An exact relation valid for fluid turbulence at high Reynolds numbers is that the third moment of velocity increments scales linearly with the separation distance in the inertial range. Experiments show that this holds true also for absolute values of velocity increments. It is argued that inertial-range intermittency is a plausible consequence of this observation, and a model supplementing these considerations is provided.

A theory for the statistical properties of spectra of chaotic Hamiltonian systems with approximate integrals of the motion is presented. Spectral statistics are determined by a random matrix ensemble that depends on a single transition parameter, which is evaluated herein semiclassically for Hamiltonians with a symmetry-breaking perturbation. At finite $\hslash$, substantial deviations from results of canonical matrix ensembles are predicted. Application is given to a coupled quartic oscillator Hamiltonian.

We report a direct observation of dynamical localization. This effect is a quantum suppression of diffusion in a system that is classically chaotic. Our experiment measures the momentum transferred from a modulated standing wave of a near-resonant laser to a sample of ultracold atoms and is a realization of a periodically driven rotor. The conceptual simplicity and experimental control over the time dependent Hamiltonian make this system an ideal testing ground for the predictions of quantum chaos.

Pattern formation in large aspect ratio, single longitudinal mode, two-level lasers with flat end reflectors, operating near peak gain, is shown to be described by a complex Swift-Hohenberg equation for class A and C lasers and by a complex Swift-Hohenberg equation coupled to a mean flow for the case of a class B laser.

We obtain bounds on the signal-to-noise ratio for quantum-nondemolition measurement of photon number, using soliton collisions. A combined phase and amplitude quadrature measurement strategy can give almost noise-free results, provided equal amplitude solitons with low relative velocities are used.

Fluorescence microscopy was used to observe the velocity profile in a Langmuir monolayer forced through a channel. The monolayer was studied in the liquid-expanded-liquid-condensed coexistence region; the flow profile was invariant as the area fraction of the condensed phase was varied from 0.07 to 0.7. The hydrodynamic problem of a semi-infinite viscous fluid driven by a surface tension gradient through a channel was solved exactly; a semielliptical velocity profile is obtained, in precise agreement with the experiments, thereby demonstrating that the flow is controlled by coupling to the subphase.

A new class of exact solutions is reported for an evolving bubble in a two-dimensional slow viscous flow. It is observed that for an expanding bubble the interface grows smoother with time, whereas the contracting-bubble solutions display a tendency to form sharp corners ("near cusps") for small values of surface tension. In the latter case, we also obtain analytic solutions that describe bubble breakup: For a large class of initial shapes, the interface will eventually develop a thin "neck" whose width goes to zero before the bubble is completely removed from the liquid.

We demonstrate collisionless decay due to phase mixing of a disturbance in an inviscid 2D fluid with sheared flow. Experiments performed on a cylindrical pure electron plasma, which behaves as a 2D inviscid fluid, show that a small amplitude quadrupole excitation ($m=2\mathrm{}$, $k=0\mathrm{}$ mode) decays exponentially. At larger amplitudes, the exponential decay is modulated by bounce motion of fluid elements trapped in the azimuthally traveling wave field, with the bounce frequency proportional to the square root of the excitation amplitude. We also show that the linear decay rate is decreased by the addition of external dissipation. We describe a calculation of the linearized response function.

The very high pressures (>1 GPa) that occur during the final stages of collapse of a cavitation bubble force the liquid near the bubble wall briefly (∼1 ns) into a metastable state of subcooling, relative to the equilibrium phase diagram. Estimates for water show that solidification in the form of high-pressure ice particles can occur at a sufficient rate to affect the collapse. This explains a number of different phenomena associated with cavitation in water.

The explicit analytic expression for the distribution function of parametric derivatives of energy levels ("level velocities") is derived for the chaotic quantum systems belonging to the quasi-1D universality class (quantum kicked rotator, "domino" billiard, disordered wire, etc.).

