A study of time reversibility reveals that a quantum chaotic system manifests the same potential for mixing as its classical counterpart under the influence of externally applied noise. The quantum-chaotic system, however, reveals its own nature below a quite small "classicalization" threshold of noise intensity: In the case of the kicked rotor there exists a quite wide regime for which the mixing property is understood neither from classical dynamics nor from quantum perturbation theory. The relationship between such a curious behavior and the pure quantum evolution without the noise is elucidated.

Quantum-classical correspondence in many-dimensional quantum chaos is investigated by use of a coupled quantum kicked-rotors model. Even when the number of rotors is only two, results obtained are drastically different from those for a single-rotor system; that is, in the semiclassical limit the coupled system restores the essential features of classical chaos under appropriate conditions. In particular, the time-reversal experiment reveals that the classical chaotic mixing is recovered almost entirely; however, the recovered mixing is "conditional" in the sense that there exists a threshold for the recovery.

We formulate information-theoretic Bell inequalities, which apply to any pair of widely separated physical systems. If local realism holds, the two systems must carry information consistent with the inequalities. Two spin-$s$ particles in a state of zero total spin violate these information Bell inequalities.

We present a theory of quantum chaos of the Hadamard-Gutzwiller model, a quantum mechanical system which describes the motion of a particle on a surface of constant negative curvature. The theory is based on periodic-orbit sum rules that can be rigorously derived from the Selberg trace formula and which provide an exact substitute, appropriate for our strongly chaotic system, for the Bohr-Sommerfeld-Einstein quantization rules. Our recent enumeration of the classical periodic orbits enables us to evaluate the sum rules numerically and to demonstrate thereby that the theory provides also a practical method to study the quantum chaos of spectra.

We have constructed a positron reemission microscope and taken images of a number of targets using it. The unique image contrast of this device is determined by the probability that positrons are remitted from a specimen surface. The surface and near-surface defect sensitivity of the positron reemission microscope is demonstrated, as well as the feasibility of imaging biological specimens and semiconductor devices. Applications are discussed.

A 1500-Å Ni(100) film is back illuminated with 5-keV positrons from a brightness-enhanced slow positron beam. Some of the positrons diffuse through the film and are emitted from the front surface by virtue of the Ni having a negative positron affinity. An immersion objective and projector lens form a 1150× image of the reemitted positrons at a 2D position-sensitive detector. With a resolution of 3000 ± 1000 Å we observe patches attributable to positron trapping at boundary layers inside the film. The advantages and ultimate capabilities of the positron reemission microscope are also discussed.

This is a study of the nonlinear interactions of solitary waves or impulses in homogeneous, extended media. We obtain the set of ordinary differential equations for the positions of the impulses in the nearest-neighbor approximation. Solutions with constant velocity lead to pattern maps that give the successive spacings of the impulses. From among the infinitely many metastable patterns given by the maps, the system chooses one asymptotically through a hierarchical evolution.

Random walk in a one-dimensional random medium of length $N$ is analyzed. It is rigorously shown that in most realizations of the medium, the mean first-passage time, $\overline{t}$, bears the following relation to $N$, for large $N:log\overline{t}\propto \sqrt{N}$. The average of $\sqrt{t}$ over the realizations of the medium, $〈t〉$, satisfies $log〈t〉\propto N$. Our formalism, though being exact, employs only elementary means and makes transparent the physics of the delay experienced by the random walker: It is due to the existence of subsegments in which the bias against motion towards the desired end is largest. Some implications of these results concerning the replica method are briefly discussed.

A new formalism of the phase-space path integral based on our previously proposed phase-space distribution function is presented. A semiclassical theory for this path integral is also developed. It is shown that the amplitude factor associated with the semiclassical "kernel" is always finite and closely related to Greene's residue, which was devised to predict the occurrence of global chaos in classical systems.

It is shown that the coarsest discretization of positions and velocities in molecular dynamics leads to qualitatively correct transport coefficients and quantitatively predictable long-time tails in the velocity autocorrelation function, but requires orders of magnitude less computer time than standard molecular-dynamics methods.

