Dynamical chaos in the integrable Toda chain induced by time discretization.

We use the Toda chain model to demonstrate that numerical simulation of integrable Hamiltonian dynamics using time discretization destroys integrability and induces dynamical chaos. Specifically, we integrate this model with various symplectic integrators parametrized by the time step τ and measure the Lyapunov time TΛ (inverse of the largest Lyapunov exponent Λ). A key observation is that TΛ is finite whenever τ is finite but diverges when τ→0.

Thermalization slowing down in multidimensional Josephson junction networks.

We characterize thermalization slowing down of Josephson junction networks in one, two, and three spatial dimensions for systems with hundreds of sites by computing their entire Lyapunov spectra. The ratio of Josephson coupling E_{J} to energy density h controls two different universality classes of thermalization slowing down, namely, the weak-coupling regime, E_{J}/h→0, and the strong-coupling regime, E_{J}/h→∞. We analyze the Lyapunov spectrum by measuring the largest Lyapunov exponent and by fitting the rescaled spectrum with a general ansatz.

Universal Anderson localization in one-dimensional unitary maps.

We study Anderson localization in discrete-time quantum map dynamics in one dimension with nearest-neighbor hopping strength θ and quasienergies located on the unit circle. We demonstrate that strong disorder in a local phase field yields a uniform spectrum gaplessly occupying the entire unit circle. The resulting eigenstates are exponentially localized.

Erratum: Lyapunov Spectrum Scaling for Classical Many-Body Dynamics Close to Integrability [Phys. Rev. Lett. 128, 134102 (2022)].

This corrects the article DOI: 10.1103/PhysRevLett.128.

Thermalization dynamics of macroscopic weakly nonintegrable maps.

We study thermalization of weakly nonintegrable nonlinear unitary lattice dynamics. We identify two distinct thermalization regimes close to the integrable limits of either linear dynamics or disconnected lattice dynamics. For weak nonlinearity, the almost conserved actions correspond to extended observables which are coupled into a long-range network.

Lyapunov Spectrum Scaling for Classical Many-Body Dynamics Close to Integrability.

We propose a novel framework to characterize the thermalization of many-body dynamical systems close to integrable limits using the scaling properties of the full Lyapunov spectrum. We use a classical unitary map model to investigate macroscopic weakly nonintegrable dynamics beyond the limits set by the KAM regime. We perform our analysis in two fundamentally distinct long-range and short-range integrable limits which stem from the type of nonintegrable perturbations.

Fragile many-body ergodicity from action diffusion.

Weakly nonintegrable many-body systems can restore ergodicity in distinctive ways depending on the range of the interaction network in action space. Action resonances seed chaotic dynamics into the networks. Long-range networks provide well connected resonances with ergodization controlled by the individual resonance chaos time scales.

Dynamical glass in weakly nonintegrable Klein-Gordon chains.

Integrable many-body systems are characterized by a complete set of preserved actions. Close to an integrable limit, a nonintegrable perturbation creates a coupling network in action space which can be short or long ranged. We analyze the dynamics of observables which become the conserved actions in the integrable limit.

Dynamical Glass and Ergodization Times in Classical Josephson Junction Chains.

Models of classical Josephson junction chains turn integrable in the limit of large energy densities or small Josephson energies. Close to these limits the Josephson coupling between the superconducting grains induces a short-range nonintegrable network. We compute distributions of finite-time averages of grain charges and extract the ergodization time T_{E} which controls their convergence to ergodic δ distributions.

Wave Packet Spreading with Disordered Nonlinear Discrete-Time Quantum Walks.

We use a novel unitary map toolbox-discrete-time quantum walks originally designed for quantum computing-to implement ultrafast computer simulations of extremely slow dynamics in a nonlinear and disordered medium. Previous reports on wave packet spreading in Gross-Pitaevskii lattices observed subdiffusion with the second moment m_{2}∼t^{1/3} (with time in units of a characteristic scale t_{0}) up to the largest computed times of the order of 10^{8}. A fundamental and controversially debated question-whether this process can continue ad infinitum, or has to slow down-stands unresolved.

Unconventional Flatband Line States in Photonic Lieb Lattices.

Flatband systems typically host "compact localized states" (CLS) due to destructive interference and macroscopic degeneracy of Bloch wave functions associated with a dispersionless energy band. Using a photonic Lieb lattice (LL), such conventional localized flatband states are found to be inherently incomplete, with the missing modes manifested as extended line states that form noncontractible loops winding around the entire lattice. Experimentally, we develop a continuous-wave laser writing technique to establish a finite-sized photonic LL with specially tailored boundaries and, thereby, directly observe the unusually extended flatband line states.

