An ensemble of uncoupled chaotic maps with spatially synchronized parametric fluctuations violates the law of large numbers. This is clearly evident in the nonstatistical features of the mean field, whose mean-square deviation (MSD) does not fall as 1/N with increasing N, where N is the number of elements in the system. In fact the MSD saturates after a critical value of N=${\mathit{N}}_{\mathit{c}}$. This amazing phenomenon is reminiscent of the nonstatistical behavior in globally coupled chaos. Interestingly though, there is no coupling in this system, and so the emergence of a subtle coherence in the global dynamics, as suggested by the existence of size-independent fluctuations, is very intriguing.

We use numerical methods to investigate stochastic and coherence properties of the fields transverse profiles in stimulated Raman scattering. In the linear regime with diffractive coupling, the amplified signal is characterized by fluctuations that are macroscopic. We find an interesting dependence of the beam-pointing fluctuations on photon conversion efficiency. Our results for the linear regime compare well with recent experiments, and we report an increase in beam-pointing fluctuations in the nonlinear regime. We discuss the results of modeling with one and two transverse dimensions.

The spectral response of a monolithic semiconductor quantum microcavity with quantum wells as the active medium displays mode splitting when the quantum wells and the optical cavity are in resonance. This effect can be seen as the Rabi vacuum-field splitting of the quantum-well excitons, or more classically as the normal-mode splitting of coupled oscillators, the excitons, and the electromagnetic field of the microcavity. An exciton oscillator strength of 4×${10}^{12}$ ${\mathrm{cm}}^{\mathrm{-}2}$ is deduced for 76-Å quantum wells.

We show experimental evidence of extremely low thresholds for subharmonic generation of ultrasonic waves in one-dimensional artifical piezoelectric plates with Cantor-like structure, as compared to the corresponding homogeneous and periodical plates. The origin of this apparent anomaly is theoretically investigated by studying anharmonic coupling between normal modes. We demonstrate that the large enhancement of nonlinear interaction results from the more favorable frequency and spatial matching of coupled modes (fractons and phonons) in the Cantor-like structure, with no need to invoke anomalous modifications of the nonlinear elastic constants.

The plasma in a modern tokamak is bounded by a separatrix between magnetic field lines that form toroidal magnetic surfaces, on which the plasma is confined, and open field lines that divert the plasma exhaust to so-called divertor plates. This separatrix is sharp in an ideal tokamak, but we show that magnetic perturbations create a stochastic region of open field lines inside the ideal separatrix which contains approximately 6 times the magnetic flux as does the strike points of these lines on the divertor plates. Since magnetic field lines are a 11/2 degree of freedom Hamiltonian system, the behavior of the field lines in a tokamak divertor is archetypal for the similar Hamiltonian systems.

The methodology underlying a novel spectral analysis is presented for inelastic electron scattering from solids. Implementation of the method involves Fourier transformation of the measured spectrum and deconvolution in the Fourier domain, spectral estimation using the maximum entropy method and line-shape analysis using Gaussian and Lorentzian functions, all performed in the Fourier domain. The utility of the method is demonstrated for the case of vibrationally inelastic electron scattering from CO adsorbed on Ru(001).

We present results of an extensive state-of-the-art ab initio study of the segregation of dopants to the Σ=5 tilt (310) grain boundary in germanium. Despite the lack of reactive bond coordination defects in this boundary, we predict a significant tendency for n-type dopants to segregate to the boundary. Our results lead to a general theory of dopant segregation at tetrahedrally bonded semiconductor defects, where lattice relaxation effects are irrelevant and segregation is driven by the mixing of localized carrier states of the defect with the hydrogenic states of the dopant.

We have isolated a tricritical point in the system water/n-hexane/1-propanol/2-propanol. Two samples of fixed composition exhibiting three-phase regions extending over temperature ranges of 4 and 1 K have been studied extensively by light scattering. Near the critical end points bounding the three-phase regions the structure factor S(q) is not of the Ornstein-Zernike form but is well fitted by S(q)=${\mathrm{\Gamma }}_1$/(1+${\mathit{q}}^2$${\xi }_1^2$)+${\mathrm{\Gamma }}_2$/(1+${\mathit{q}}^2$${\xi }_2^2$). The second length scale ${\xi }_2$ is nondivergent and is independent of the primary length scale.

We investigate a continuum formulation of surface growth with a power-law distribution of the magnitudes of regional advances. An exact theory predicts a sharp transition of the scaling behavior from power-law noise domination to a Gaussian noise regime as the power increases. Excellent agreement with simulations is obtained. This formulation describes Zhang’s ballistic deposition model with power-law noise and possibly recent fluid displacement experiments.