The quantum mechanics of noninteracting electrons is studied in a nonintegrable elliptic billiard with a uniform magnetic field applied perpendicularly. We make an attempt to establish a connection between chaotic dynamics and macroscopic quantum observables. For small two-dimensional systems, a remarkable reduction and large fluctuations of the diamagnetic susceptibility are found in the corresponding classically chaotic region.

A new non-Markovian, correlated-jump model for phase fluctuations of an electromagnetic field is introduced. The phase-diffusion, generalized telegraph, Burshtein, and Brownian-motion-like models are all obtained from this model in the proper limits. The spectrum and correlation functions of the stochastic field are predicted, and detailed line shapes of the Mollow triplet of resonance fluorescence are given and shown to depend on the field intensity, a purely non-Markovian effect. Two different experimental procedures are proposed for the determination of the stochastic parameters of a laser field.

Phase transitions of trapped particles and ions, observed initially in 1959 by collisional cooling and recently by laser cooling, are explained as order-chaos transitions. Here, two trapped ${\mathrm{Ba}}^{+}$ ions are examined experimentally and by computer solution of the equations of motion. The ordered state, quasiperiodic with two frequencies, becomes chaotic when a bifurcation introduces a third frequency at a critical value of a control parameter. This route evolves from the nonlinear Coulomb coupling of the ion pair's axial and radial motions, displaying frequency locking and hysteresis, which is observed.

A continuous-time dynamic model of a network of $N$ nonlinear elements interacting via random asymmetric couplings is studied. A self-consistent mean-field theory, exact in the $N\to \infty$ limit, predicts a transition from a stationary phase to a chaotic phase occurring at a critical value of the gain parameter. The autocorrelations of the chaotic flow as well as the maximal Lyapunov exponent are calculated.

Traditionally, radiation-scattering experiments are conceived in terms of cylindrical geometry where the symmetry axis is the line between the source and the target. When the target becomes extended, as is the case in many real-life measurements, the analysis or the prediction of spectra becomes difficult. By definition of the axis of symmetry as being between the source and the detector, the extended target can be described in toroidal geometry with the surface of each toroid being a contour of constant scattering angle. With the scattering cross section constant over each contour, the calculation of total scattering intensities is greatly simplified.

The critical $\mathrm{O}\mathrm{}\left(n\right)\mathrm{}$ model on a finite honeycomb lattice is solved by the Bethe-Ansatz method. Amplitudes of the dominant finite-size corrections to part of the eigenspectrum are obtained analytically. A comparison with Cardy's predictions from the theory of conformal invariance leads to the exact results for the conformal anomaly and scaling dimensions.

We present novel calculations for the archetypal bistability dynamics driven by a correlated Gaussian random force (colored noise). Our focus is on the behavior at weak noise, which is difficult to solve theoretically as well as numerically. Precise numerical results for the smallest eigenvalue ${\lambda }_1\left(\tau \right)$ [or rate of escape $\Gamma \left(\tau \right)=\frac{1}{2}{\lambda }_1\left(\tau \right)$] at small to moderate to large noise correlation times $\tau$ are compared and interpreted versus a whole set of recent but conflicting theoretical predictions.

We present a solution of the mode-coupling equations for the dynamics of critical fluctuations which incorporates the crossover from the singular behavior of the transport properties of fluids asymptotically close to the critical point to the regular behavior of these properties far away from the critical point. Good agreement is obtained with experimental thermal diffusivity, thermal conductivity, and viscosity data for carbon dioxide at all temperatures and pressures where critical effects in these transport properties are observed.

We show that an evolving geometric phase induces a frequency shift. We report an optical experiment where we employ this effect to offset the frequency of a laser beam.

Spectral fluctuation properties in the optical-fluorescence excitation spectrum of N${\mathrm{O}}_2$ are investigated. For this purpose new high-resolution measurements have been performed. We analyze the distribution of intensities and of level spacings and the spectral rigidity. Together with the consideration of effects of missing and spurious lines, the presence of random-matrix fluctuations is demonstrated unambiguously.