Transport of localized and extended excitations in chains embedded with randomly distributed linear and nonlinearn-mers

Abstract

We examine the transport of extended and localized excitations in one-dimensional linear chains populated by linear and nonlinear symmetric identical n-mers (with n=3, 4, 5, and 6), randomly distributed. First, we examine the transmission of plane waves across a single linear n-mer, paying attention to its resonances, and looking for parameters that allow resonances to merge. Within this parameter regime we examine the transmission of plane waves through a disordered and nonlinear segment composed by n-mers randomly placed inside a linear chain. It is observed that nonlinearity tends to inhibit the transmission, which decays as a power law at long segment lengths. This behavior still holds when the n-mer parameters do not obey the resonance condition. On the other hand, the mean square displacement exponent of an initially localized excitation does not depend on nonlinearity at long propagation distances z, and shows a superdiffusive behavior ∼z(1.8) for all n-mers, when parameters obey the resonance merging condition; otherwise the exponent reverts back to the random dimer model value ∼z(1.5).

Observation of Local Symmetry in a Photonic System

“…Already this is an unprecedented achievement in approaching the fundamental problem of local symmetries and, while not providing a direct technological application at this early stage, it represents the first step in a completely new direction of future research: Namely, to harness the knowledge of the hidden encoding of local symmetries in the dynamical evolution in order to understand and in turn manipulate it within a large variety of (discrete or, as an extension, continuous) wave‐mechanical systems. As an example, an interesting setup where local symmetries are inherently present is the random dimer model and its extended versions . A combination of the nonlocal continuity framework and the spatiotemporal correlations revealed in the wavepacket evolution with, for example, localization measures in (partially) disordered systems yields an exciting direction of future research beyond the fundamental demonstration of the present work.…”

Transfer efficiency enhancement and eigenstate properties in locally symmetric disordered finite chains

“…The presence of spatial correlations between the constituents of an otherwise disordered medium generally causes a delocalization of wave excitations and enhanced transport, with the detailed system response depending on the type of correlated disorder 18 . Correlation can be shortranged 19,20 , in the form of ordered clustered elements such as dimers 16,[21][22][23][24] , trimers 25 , or polymers 26,27 , it can have longrange character 18,28,29 , while also mixed short-and long-range correlations 30 as well as subsystem disorder 31 have been explored. Further, delocalization may be facilitated by correlations between onsite elements alone 32 , between hoppings 29 , or between onsite and hopping elements 21,33 .…”