We study the effect of interparticle interaction $U$ on the spectrum of the Harper model and show that it leads to a pure-point component arising from the multifractal spectrum of the noninteracting problem. Our numerical studies allow us to understand the global structure of the spectrum. An analytical approach developed permits us to understand the origin of localized states in the limit of strong interaction $U$ and fine spectral structure for small $U$.

We have executed a series of Young's two-slit experiments to measure the spatial coherence of soft x rays produced by high order harmonic generation in helium within the 270 to 480 Å wavelength range. We find that the harmonics exhibit good fringe visibility and high spatial coherence, though the coherence is somewhat degraded at high intensity because of the production of free electrons through optical field ionization during the harmonic generation.

A wave traveling upward through a particle bed is observed to steepen and form a shock as the surface is approached. This steepening is due to the increase in the local speed of sound that is induced by the local pressure increase in the upward moving phase of the wave behind the wave front. The pressure increase leads to an increase in the local coordination number which in turn increases the local elastic modulus and the sound speed.

The quantum kicked rotor is investigated by field theoretical methods. It is shown that the effective theory describing the long wavelength physics of the system is precisely the supersymmetric nonlinear $\sigma$ model for quasi-one-dimensional metallic wires. This proves that the analogy between chaotic systems with dynamical localization and disordered metals can indeed be exact. The role of symmetries is discussed.

We show that the longitudinally multimode class- $B$ laser can behave as a chain of locally coupled oscillators, each being associated to one mode. Propagation of waves in the laser spectrum is demonstrated theoretically and experimentally in the case of a Nd-doped fiber laser. By extracting the dispersion curves, we show that the group and phase velocities always have opposite signs. This property is a direct consequence of the mode coupling nature (cross saturation), and does not seem to depend on the model details.

We present a theoretical and experimental study of the propagation, decay, and interaction of optical vortices in media with an anisotropic nonlocal nonlinearity. The initial stage of decay of a circular vortex is characterized by charge dependent rotation, and stretching of the vortex. Our results suggest that a compact vortex of unit topological charge cannot exist in such media, but that a counterrotating vortex pair can form a bound state. Some analogies and differences between optical vortices and the classical dynamics of vortices in an ideal fluid are described.

The one-dimensional surrogate (1D) of energy dissipation rate has often been used in place of the true one in investigations of the Kolmogorov refined similarity hypothesis and the multifractal nature of isotropic turbulence. Direct numerical simulations, reported here, show that the use of the 1D surrogate can lead to fundamental changes in statistics. The conditional and unconditional probability densities of the Kolmogorov variable built from the true dissipation are never bimodal and always nearly Gaussian.

We have calculated dispersion coefficients for tracer particles in a fluid flowing through a porous medium consisting of randomly packed spheres. At high Péclet numbers, where the motion of the tracer is determined largely by convection, we found evidence that the dispersion coefficient is diverging and that the dispersion process is anomalous. A transient region of anomalous dispersion has been predicted theoretically. However, our simulations suggest that, rather than being transient, this effect persists. We argue that our findings are consistent with the available experimental data.

When an ensemble of interacting identical particles is put inside a confining potential it is usually the case that the particle trajectories are chaotic and thus exhibit sensitive dependence on initial conditions. However, if their velocities are randomly reset at a regular time interval $\tau$ according to a prescribed probability distribution, then it might happen that all the particles will eventually converge to some unique yet irratic orbit in the physical space, depending on the pertinent physical parameters of the system and $\tau$. We suggest that this is a rather general phenomenon, and give an argument in favor of this view. Scaling properties for the threshold reset time are also derived.

By using numerical simulations, we investigate the dynamics of a quantum system of interacting bosons. We find an increase of properly defined mixing properties when the number of particles increases at constant density or the interaction strength drives the system away from integrability. A correspondence with the dynamical chaoticity of an associated $c$-number system is then used to infer properties of the quantum system in the thermodynamic limit.

We demonstrate efficient nonlinear frequency conversion in atomic Pb vapor under conditions where the linear susceptibility and the effective nonlinear susceptibility are of the same order. This is accomplished by using electromagnetically induced transparency to prepare a near-maximal atomic coherence on a Raman transition. This strongly driven transition is used to convert an intense laser beam from 425 to 293 nm with an efficiency of $\sim 40\%$.