Two-color phase control in the total ion yield of ionization is successfully demonstrated in a tunneling regime by using a 100-fs Ti:sapphire laser and its third harmonic. Adding the third harmonic with an intensity of only 10% enhances the ion yield by a factor of 7. In photoelectron spectra, above threshold ionization peaks due to the third harmonic disappear when two colors are superimposed, resulting in a continuum spectrum. This shows two-color interference clearly. The intensities of high-order harmonics in the plateau region are enhanced by an order of magnitude.

We report the first measurement of the distrubution function of the fluctuations on the total transmission of multiple scattered light. The shape of the distribution is predominantly Gaussian. A non-Gaussian contribution to the distribution function is found, caused by correlation in the cubed intensity. The scattering diagrams responsible for this new correlation are calculated without free parameters, and a good agreement is found between experiment and theory.

We calculate the electron mobility for a quantum Lorentz model, which provides a realistic description of electrons in helium gas, to second order in the gas density. We show that this provides sufficient theoretical information to allow for an experimental observation of the famous logarithmic term in the density expansion. Detailed predictions and a discussion of a suitable parameter range for such an experiment are given.

An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and which correspond to creeping waves. A new family of resonances in the two-disk scattering system can be well described which is completely missing if only the traditional periodic orbits are used.

Propagation of electromagnetic wave packets through 1D photonic band gap materials has been studied using 12 fs optical pulses. The measured transit time is found to be paradoxically short (implying superluminal tunneling) and independent of the barrier thickness for opaque barriers, in analogy to the behavior of electrons tunneling through potential barriers. Shortening of Fourier-limited incident wave packets is observed upon transmission through these linear systems. Although in apparent conflict with causality and the uncertainty principle, neither of these general principles is violated because of the strong attenuation suffered by the transmitted signals.

We show that for many physical systems the dependence of attractor basin geometry on parameter variations and noise can be characterized by power laws. We introduce new invariants—the basin immunities—that quantify this dependence and we analyze their origin and properties. Results from extensive numerical experiments are presented; examples include the driven pendulum and the Hénon map. Potential applications of basin immunities include quantifying the effect of parameter uncertainties and noise on the behavior of nonlinear devices, as well as improving parameter estimation algorithms.

We report experimental realization of high-dimensional chaos in a semiconductor laser with delayed feedback from a T-shaped cavity. We study the transition phenomena from regular to high-dimensional chaotic behavior and analyze the time series quantitatively. Correlation dimensions up to $C_2\simeq 7$ are determined reliably from experimental data by a combination of a singular value analysis and a Grassberger-Procaccia algorithm. Modeling the dynamical behavior using semiclassical delay rate equations provides a basic understanding of the observed delay-induced instabilities.

We report the first observation of large soft-x-ray amplification ($gl=7.2\mathrm{}$) in a discharge-created plasma. A fast, ∼40 kA, current pulse from a compact discharge was used to excite plasma columns up to 12 cm in length in 4-mm channels, producing population inversion in the $J=0\mathrm{}-1$ line of Ne-like Ar and resulting in a gain of 0.6 ${\mathrm{cm}}^{-1\mathrm{}}$ at 46.9 nm. The beam divergence was measured to be <9 mrad.

Magnetized electron columns evolve in ($r,\theta$) as 2D vortices in an incompressible inviscid fluid. Over a wide range of parameters, beat-wave resonance damping is observed to be the dominant vortex symmetrization mechanism. In this process, a (Kelvin or diocotron) surface wave decays to another surface wave of longer wavelength, with concomitant transport of vorticity.

An important physical phenomenon, quasinondestructive reading, has been observed for the first time in a photorefractive polymeric material, PMMA (poly-methylmethacrylate):DTNBI (1,3-dimethyl-2,2-tetramethylene-5-nitrobenzimidazoline):${\mathrm{C}}_{60}$. In addition, a maximum steady-state diffraction efficiency of 7% (125 μm sample thickness) and a net two-beam coupling gain of 16 ${\mathrm{cm}}^{-1\mathrm{}}$ are observed in this polymer. A two-trap-level model, in which the levels are populated sequentially, qualitatively mimics the intensity-dependent decay rate and the transition to quasinondestructive reading.