This paper establishes the universality of parametric correlations of eigenfunctions in chaotic and weakly disordered systems. We introduce the framework of the Gaussian random matrix process to demonstrate this universality quite generally, as well as to obtain predictions for a number of parametric correlators, one of them analytically. We present numerical evidence from both a nuclear model in its chaotic regime and a disordered system (Anderson model).

Measuring the phase dynamics of the beat note in the output of a HeNe Zeeman laser, we (i) unravel the interplay of phase locking and correlated spontaneous emission, (ii) observe the phase-diffusion noise reduced to $\frac{1}{14}$ of the Schawlow-Townes quantum level (the largest reduction of quantum noise reported so far), and (iii) show that balanced pumping of the two upper laser levels would achieve correlation of the laser phase noise with no locking at all. The resulting reduction in the phase noise of the beat note allows interferometric measurements of vastly enhanced sensitivity.

We consider layers of noncohesive granular materials of mean height $h$ subject to vertical vibration $z=A\cos \left(\omega t\right)$. Above $\gamma \equiv A{\omega }^2/g\simeq 1$, convection begins, creating a heap of height $L$. We find that for particles of diameter $d<\mathrm{}1\mathrm{mm}$ the pressure $P$ of the surrounding gas plays a key role: $L=b\tanh \left(\mathrm{KP}\right)+c$, where $b$ and $K$ depend on $h$, the gas viscosity, $d$, $\gamma$, and $A$. Convection is significantly suppressed if the shaker sidewalls are permeable, showing that gas trapped in the granular material is a major source of heaping. We consider criteria to determine when gas effects are relevant.

The interaction between a diffusive instability and a quasineutral zero mode favors the onset of resonant structures in systems exhibiting inversion symmetry and stabilizes reentrant hexagonal patterns when this symmetry is absent.

Using a novel device that enables the real-time measurement of high-order structure functions in turbulence with superior statistical accuracy, we study the shape of the structure function at scales where it is influenced by viscosity. The experiments on a variety of laboratory turbulent flows demonstrate that this shape is universal. We argue that it reflects a fundamental property of multifractals: multiscaling. We present accurate experimental scaling functions $\zeta \left(p\right)$ and, finally, comment on the nature of the skewness of the distribution function of velocity increments by comparing transverse and longitudinal distribution functions.

Based on an accurate computation of the first 1851 quantal energy levels of the truncated hyperbola billiard, we have found an anomalous long-range modulation in the integrated level density. It is shown that the observed anomaly can be explained by an additional term in Gutzwiller's trace formula. This term is given as a sum over families of closed, nonperiodic orbits which are reflected in a point of the billiard boundary where the boundary is continuously differentiable, but its curvature radius changes discontinuously.

The Lyapunov exponents and the Kolmogorov-Sinai (KS) entropy for a two-dimensional Lorentz gas at low densities are defined for general nonequilibrium states and calculated with the use of a Lorentz-Boltzmann type equation. In equilibrium the density dependence of these quantities, predicted by Krylov, is recovered and explicit expressions are obtained. The relationship between KS entropy, Lyapunov exponents, and diffusion coefficients, developed by Gaspard and Nicolis, is generalized to a wide class of nonequilibrium states.

Chaotic properties of a Lorentz lattice gas are studied analytically and by computer simulations. The escape rates, Lyapunov exponents, and Kolmogorov-Sinai entropies are estimated for a 1D example using mean-field theory, and the results are compared with simulations for a range of densities and scattering parameters of the lattice gas. Computer results show a distribution of values for the dynamical quantities with average values in good agreement with mean-field theory, and consistent with the escape-rate formalism for the coefficient of diffusion.

We present a method for the anticontrol or maintenance of chaos designed for easy application to physical and biological systems. The method is based on the return map of the experimental data and requires only small, very infrequently applied time-dependent perturbations of a single system parameter and does not require any model equations for or a priori knowledge of the system dynamics. The method is shown to be able to reliably sustain chaos in a magnetomechanical ribbon experiment.

