We have observed up to 8 orders (n) in the spectra of parametric x-radiation (PXR) in the range 5–40 keV, produced by the interaction of a 90 MeV electron beam with mosaic graphite and single silicon crystals. The measured yields and intensity ratios, I(n≥2)/I(n=1), in graphite are not in agreement with the theory of PXR for mosaic crystals. In comparison, the ratios of intensities in silicon are close to the predictions of PXR theory for perfect crystals. The bandwidths of spectral lines measured in both silicon and graphite are in good agreement with theoretical predictions.

Using a two-photon interferometer, we have measured the time delay for a photon to tunnel across a barrier consisting of a 1.1-μm-thick 1D photonic band-gap material. The peak of the photon wave packet appears on the far side of the barrier 1.47±0.21 fs earlier than it would if it were to travel at the vacuum speed of light c. Although the apparent tunneling velocity (1.7±0.2)c is superluminal, this is not a genuine signal velocity, and Einstein causality is not violated. The measured tunneling time is consistent with the group delay (‘‘phase time’’), but not with the semiclassical time.

A new theoretical approach to the unsteady detonation in condensed explosives was developed in our laboratory. The experimental results presented in this paper represent the first study of the propagation of front waves moving transverse to the detonation front. It also appears that the velocity of these waves does not depend on the explosive confinement.

Long range intercluster structural order has been observed in the late, diffusion-limited stages of cluster-cluster aggregation of colloidal monolayers at liquid surfaces. The structure factor S(q,t) scales as ${\mathit{q}}_{\mathit{m}\mathit{f}}^{\mathrm{-}\mathit{d}}$(t)F(q/${\mathit{q}}_{\mathit{m}}$), the exponent being the fractal dimension of two dimensional diffusion-limited cluster aggregation. Such scaling is not observed when the aggregation is reaction limited.

The analysis of time series generated by spatiotemporal chaotic systems is discussed. We find that a Grassberger-Procaccia algorithm with a suitable normalization for the correction of systematic errors caused by the shape of the attractor is a reliable method for distinguishing between high-dimensional chaos and noise. We show that even a quantitative description of the attractor is possible by means of dimension densities. The results obtained from the time series are in good agreement with values calculated directly from the generating equations of motion.

We analyze a randomly perturbed quantum version of the baker’s transformation, a prototype of an area-conserving chaotic map. By simulating the perturbed evolution, we estimate the information needed to follow a perturbed Hilbert-space vector in time. We find that the Landauer erasure cost associated with this grows very rapidly and becomes larger than the maximum statistical entropy given by the logarithm of the dimension of Hilbert space. The quantum baker’s map displays a hypersensitivity to perturbations analogous to behavior found in the classical case. This hypersensitivity characterizes ‘‘quantum chaos’’ in a way that is relevant to statistical physics.

We compare the influence of perturbations of classically regular respectively chaotic Hamiltonians on their eigenfunctions. A generic measure of the perturbation strength is given by the average spreading width, which semiclassically is a phase-space integral. Thus, contrary to common assumption, the spreading width cannot be an indicator of regularity or chaos. The distribution of expansion coefficients of perturbed eigenfunctions in terms of unperturbed ones is markedly different for the two cases and may serve as a quantum signature of chaos referring to states rather than to spectra.

We report on the first observation of self-trapping of an optical beam due to the photorefractive effect. The self-trapping occurs at microwatt light power levels, is intensity independent, and results in significant spatial pulse reshaping.

We consider two-dimensional flow stirred by a small-scale, white-in-time random noise in the zero viscosity limit. Numerical simulations show that, after a transient state, an inertial-range energy spectrum E(k)∝${\mathit{k}}^{\mathrm{-}\mathit{x}}$ with x=5/3±0.05 is established by the inverse cascade process. This range grows in time until a Bose condensate is formed at the largest scales in the system (k≊1). Prior to condensate formation the statistics of velocity differences are extremely close to Gaussian, and only after Bose condensation strong deviations from Gaussian statistics are detected at small scales. The structures responsible for this effect are identified.

The single-band description of Bloch electrons in magnetic fields (e.g., by Harper’s equation) leads to classically integrable Hamiltonians and thus fails for lateral surface superlattices (LSSLs) where chaotic trajectories prevail near the classical limit. We derive a new model [Eq. (18)], which is reminescent of Harper’s equation, but is exact under the most general conditions and exhibits chaos in the classical limit. A matrix continued fraction expansion allows us to study the influence of classical chaos on the fractal spectrum known as Hofstadter’s butterfly and to make predictions on its observability in LSSLs.

