We present a quantum-mechanical treatment of the influence of collisional dephasing processes on the statistical properties of superfluorescence (SF). The theory, which treats nonlinear propagation effects as well as quantum noise, shows how the nature of the cooperative emission process changes from that of SF to that of amplified spontaneous emission as the collisional dephasing rate is varied. The predictions of how the SF delay time varies with the collisional dephasing rate are in good agreement with the results of a recent experiment [M. S. Malcuit, J. J. Maki, D. J. Simkin, and R. W. Boyd, Phys. Rev. Lett. 59, 1189 (1987)].

Theoretical predictions of the behavior of a light beam crossing a plane interface between a linear and nonlinear dielectric medium indicate staircased multiple threshold switching in nondiffusive media when an incident Gaussian beam instead of a plane wave is assumed. We report experimental findings showing unexpected high-contrast single-threshold switching, which may have important implications for optical signal processing. No evidence was found for the existence of bistable behavior indicated by previous experiments.

Nonclassical light beams generated by the degenerate optical parametric oscillator operating below threshold are analyzed in terms of photoelectron-counting sequences. The positive-P representation is used to calculate the generating function for photoelectron statistics in a closed form. This generating function is used to derive expressions for the photoelectron-counting and waiting-time distributions. The dependence of these distributions on mean photon number inside the cavity and efficiency of detection is studied. The relationship between photoelectron-counting sequence and the photon emission sequence is used to present a simple physical picture of light beams produced by the degenerate parametric oscillator.

The three-photon ionization spectrum of Na has been investigated in the 5390–6000-Å region. The behavior of electrons and ions produced at the observed resonances has been analyzed as a function of the experimental parameters laser intensity, beam density, and focusing conditions with the aim of elucidating the role of long-range collective interactions between electrons and ions during the collection phase. The dependence of electron current on the externally applied electric field has been especially investigated as a determinant test of phenomena under study. Important deviations of the observed dependences from those usually expected for noninteracting particles are explained in terms of collective plasma interactions.

The time-space behavior of ions and electrons, whose density and temperature are typical of laser multiphoton-ionization experiments, is analyzed from the point of view of the fluid approximation taking into account all nonlinear terms. The analytic methods of solution, already presented, are applied to describe the three-dimensional coupled motion of both ions and electrons, including also the growth of charges during the laser pulse. The theoretical predictions are compared with the experimental results observed in a three-photon ionization experiment in Na, with special regard to the analysis of the electron current behavior as a function of the externally applied electric field.

We consider quantum-mechanically partially polarized light propagating through a Kerr-like medium. Using the usual form of the induced polarization P=A(E⋅${\mathrm{E}}^{\mathrm{*}}$)E+B(E⋅${\mathrm{E})\mathrm{E}}^{\mathrm{*}}$, the theory is formulated in terms of an effective Hamiltonian which is quartic in terms of the operators for two orthogonally polarized modes. Exact solutions in closed form for the Heisenberg equations of motion are obtained. These solutions are used to evaluate the physical behavior of various observables as the field propagates through a nonlinear medium. We also present explicit results for the time evolution of the input coherent and Fock states of the field. We show the generation of states that are macroscopic superposition of coherent states. We also find that if the input field is completely polarized, then due to quantum effects the output field becomes partially polarized. This is in contrast to the classical prediction and can have an important bearing on questions like topological phases of light propagating through a nonlinear medium. Numerical results for the energy in each mode, the correlation between two modes, and the higher-order correlations are presented. The input photon statistics is found to make a considerable difference in the dynamics.

We show how a Saffman-Taylor-type fingering instability emerges in lattice-gas hydrodynamics. We discuss linear stability and the effect of noise which is intrinsic to the algorithm. Noise leads to a tip-splitting instability of the evolving finger.

The hydrodynamical equations (Navier-Stokes and the evolution of a scalar field) for an anisotropically stirred fluid are studied through renormalization-group methods. The departure from isotropy is assumed to be small. The zeroth order of the expansion around the isotropic state provides the isotropic turbulent Prandtl number. The first order of this expansion produces a new coupling term between the renormalized scalar and Navier-Stokes equations. As to the second order, it induces anisotropic corrections to the transport tensors. The resulting corrections to the turbulent Prandtl numbers are evaluated.