Freely decaying 2D turbulence in magnetized electron columns has been measured using a phosphor screen/CCD camera diagnostic. The relaxation towards axisymmetric equilibrium is hindered by medium-sized coherent vorticity holes which persist for hundreds of column rotations despite the strong negative rotational shear. These holes tend to settle into symmetric configurations in the column, give a negative skew to the measured vorticity fluctuations, and are eventually destroyed due to a slow outward radial creep.

We report the presence of short wavelength bifurcations from synchronous chaotic states in coupled oscillator systems. The bifurcations immediately excite the shortest spatial wavelength mode present in the system as the coupling between the oscillators is increased beyond a critical value. An associated size instability places an upper bound on the number of oscillators that can support stable synchronous chaotic oscillations; an exact expression is given for the upper bound. Results are demonstrated with numerical simulations and electronic circuits.

It is shown that globally coupled oscillators with pulse interaction can synchronize under broader conditions than widely believed from a theorem of Mirollo and Strogatz. This behavior is stable against frozen disorder. Beside the relevance to biology, it is argued that synchronization in relaxation oscillator models is related to self-organized criticality in stick-slip-like models.

The coherent backscattering of light from disordered samples was studied with a new technique, which allowed for a very accurate determination of the enhancement factor in exact backscattering. Using circularly polarized light, the enhancement factor in the polarization conserving channel was found to be $2.00\pm 0.01$ in the weak scattering regime and was found to drop gradually below this value for stronger scattering. We argue that this behavior of the enhancement factor is the first direct experimental manifestation of recurrent multiple scattering events.

We report on an investigation of second Stokes generation in a Raman amplifier, during which we observed a pattern of narrow, approximately radial lines in the second Stokes far-field distribution. This previously unreported phenomenon, and other features in the far field, can be explained by a combination of diffuse scattering and four-wave mixing.

The structure and dynamics of penta-hepta defects (PHD's) in hexagonal patterns are studied in the framework of coupled amplitude equations for the underlying plane waves. An analytical solution for the phase field of moving PHD is found in the far field, which generalizes the static solution due to Pismen and Nepomnyashchy. The mobility tensor of the PHD is calculated using a combined analytical and numerical approach. The results for the velocity of a PHD climbing in slightly nonoptimal hexagonal patterns are compared with numerical simulations of amplitude equations. The interaction of penta-hepta defects in optimal hexagonal patterns is considered.

We study the dynamical exponent $z$ for the directed percolation depinning (DPD) class of models for surface roughening in the presence of quenched disorder. We argue that $z$ for $d+1\mathrm{}$ dimensions is equal to the exponent $d_{\min }$ characterizing the shortest path between two sites in an isotropic percolation cluster in $d$ dimensions. To test the argument, we perform simulations and calculate $z$ for DPD, and $d_{\min }$ for percolation, from $d=1\mathrm{}$ to $d=6\mathrm{}$.

A Comment on the Letter by J. Rosendahl, M. Vekic, and J. E. Rutledge, Phys. Rev. Lett. 73, 537 (1994). The authors of the Letter offer a Reply.

A Reply to the Comment by Ian Sammis and J. M. Carlson.

It is common for a periodically driven nonlinear system to have coexistent attractors. Specifically, we are interested in the case where one of these attractors is a limit cycle whose period is an integer multiple of that of the driving. Suppose that in a given application the system is desired to evolve with this limit cycle with a particular phase relative to the driving. In this Letter we propose a technique combining the effect of noise and the effect of a bias periodic signal with a properly chosen phase to accomplish this task.

We investigate the classical and quantum dynamics of atoms moving in a phase-modulated standing light field. In both cases the width of the momentum distribution exhibits characteristic oscillations as a function of the modulation amplitude. We argue that at the maxima of these oscillations the system is chaotic, whereas in the valleys it is almost regular. Quantum localization appears only in the chaotic regime. We connect our analysis with a recent experiment [F. Moore et al., Phys. Rev. Lett. 73, 2974 (1994)].