) with a scaling exponent α greater than a threshold value (α c ∼ 1.45), there is a broad energy band of extended (delocalized) states. Alternatively, the extended states can be produced by the presence of short-range correlations (SRC) in binary random sequences [4,14,15], e.g., the random-dimer model [5,16]. Consequently, short-and long-range correlations are used to examine the localization-delocalization transition in disordered chains [4,5,8,14,16].…”

“…Alternatively, the extended states can be produced by the presence of short-range correlations (SRC) in binary random sequences [4,14,15], e.g., the random-dimer model [5,16]. Consequently, short-and long-range correlations are used to examine the localization-delocalization transition in disordered chains [4,5,8,14,16]. Also, heat conduction in 1D harmonic chains with correlated disorder has long been a subject of investigation [17,18].…”

Role of Correlations and Off-Diagonal Terms in Binary Disordered One-Dimensional Systems

“…dual random dimer models (DRDM), where two heavy atom never come in pairs) or N -mers, where heavy particles always occupy a series of neighboring N sites. N -mer correlations have been studied in various systems such as photons in dielectric waveguide [19,20], acoustic waves [21] or electrons in crystalline lattice [22]. The off-diagonal disorder arises quite naturally, as the differences in the on-site energies change the tunneling amplitude values.…”