Quasiperiodic driving of Anderson localized waves in one dimension.

We consider a quantum particle in a one-dimensional disordered lattice with Anderson localization in the presence of multifrequency perturbations of the onsite energies. Using the Floquet representation, we transform the eigenvalue problem into a Wannier-Stark basis. Each frequency component contributes either to a single channel or a multichannel connectivity along the lattice, depending on the control parameters.

Flatbands under correlated perturbations.

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}.

Observation of asymmetric transport in structures with active nonlinearities.

A mechanism for asymmetric transport which is based on parity-time-symmetric nonlinearities is presented. We show that in contrast to the case of conservative nonlinearities, an increase of the complementary conductance strength leads to a simultaneous increase of asymmetry and transmittance intensity. We experimentally demonstrate the phenomenon using a pair of coupled Van der Pol oscillators as a reference system, each with complementary anharmonic gain and loss conductances, connected to transmission lines.

Modulation properties of optically injection-locked quantum cascade lasers.

A rate equation analysis on the modulation response of an optical injection-locked quantum cascade laser is outlined. It is found that the bifurcation diagram exhibits both bistable and unstable locked regions. In addition, the stable locked regime widens as the linewidth enhancement factor increases.

Scaling theory of heat transport in quasi-one-dimensional disordered harmonic chains.

We introduce a variant of the banded random matrix ensemble and show, using detailed numerical analysis and theoretical arguments, that the phonon heat current in disordered quasi-one-dimensional lattices obeys a one-parameter scaling law. The resulting β function indicates that an anomalous Fourier law is applicable in the diffusive regime, while in the localization regime the heat current decays exponentially with the sample size. Our approach opens a new way to investigate the effects of Anderson localization in heat conduction based on the powerful ideas of scaling theory.

Nonlinear waves in disordered chains: probing the limits of chaos and spreading.

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.

One-parameter scaling theory for stationary states of disordered nonlinear systems.

We show, using detailed numerical analysis and theoretical arguments, that the normalized participation number of the stationary solutions of disordered nonlinear lattices obeys a one-parameter scaling law. Our approach opens a new way to investigate the interplay of Anderson localization and nonlinearity based on the powerful ideas of scaling theory.

Probing localization in absorbing systems via Loschmidt echos.

We measure Anderson localization in quasi-one-dimensional waveguides in the presence of absorption by analyzing the echo dynamics due to small perturbations. We specifically show that the inverse participation number of localized modes dictates the decay of the Loschmidt echo, differing from the Gaussian decay expected for diffusive or chaotic systems. Our theory, based on a random matrix modeling, agrees perfectly with scattering echo measurements on a quasi-one-dimensional microwave cavity filled with randomly distributed scatterers.

Critical fidelity at the metal-insulator transition.

Using a Wigner Lorentzian random matrix ensemble, we study the fidelity, F(t), of systems at the Anderson metal-insulator transition, subject to small perturbations that preserve the criticality. We find that there are three decay regimes as perturbation strength increases: the first two are associated with a Gaussian and an exponential decay, respectively, and can be described using linear response theory. For stronger perturbations F(t) decays algebraically as F(t) approximately t(-D2(mu)), where D2(mu) is the correlation dimension of the local density of states.