We have experimentally checked on a ${\mathrm{CO}}_2$ laser with modulated losses the universality law set by Oppo and Politi [Phys. Rev. A 30, 435 (1984)] for the collision of Feigenbaum cascades. The scaling properties of the first three period-doubling bifurcations are in good agreement with their predictions, but fast passage effects and a limited signal-to-noise ratio impose severe limits on precise quantitative measurements.

We show that the approach by Pegg and Barnett [Phys. Rev. A 39, 1665 (1989)] to construct a phase operator through a limiting procedure does not give a satisfactory description of the phase properties of the quantized electromagnetic field. We refute the claim that their approach predicts the same results of physical experiments on phase properties as the conventional Hilbert space approach. Their procedure could only be used as a definition of the phase, but it is not a good definition because the ‘‘phase’’ states they used to construct their ‘‘phase’’ operator are not of precisely defined phase contrary to their assertion.

We assess the objections raised by Ma and Rhodes [preceding Comment, Phys. Rev. A 43, 2576 (1991)]. These objections seem to arise from a misinterpretation of our theory and a confusion between states of precise phase and states of precise field.

We compare the recent results of Ramos, Pyper, and Malli [Phys. Rev. A 38, 2729 (1988)] on sixth-row hydrides with our previous results and experiment. It is shown that the four-component Dirac-Fock method yields poor ${\mathit{D}}_{\mathit{e}}$’s and an unrealistic description of bonding compared to previous calculations and experiment.

The comment by Balasubramanian, Christiansen, and Pitzer [preceding Comment, Phys. Rev. 43, 2581 (1991)] is misleading since it compares the results of their effective-core-potential calculations including the so-called spin-orbit configuration-interaction method (SOCI) that were performed to derive accurate dissociation energies, with our fully ab initio relativistic computations that were not extended beyond the relativistic molecular orbital self-consistent-field level, which was entirely adequate to achieve the different objectives behind our ab initio computations.

Electric dipole moments of H(n=2) induced in ${\mathrm{H}}^{+\mathrm{-}}$He and H-He collisions are investigated at incident energies of 5–25 keV. For these collision systems, an energy-dependent forward-backward asymmetry (dipole moment) of the emitted Lyman-α radiation as a function of an external electric field is observed. In ${\mathrm{H}}^{+\mathrm{-}}$He collisions, the measured dipole moment is positive, corresponding to an electron trailing behind the proton. The same analysis applied to the H-He system shows the electron riding in front of the proton. The observed differences between H and ${\mathrm{H}}^{+}$ impact are partly explained with the help of a simple model which assumes different cross sections for excitation into the different Stark states.

Measurements of the absolute photoabsorption cross section near the K edge of Xe are presented. A region of increased slope extending from threshold to 600 eV above it is detected. Similar regions were found in Ar and Kr but of much smaller range. Theoretical cross sections using the hydrogenic approximation yield poor agreement with the data. Recent relativistic calculations including full relaxation and overlap correction are in excellent agreement with our measurements. The data yields an estimate of 11% for the contribution of multielectronic excitations to the cross section, somewhat lower than, but in reasonable agreement with, theory.

I show how coherence on a long-time scale between two dressed states of the same doublet can be produced. Such a coherence leads to additional vacuum-field Rabi splittings at new frequencies in the cavity transmission and in sideways fluorescence. These additional vacuum-field Rabi splittings are shown to be analogous to the dephasing-induced coherences in nonlinear optics.

A system of two colliding neutral or ionized atoms with excited states that exhibit fine-structure splitting is shown to emit resonance fluorescence, the quantum features of which can reveal the collisional dynamical correlations between the atoms. Time-resolved measurements of quantum noise (squeezing properties) of the emitted field are shown to yield detailed information on the dynamical correlations. Notably, they disclose the phase between the dynamically correlated two-atom adiabatic states, which is not available from conventional spectroscopy. Such phase information can be a sensitive probe of collision dynamics. It is also important for the achievement of enhanced selectivity in laser-induced reactive collisions or dissociation, based on controllable coherent superpositions of adiabatic states.