The influence of surface roughness on the dynamics of a quantized-vortex tangle has been studied by numerical simulation. A considerable improvement in the predicted critical velocity behavior is obtained.

We have made measurements of the layer-by-layer growth of solid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ from the superfluid onto a graphite substrate, and at temperatures below 0.95 K and up to eight layers we have observed remarkable and unexpected behavior which gives clear evidence of a two-stage layering transition. It is speculated that the two stages may result from the different binding energies at step and kink sites (possibly involving quantum kinks) or an incommensurate-commensurate transition.

In situ x-ray scattering studies of the Au(110) electrode surface have been carried out in 0.1M NaF, NaCl, NaBr, LiCl, CsCl, and ${\mathrm{HClO}}_4$ solutions under potential control. At sufficiently negative potentials, in the salt solutions the surface forms a (1×3) reconstruction rather than a (1×2) reported for the clean vacuum surface. Above a critical threshold potential, the (1×3) reconstruction vanishes and the surface forms a (1×1) structure.

Atomic force microscope images show that self-assembled monolayers of octadecyltrichlorosilane form on mica by nucleating isolated, self-similar domains. With increasing coverage, the fractal dimension of the growing domains evolves from 1.6 to 1.8. At higher coverage, continued growth is limited by adsorption from solution. Monte Carlo simulations that include, for the first time, adsorption as well as surface diffusion qualitatively reproduce both the growth kinetics and evolution of fractal structure, much better than a two-dimensional diffusion-limited-aggregation model.

Junction capacitance transient measurements were employed to study the thermal emission of electrons trapped in deep (D) defects in lightly n-doped a-Si:H samples. We conclude that a novel defect relaxation process occurs upon a change of change state of the defect such that an electron’s thermal release rate is inversely proportional to its residence time in the defect. Supplemental spin transient measurements indicate that both ${\mathit{D}}^{\mathrm{-}}$/${\mathit{D}}^0$ and ${\mathit{D}}^0$/${\mathit{D}}^{+}$ transitions must be involved. A good fit to our data is obtained if we assume a non-Markovian process for the ${\mathit{D}}^0$/${\mathit{D}}^{+}$ transition.

A general expression for the energy loss probability in scanning transmission electron microscopy (STEM) is derived. The method uses a Green’s function for the incident and scattered electrons and then folds the specimen into a local response function. Our expression is appropriate to any target geometry and dielectric response. As an application, the energy loss spectrum of a STEM electron moving close to an Al sphere half-embedded in an Al planar surface is calculated. The coupling between different l modes, neglected in earlier theoretical approaches, is taken into account.

We observe anomalous magnetic field dependence of the microwave vortex response of epitaxial ${\mathrm{Y}}_1$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ films, which we identify as a crossover from flux pinning to flux flow, occurring near a characteristic field ${\mathit{H}}^{\mathrm{*}}$(T). We show that the presence of the crossover depends only on adequate softening of the pinning potential U(T,H) (i.e., it is independent of the nature of the vortex transition). However, the data are in good agreement with a thermal activation model in which U(T,H)=A(T)./H. A separate analysis of the high-field, high-frequency superconducting transition yields a measure of the upper critical field ${\mathit{H}}_{\mathit{c}2}$.

The melting transition in twinned and untwinned single crystals is measured resistively in fields up to 8 T as a function of the angle between the c axis and the a-b plane. The angular dependence follows the Lindemann criterion with ${\mathit{c}}_{\mathit{L}}$=0.15. The suppression of melting by strong pinning by twin boundaries is demonstrated.

Experimental results of the muon-spin-relaxation rate, the pressure dependence coefficient and the isotope effect coefficient of the transition temperature of extreme type-II superconductors are analyzed in terms of an ansatz leading to a parabolic dependence of the transition temperature on condensate density. The resulting universal properties and trends are remarkably consistent with experiment and imply crucial constraints on the microscopic theory.

We treat the Kondo effect in one-dimensional interacting systems. We find that for repulsive interaction and off half filling, the Kondo temperature ${\mathit{T}}_{\mathit{K}}$∝(J${\mathrm{\tau }}_0$${)}^{2/\mathrm{\eta }}$, where η is the nonuniversal spin-density-wave exponent of the host system, J the Kondo coupling, and ${\mathrm{\tau }}_0$ the short-time cutoff. We also show that the wave-function orthogonality theorem remains true in a Luttinger liquid except that interactions reduce the power with which the overlap vanishes in the thermodynamic limit.

The Wolff algorithm is now accepted as the best cluster-flipping Monte Carlo algorithm for beating ‘‘critical slowing down.’’ We show how this method can yield incorrect answers due to subtle correlations in ‘‘high quality’’ random number generators.