A new type of phase matching based on the ring-shaped pump beam for efficient harmonic generation is studied theoretically and experimentally. The ring-shaped pump beam is shown to provide self-organized phase-matching conditions for a wide range of vapor density/refractive index variation. Because of symmetry self-phase matching may automatically compensate the phase mismatch created by the optical Kerr effect, as well as the negative influence of nonuniform spatiotemporal pump beam distribution. Self-phase matching is expected to be very efficient for frequency tripling of broadband and/or ultrashort pulses, as well as for high order harmonic generation. A factor of 4–5 improvement in the conversion efficiency of 1.06μ radiation tripling in Rb, Na vapor is obtained, when a disk-shaped beam is replaced by a ring-shaped beam. The high conversion efficiency ∼1.5% for a very short interaction length (l∼4 cm) is achieved.

We extend the Gross-Pitaevskii equation for neutral superflows to a model with a roton minimum in the dispersion curve. The flow around an obstacle shows dramatic differences compared to the case without roton minimum: a stationary modulation pattern bifurcates supercritically and transforms continuously into a Čerenkov cone when the speed at infinity exceeds the Landau critical speed for the rotons. This yields a Čerenkov-like drag. An analytical approach to the problem is sketched in the weak amplitude limit.

Two rational numbers are associated to each periodic orbit of Smale’s horseshoe, and practical algorithms are given for their calculation. Using these quantities, it is possible to decide in many cases whether or not a given orbit must always be created after some other given orbit in any two-dimensional transition to chaos. A statement of ‘‘weak universality’’ for the bifurcation sequence as a whole is formulated.

We introduce a novel technique to find the asymptotic time behavior of deterministic systems exhibiting anomalous diffusion. The procedure is tested for various classes of simple but physically relevant 1D maps and the possible relevance of our findings for more complicated problems is briefly discussed.

An analog circuit implementation of the chaotic Lorenz system is described and used to demonstrate two possible approaches to private communications based on synchronized chaotic systems.

The phenomenon of Anderson localization in the quantum kicked rotator is analyzed by means of concepts which were originally introduced in condensed matter physics. A diagrammatic language similar to the impurity diagram technique employed in the theory of disordered conductors is developed. The method is applied to a calculation of the quantum return probability and leads to results which coincide (apart from numerical factors) with recent numerical findings.

We demonstrate for the first time that in a homogeneous nonamplifying physical system described by the nonlinear Schrödinger equation, the combined effects of two different perturbations (delayed nonlinear response and higher-order dispersion) can lead to adiabatic compression of fundamental solitons. This is unexpected since each of these perturbations operating independently destroys soliton propagation. Experimentally this is demonstrated by showing that 95 fsec fundamental solitons are redshifted from 1.57 to 1.62 μm and adiabatically compressed to 55 fsec in 65 m of a single-mode silica fiber with modified dispersion.

The nonlinear polarization close to the band gap of GaAs is studied by spectrally and temporally resolved four-wave mixing. Excitonic and free carrier contributions both excited within the bandwidth of the 100 fs pulses are distinguished for the first time. The excitonic part dominates at carrier densities below ${10}^{16}$ ${\mathrm{cm}}^{\mathrm{-}3}$. At higher density, nonthermalized free carriers give rise to an additional component resonant to the pulse that shows a photon-echo-like time behavior. Monte Carlo simulations including the coherent polarization and the scattering dynamics of the carriers account for the data.

The response of weakly disordered metallic grains to Aharonov-Bohm flux suggests a rescaling in which statistical correlators become universal. We derive an exact expression for a correlator of level ‘‘velocities,’’ and provide numerical evidence which suggests that the universality extends to a wider class of systems and generalizes to arbitrary perturbations providing a new characterization of quantum chaos. These results are applied to Fermi velocities of complex lattices.

We present measurements of local temperature fluctuations from a convection cell of aspect ratio 1, using gas at room temperature, for Rayleigh numbers (Ra) ranging from 5×${10}^5$ to 1×${10}^{11}$. The thermal boundary layer thickness is measured; its scaling is close to ${\mathrm{Ra}}^{\mathrm{-}2/7}$ for Ra≥2×${10}^7$. A second length scale is measured through the cutoff frequency of the power spectrum, which we relate to the velocity of the large scale circulation. The Rayleigh number dependence of this length changes at Ra=2×${10}^9$.