Photoelectron-initiated avalanches can be used to enhance ionization and dissociation, monitor surface properties, and test models of low-pressure glow discharges. In this work we explore the effects that discharge power and frequency have on electron avalanching and find that lower-powered discharges exhibit inherently larger gain. Transient changes in both current (optogalvanic effect) and optical emission intensity are enhanced three- to fivefold relative to higher-powered discharges. Monte Carlo simulations show that sheath thickness, and not voltage, is the primary parameter that determines the extent of avalanching and current gain. A self-consistent single-beam fluid model shows that optogalvanic oscillations are produced by overcompensation of the plasma potential in releasing excess negative charge produced by photoemission at the cathode. The beam model is in good qualitative but only fair quantitative agreement with experimental observations because of implicit assumptions about electron scattering. Multibeam and hybrid particle-fluid codes should provide a better quantitative description. For materials-processing applications these results imply that photoinitiated avalanches are best used in enhancing low-powered discharges. Similarly, reactive surfaces are most sensitively monitored in situ using optogalvanic detection of photoemitted electrons in weak discharges. We also find the photoelectric yield sensitive to discharge frequency when photon energies near the excitation threshold are used. This effect is attributed to surface charging that shifts the photoelectric threshold energy.

We have performed time-resolved observations of the current, optical emission, and electric field profiles in an Ar +2% K dc glow discharge, following the pulsed-laser-induced photoelectron emission on the cathode. These observations indicate that (1) The photoelectron-initiated avalanche results in a strong perturbation of the charge distribution in the discharge. This can be observed as a considerable shortening of the sheath length. (2) This leaves the discharge in a nonstationary regime, with a highly enhanced conductance. It then relaxes to the initial, steady-state regime in a time which is about 100 μs in our conditions. This time is both considerably larger than the ion transit time in the sheath and shorter than the ambipolar diffusion time. Self-consistent macroscopic simulations have been done and found to be in excellent qualitative agreement with the observations. Monte Carlo microscopic simulations of the ionization in the sheath have also been performed to point out some shortcomings of the ‘‘beam model’’ used in the self-consistent simulations.

The wetting layer formed by a phase-separated binary liquid mixture in contact with a glass substrate is observed to have a large nonequilibrium response in thickness to small temperature perturbations. An independent theoretical and physical picture is developed, which also provides a direct means of measuring the forces responsible for wetting and their effect on the dynamics of diffusion-limited interfacial motion. As an example, the curvature and anharmonicity of the minimum in the effective interface potential are found.

Circular polarization of spectral lines due to Δn=1 transitions between highly excited states (n=6–8) of low-Z hydrogenic ions (C vi and O viii) has been computed under tokamak plasma conditions. The numerical model includes relativistic corrections, the Zeeman effect, the motional Stark effect, and Doppler broadening. The motional Stark effect in spectral line profiles is negligible because of Doppler broadening. The Zeeman effect is described by the intensity-averaged splitting factor, which is equal to unity and independent of the Stark effect for all Rydberg lines (provided the n shells are well separated). The circular polarization of the line is proportional to the component of the magnetic field in the direction of the observation direction. An analytical expression for the polarization, as a function of the intensity-averaged Zeeman splitting and a characteristic linewidth, is formulated by fitting the numerical results obtained for a variety of plasma conditions and spectral lines.

We performed experiments and computer simulations in order to investigate whether the rain drops on a window pane are in a ‘‘self-organized critical state,’’ as proposed by Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988); J. Stat. Phys. 51, 797 (1988)]; and Tang and Bak [Phys. Rev. Lett. 60, 2347 (1988)]. In contrast to the expected behavior, we found that the coverage fluctuations exhibit an $f^{\mathrm{-}2}$ power spectrum, and the characteristic distribution functions of the elementary events have no power-law dependence.