Weakly Nonergodic Dynamics in the Gross-Pitaevskii Lattice.

The microcanonical Gross-Pitaevskii (also known as the semiclassical Bose-Hubbard) lattice model dynamics is characterized by a pair of energy and norm densities. The grand canonical Gibbs distribution fails to describe a part of the density space, due to the boundedness of its kinetic energy spectrum. We define Poincaré equilibrium manifolds and compute the statistics of microcanonical excursion times off them.

Interacting ultracold atomic kicked rotors: loss of dynamical localization.

We study the fate of dynamical localization of two quantum kicked rotors with contact interaction, which relates to experimental realizations of the rotors with ultra-cold atomic gases. A single kicked rotor is known to exhibit dynamical localization, which takes place in momentum space. The contact interaction affects the evolution of the relative momentum k of a pair of interacting rotors in a non-analytic way.

Fractional lattice charge transport.

We consider the dynamics of noninteracting quantum particles on a square lattice in the presence of a magnetic flux α and a dc electric field E oriented along the lattice diagonal. In general, the adiabatic dynamics will be characterized by Bloch oscillations in the electrical field direction and dispersive ballistic transport in the perpendicular direction. For rational values of α and a corresponding discrete set of values of E(α) vanishing gaps in the spectrum induce a fractionalization of the charge in the perpendicular direction - while left movers are still performing dispersive ballistic transport, the complementary fraction of right movers is propagating in a dispersionless relativistic manner in the opposite direction.

The Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed Transport.

We consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there exist finite-power, constant-intensity nonlinear supermodes (NS), resulting from the balance between gain, loss, nonlinearity, coupling and dissimilarity. The system is shown to possess non-reciprocal dynamics enabling directed power transport functionality.

Landau-Zener Bloch Oscillations with Perturbed Flat Bands.

Sinusoidal Bloch oscillations appear in band structures exposed to external fields. Landau-Zener (LZ) tunneling between different bands is usually a counteracting effect limiting Bloch oscillations. Here we consider a flat band network with two dispersive and one flat band, e.

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}.

Enhancement of chaotic subdiffusion in disordered ladders with synthetic gauge fields.

We study spreading wave packets in a disordered nonlinear ladder with broken time-reversal symmetry induced by synthetic gauge fields. The model describes the dynamics of interacting bosons in a disordered and driven optical ladder within a mean-field approximation. The second moment of the wave packet m(2)=gt(α) grows subdiffusively with the universal exponent α≃1/3 similar to the time-reversal case.

Decohering localized waves.

In the absence of confinement, localization of waves takes place due to randomness or nonlinearity and relies on their phase coherence. We quantitatively probe the sensitivity of localized wave packets to random phase fluctuations and confirm the necessity of phase coherence for localization. Decoherence resulting from a dynamical random environment leads to diffusive spreading and destroys linear and nonlinear localization.

Energy carriers in the Fermi-Pasta-Ulam β lattice: solitons or phonons?

We investigate anomalous energy transport processes in the Fermi-Pasta-Ulam β lattice, in particular, the maximum sound velocity of the relevant weakly damped energy carriers. That velocity is numerically resolved by measuring the propagating fronts of the correlation functions of energy-momentum fluctuations at different times. We use fixed boundary conditions and stochastic heat baths.

Delocalization and spreading in a nonlinear Stark ladder.

We study the evolution of a wave packet in a nonlinear Stark ladder. In the absence of nonlinearity all normal modes are spatially localized giving rise to an equidistant eigenvalue spectrum and Bloch oscillations. Nonlinearity induces frequency shifts and mode-mode interactions and destroys localization.

Control of wave packet spreading in nonlinear finite disordered lattices.

In the absence of nonlinearity all normal modes (NMs) of a chain with disorder are spatially localized (Anderson localization). We study the action of nonlinearity, whose strength is ramped linearly in time. It leads to a spreading of a wave packet due to interaction with and population of distant NMs.

Light scattering by a finite obstacle and fano resonances.

The conditions for observing Fano resonances at elastic light scattering by a single finite-size obstacle are discussed. General arguments are illustrated by consideration of the scattering by a small (relative to the incident light wavelength) spherical obstacle based upon the exact Mie solution of the diffraction problem. The most attention is paid to recently discovered anomalous scattering.