We demonstrate that friction is not always an exact number. In a simple lubricated system (atomically smooth mica separated by molecularly thin films of squalane), sinusoidal shear forces were applied for millions of cycles. The kinetic friction increased steadily over repetitive cycles and collapsed intermittently to the average value. Individual slip cycles also consisted of a cascade of smaller slip events. The distribution of fluctuation size and duration followed a power law.

We show that the “fluctuation theorem,” a consequence of the chaotic hypothesis of G. Gallavotti and E. G. D. Cohen [Phys. Rev. Lett. 74, 2694–2697 (1995); J. Stat. Phys. 80, 931–970 (1995)] can be interpreted as extending to arbitrary forcing fields Green-Kubo's formulas, hence Onsager's reciprocity, in a class of reversible nonequilibrium statistical mechanical systems.

We demonstrate a family of two-dimensional steady viscous flows which have singular continuous (fractal) Fourier spectra. Such flows represent a novel intermediate stage between order and Lagrangian chaos: The motion of individual fluid particles in them is neither entirely correlated nor completely disordered. In the considered setup these flows are presented by the exact solutions of the Navier-Stokes equations and occupy a parameter subset of positive measure. Onset of this unusual state follows the formation of steady eddies and is caused by the development of singularities of return times along the particle paths near the stagnation points.

Generation of magnetic field energy, without mean field generation, is studied. Isotropic mirror-symmetric turbulence of a conducting fluid amplifies the energy of small-scale magnetic perturbations if the magnetic Reynolds number is high, and the dimensionality of space d satisfies $2.103<d<\mathrm{}8.765\mathrm{}$. The result does not depend on the model of turbulence, incompressibility, and isotropy being the only requirements.

We investigate the phase space localization properties of eigenstates of a quantum system possessing a chaotic classical limit. Parametric variation of the system suggests introducing a measure of correlations between state overlap intensities and level velocities to infer information about the extent of eigenstate localization. Random matrix theory predicts no correlations. Yet when applied to the chaotic stadium billiard, we find large correlations reflecting the significant eigenstate scarring due to the parametric action variations of the orbits homoclinic to the central trajectory underlying the wave packet. The analysis can be applied to data taken with quantum dots in the Coulomb-blockade regime and microwave cavities.

Spatiotemporal chaos is produced by extended systems modeled by one-way coupled map lattices. It is shown that for sufficiently large coupling the spatiotemporal chaos of two identical one-way coupled map lattices can be entirely synchronized by using a single driving key. This synchronization of spatiotemporal chaos is used to perform spread-spectrum communication, which is much more effective (one key and many channels), and more robust and safe against external imitations and attacks (keys and transmission signals are hyperchaos with very high dimensions) than the approaches currently used for secure communication by synchronizing low-dimensional chaos.

This paper presents two-dimensional particle dynamics simulations of a vertically vibrated layer of granules, wherein a spontaneous formation of parametric surface waves appears. The investigation of the dynamic process and mechanism that leads to the formation of the granular surface waves has revealed that the dissipation coefficient in shear direction plays a crucial role in the formation of wave patterns. Scaling relations between the units in simulations and experiments are evaluated. Simulation results are shown to compare well with experimental ones.

Using experiments as well as lattice Boltzmann and finite difference simulations we study creeping flow in a Hele-Shaw cell at Reynolds numbers below unity. We describe an “echo” technique that is very sensitive to effects of hydrodynamic irreversibility. By combining experimental and numerical studies we show that the irreversibility observed in the experiments is due to inertial forces. As a by-product we validate the numerical techniques used—in particular the recently introduced lattice Boltzmann model.

Numerical simulation of a two-dimensional ideal fluid is performed to study the dynamical relaxation and final equilibrium of a vortex ring in a disk. Vorticity mixing and its implication on the final state are carefully studied and compared to the statistical theory. We conclude that, although the ergodicity assumption in the statistical theory may not always be true, strong mixing does occur in particular regions and the flow then closely follows the statistical prediction in these regions.