We observe a crossover from strong to weak chaos in the spatiotemporal evolution of multiple site excitations within disordered chains with cubic nonlinearity. Recent studies have shown that Anderson localization is destroyed, and the wave packet spreading is characterized by an asymptotic divergence of the second moment m2 in time (as t 1/3 ), due to weak chaos. In the present paper, we observe the existence of a qualitatively new dynamical regime of strong chaos, in which the second moment spreads even faster (as t 1/2 ), with a crossover to the asymptotic law of weak chaos at larger times. We analyze the pecularities of these spreading regimes and perform extensive numerical simulations over large times with ensemble averaging. A technique of local derivatives on logarithmic scales is developed in order to quantitatively visualize the slow crossover processes.

Macroscopically degenerate flat bands (FB) in periodic lattices host compact localized states which appear due to destructive interference and local symmetry. Interference provides a deep connection between the existence of flat band states (FBS) and the appearance of Fano resonances for wave propagation. We introduce generic transformations detangling FBS and dispersive states into lattices of Fano defects. Inverting the transformation, we generate a continuum of FB models. Our procedure allows us to systematically treat perturbations such as disorder and explain the emergence of energy-dependent localization length scaling in terms of Fano resonances.

A mechanism for asymmetric transport based on the interplay between the fundamental symmetries of parity (P) and time (T ) with nonlinearity is presented. We experimentally demonstrate and theoretically analyze the phenomenon using a pair of coupled van der Pol oscillators, as a reference system, one with anharmonic gain and the other with complementary anharmonic loss; connected to two transmission lines. An increase of the gain/loss strength or the number of PT -symmetric nonlinear dimers in a chain, can increase both the asymmetry and transmittance intensities.PACS numbers: 42.25.Bs, 11.30.Er Directed transport is at the heart of many fundamental problems in physics. Furthermore it is of great relevance to engineering where the challenge is to design on-chip integrated devices that control energy and/or mass flows in different spatial directions. Along these lines, the creation of novel classes of integrated photonic, electronic, acoustic or thermal diodes is of great interest. Unidirectional elements constitute the basic building blocks for a variety of transport-based devices such as rectifiers, pumps, molecular switches and transistors.The idea was originally implemented in the electronics framework, with the construction of electrical diodes that were able to rectify the current flux. This significant revolution motivated researchers to investigate the possibility of implementing this idea of "diode action" to other areas. For example, a proposal for the creation of a thermal diode, capable of transmitting heat asymmetrically between two temperature sources, was suggested in Ref.[1]. Another domain of application was the propagation of acoustic pulses in granular systems [2].A related issue concerns the possibility of devising an optical diode which transmits light differently along opposite propagation directions. Currently, such unidirectional elements rely almost exclusively on the Faraday effect, where external magnetic fields are used to break space-time symmetry. Generally this requires materials with appreciable Verdet constants and/or large size non-reciprocal devices -typically not compatible with on-chip integration schemes or light-emitting wafers [3]. To address these problems, alternative proposals for the creation of optical diodes have been suggested recently. Examples include optical diodes based on second harmonic generation in asymmetric waveguides [4] and nonlinear photonic crystals [5], photonic quasi-crystals and molecules [6], or asymmetric nonlinear structures [7]. Most of these schemes, however, suffer from serious drawbacks making them unsuitable for commercial or smallscale applications. Relatively large physical sizes are often needed while absorption or direct reflection dramatically affects the functionality leading to an inadequate balance between figures of merit and optical intensities. In other cases, cumbersome structural designs are necessary to provide structural asymmetry, or the transmitted signal has different characteristics than the incident one.In this Letter ...

We probe the limits of nonlinear wave spreading in disordered chains which are known to localize linear waves. We particularly extend recent studies on the regimes of strong and weak chaos during subdiffusive spreading of wave packets [Europhys. Lett. 91, 30001 (2010)] and consider strong disorder, which favors Anderson localization. We probe the limit of infinite disorder strength and study Fröhlich-Spencer-Wayne models. We find that the assumption of chaotic wave packet dynamics and its impact on spreading is in accord with all studied cases. Spreading appears to be asymptotic, without any observable slowing down. We also consider chains with spatially inhomogeneous nonlinearity, which give further support to our findings and conclusions.

Flatband networks are characterized by the coexistence of dispersive and flatbands. Flatbands (FBs) are generated by compact localized eigenstates (CLSs) with local network symmetries, based on destructive interference. Correlated disorder and quasiperiodic potentials hybridize CLSs without additional renormalization, yet with surprising consequences: (i) states are expelled from the FB energy E_{FB}, (ii) the localization length of eigenstates vanishes as ξ∼1/ln(E-E_{FB}), (iii) the density of states diverges logarithmically (particle-hole symmetry) and algebraically (no particle-hole symmetry), and (iv) mobility edge curves show algebraic singularities at E_{FB}. Our analytical results are based on perturbative expansions of the CLSs and supported by numerical data in one and two lattice dimensions.

Certain tight binding lattices host macroscopically degenerate flat spectral bands. Their origin is rooted in local symmetries of the lattice, with destructive interference leading to the existence of compact localized eigenstates. We study the robustness of this localization to disorder in different classes of flat band lattices in one and two dimensions. Depending on the flat band class, the flat band states can either be robust, preserving their strong localization for weak disorder W , or they are destroyed and acquire large localization lengths ξ that diverge with a variety of unconventional exponents ν, ξ ∼

Properly modulated flatband lattices have a divergent density of states at the flatband energy. Quasiperiodic modulations are known to host a metal insulator transition already in one space dimension. Their embedding into flatband geometries consequently allows for a precise engineering and fine tuning of mobility edges. We obtain analytic expressions for singular mobility edges for two flatband lattice examples. In particular, we engineer cases with arbitrarily small energy separations of mobility edge, zeroes, and divergencies.

We study the time evolution of wave packets in one-dimensional quasiperiodic lattices which localize linear waves. Nonlinearity (related to twobody interactions) has a destructive effect on localization, as observed recently for interacting atomic condensates (Lucioni et al 2011 Phys. Rev. Lett. 106 230403). We extend the analysis of the characteristics of the subdiffusive dynamics to large temporal and spatial scales. Our results for the second moment m 2 consistently reveal an asymptotic m 2 ∼ t 1/3 and an intermediate m 2 ∼ t 1/2 law. At variance with purely random systems (Laptyeva et al 2010 Europhys. Lett. 91 30001), the fractal gap structure of the linear wave spectrum strongly favours intermediate self-trapping events. Our findings give a new dimension to the theory of wave packet spreading in localizing environments.