The stability at finite wave numbers of a dense simple fluid subjected to a large shear is examined using generalized hydrodynamics and hard-sphere kinetic theory. For a fixed density below the equilibrium freezing density, for molecular-scale wave numbers, and for a critical shear rate, the fluid is found to become unstable with respect to density waves in the direction of the velocity gradient. For a given density the critical shear rates obtained are close to those found by Erpenbeck [Phys. Rev. Lett. 52, 1333 (1984)] in his nonequilibrium-molecular-dynamics simulations of shear-induced ordering.

In this paper we present various treatments of plasma wake-field phenomena which employ multiple-fluid models. These models generalize the one-dimensional, nonlinear, relativistic single-fluid model which has been used extensively in previous plasma wake-field calculations. Using a two-fluid model, we discuss the interaction of a low-energy continuous electron beam with wake-field-generated plasma waves. The phenomena of continuous-beam modulation and wave period shortening are discussed. The relationship between these effects and the two-stream instability is also examined. Also, using a three-fluid model, effects due to plasma electron temperature in nonlinear plasma wake-fields are examined and compared to previous work. Finally, the consequences of ion motion induced by large-amplitude electron plasma waves are calculated by including the fluid behavior of the ions.

Many-electron effects on dynamical correlations in dense helium are studied by means of self-consistent-field molecular dynamics, a computational method that combines a Hartree-Fock solution of the electronic structure of an arbitrary collection of atoms with molecular dynamics. Pair correlation functions, velocity autocorrelation functions, and coefficients of self-diffusion are calculated for helium at densities between 0.1 and 1.5 g/${\mathrm{cm}}^3$ and at temperatures of 1 and 5 eV. Comparisons are made to results computed with semiempirical pair potentials derived from low- and high-density experimental data. With increasing density, the self-consistent-field molecular-dynamics results progressively diverge from the results of molecular-dynamics simulations using Hartree-Fock pair potentials, reflecting the onset of many-atom screening effects within local clusters of atoms. This dynamic screening results in a 30% increase in the diffusion coefficient over that obtained in a molecular-dynamics simulation employing pair interaction potentials.

A thermodynamic generalization of the Saha equation for the case of a two-temperature plasma is given on basis of a modification of the free energy. The resulting equation depends in the first approximation on the electron temperature only. This result has been obtained earlier on basis of kinetic arguments.

The statistical mechanics of the distribution of Hamiltonian matrix elements in the intermediate coupling regime is discussed. Starting from an integrable limit, a coupling of increasing strength is imposed in a manner pioneered by Dyson [J. Math. Phys. 3, 421 (1962)]. In the long-time limit one approaches the Gaussian orthogonal ensemble distribution. Equivalent results can be obtained by the method of maximum entropy. The special case of a two-level system is worked out in detail. Except for the strictly integrable limit, the spacing distribution for small spacings is shown to be proportional to the spacing. The intensity distribution for small intensities is proportional to the Porter-Thomas distribution. The dependence of these distributions on the coupling-strength parameter, which measures the deviations from regular behavior, is discussed.

This paper focuses on a method proposed for determining f(α) (the singularity spectrum of a multifractal) directly from experimental data, without first calculating the ‘‘generalized dimensions’’ $D_q$ and applying the usual Legendre transforms. We describe the method, which is based on theorems by Shannon, Eggelston, and Billingsley, and apply it to one-dimensional cuts of the dissipation field of fully developed turbulence in laboratory and atmospheric flows. The accuracy of this method can be understood in terms of computation of conventional thermodynamic quantities in microcanonical and canonical ensembles. Comparisons with other direct and indirect methods of computing f(α) are made.

For Hopfield’s neural network model we compute the size of the domains of attraction of p stored patterns, i.e., the fraction of all initial microscopic states that will lead to pattern reconstruction. For p<5 this can be done analytically by solving the evolution equations for the overlaps. For p≥5 we solve the evolution equations numerically. We consider only the case where the number of patterns stored is much smaller than the number of neurons.