The recently observed process of nuclear γ deexcitation, called the electronic-bridge mechanism, is investigated in an intense laser field. In this process the nuclear excitation energy is transferred into an electronic excitation, which, in turn, results in the emission of an x-ray photon. The analysis of the process of deexcitation, whose energy somewhat differs from the energy difference of two bound states in the electronic shell shows that it can be drastically modified by an intense laser field if the condition of N-photon resonance is met. The transition probability per unit time of the laser-assisted process is derived for s states and the ratio η of this probability to that of the spontaneous γ decay is given for EL transitions. The expressions are also extended to the case of two laser beams of different photon energies but of a parallel state of polarization.

We consider a network of N symmetrically interconnected neurons. Through the procedure of adiabatic elimination (separation of time scales), the dynamics of a single neuron is obtained, in closed form, from the system of coupled differential equations that describe the N-neuron problem. For the deterministic case, our approach yields an explicit form for the single-neuron ‘‘self-coupling’’ term ${\mathit{J}}_{11}$. The case of noisy neurons containing both Langevin and multiplicative noise (in the synaptic connections) is also considered.

We have studied a spin-1/2 system interacting with a classical stochastic oscillator in the overdamped regime, simulating a thermal bath. Our aim is to understand the influence of the reaction field, i.e., the effect of the dipole on its bath, which is usually neglected in the current treatments. We have faced the problem of the role of this reaction field with the help of computer simulation. We found that the trajectories of the dipole x component exhibit behaviors suggesting that, in some range of the parameters of the system, the model should have a bistable character. Moreover, the average equilibrium value of the dipole along the z axis shows a significant deviation from the ‘‘weak-coupling predictions’’ of either classical or quantum statistical mechanics. We have explained all these properties via a renormalization procedure which, in the strong-coupling regime, makes the Hamiltonian of interest very different from the bare Hamiltonian. Among other things, this renormalized Hamiltonian leads to a bimodal distribution for the energy, in excellent agreement with the numerical simulations.

Experimental determinations of correlation functions typically involve events of differing particle number. In order to interpret such data, it is important to relate these measurements to fixed-number correlations. We exhibit the total correlation function in terms of fixed n correlations and fluctuations with respect to the average. We note that moments, constructed as integrals of the appropriate correlation functions, can be dominated in the case of broad distributions by cumulant moments constructed from single-particle density fluctuations.

We consider the time-periodic behavior of oscillator arrays subject to global coupling. Results are presented for experiments on an electrical circuit comprised of p-n diode junctions, as well as numerical simulations of an array of iterative maps. In the vicinity of a single-element period-doubling bifurcation, a large number of periodic attractors coexist, differing by the degree of synchronization of the array. Certain general features of the observed dynamical behavior can be understood using a combination of stability analysis, symmetry considerations, combinatorics, and relative sizes of the basins of attraction.

A second-order algorithm for the numerical integration of colored-noise stochastic processes is presented. It goes beyond recent efforts in this direction that are really only 3/2 order. Generation of the noise for this algorithm requires the generation of two uniformly distributed random numbers at each integration step. Some of the earlier algorithms require four, or if they also only use two, they do so without requiring all cross correlations to hold up to second order as in the algorithm presented here. Several numerical results are presented that demonstrate the improvement over the well-known first-order algorithm.

We propose a model embedded-atom (many-body) potential and test it against an effective, density-independent, pairwise-additive potential in a variety of nonequilibrium molecular-dynamics simulations of plastic deformation under high stress. Even though both kinds of interactions have nearly the same equilibrium equation of state, the defect energies (i.e., vacancy formation and surface energies) are quite different. As a result, we observe significant qualitative differences in flow behavior between systems characterized by purely pairwise interactions versus higher-order many-body forces.

Two-dimensional, infinitely degenerate Potts-model simulations were performed on four different lattices at zero and finite temperatures in order to examine the effects of lattice anisotropy and temperature on domain growth. The discrete lattice of the Potts model causes deviations from universal domain growth behavior by weakening the vertex angle boundary conditions that form the basis of von Neumann’s law. Smoothing the Wulff plot of the lattice (e.g., by extending spin interactions to a longer range) or increasing the temperature at which the simulation is performed can overcome the anisotropy inherent in discrete lattice simulations. Excellent overall agreement (kinetics, topological distribution, domain size distributions) between the low lattice anisotropy Potts-model simulations and the soap froth suggests that the Potts model is useful for studying domain growth in a wide variety of physical systems.