We examine a quantum optical model describing absorption of photons above an ionization threshold in multiphoton ionization. We calculate 12-photon ionization of the hydrogen atom by a strong, linearly polarized laser pulse. The angular momentum distribution of photoelectrons in the consecutive peaks depends on the intensity of the laser but reveals the presence of only a few of the lowest angular momenta. No ‘‘peak switching’’ is observed, but a finite-number-of-continua model becomes unstable at an intensity of ∼${10}^{\mathrm{-}3}$ a.u. (∼${10}^{14}$ W/${\mathrm{cm}}^2$).

Weakly coupled, nonequilibrium plasmas have often been described by assigning separate temperatures to the electron and ion velocity distributions. In this paper we present a model for the complete phase-space probability function which describes a two-temperature ensemble for arbitrary coupling. We discuss the ‘‘thermodynamics’’ predicted by the model, and in the limit of weak electron-ion coupling, we obtain explicit expressions for both the static and dynamic structure factors, which remain valid even for strong ion-ion coupling. When the ions become weakly coupled, our results for the static structure factors reduce to those of Salpeter. However, even in this limit there remains a small difference from Salpeter’s dynamic structure factor due to the nonergodicity of the ensemble.

The steady-state and dynamic properties of the transition to oscillatory convection in a low-Prandtl-number fluid, dilute ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, are presented. Critical slowing down is observed and characterized by a phenomenological Landau-Hopf equation in analogy with equilibrium mean-field critical phenomena. In contrast to the onset of classical time-independent Rayleigh-Bénard convection, where appreciable rounding is typically observed, there is no measurable rounding at the oscillatory onset down to a reduced Rayleigh number of 3×${10}^{\mathrm{-}4}$. Possible reasons for this are discussed. Different functional singularities are observed for the rms amplitudes of the fundamental and first harmonic spectral components of the oscillation. Finally, the Prandtl-number dependence of the parameters of the dynamics is presented.

We formulate a group-theoretical projection technique for the quantum-statistical description of systems with exactly conserved charges corresponding to local non-Abelian gauge symmetries. The formalism is specified for SU(N) internal symmetry and a partition function related to a mixed canonical–grand-canonical ensemble is defined. Its perturbation expansion is derived, and we point out potential applications. We also study single-particle Green’s functions for the calculation of mixed ensemble averages with the help of a generalized Wick’s theorem and find that a connected-graphs expansion is impossible.

The propagation of light rays in a plasma is considered for small density fluctuations superimposed upon a given background density profile. The lowest-order angular spreading, focusing, and drift effects are calculated in the geometrical-optics limit using a statistical random-walk approach. This method is an economical semianalytic alternative to a purely numerical ray-trace approach and is of particular but not exclusive interest in describing the propagation of laser light in laser-produced plasmas. The model is applied to a simple fluctuation spectrum characterized by an rms amplitude and by a correlation length. Results are presented for the evolution of the intensity profiles of beams incident on a plane-parallel linear-profile plasma slab as a function of the angle of incidence. Comparisons of these results with numerical Monte Carlo ray-trace solutions show good agreement. Density fluctuations as small as a few percent of the critical density can, for example, produce significant angular broadening in the specularly reflected beam and reduce the sensitivity of the absorption fraction to the incidence angle, particularly near normal incidence.

The three-dimensional diffusion of an asymmetric-top molecule is described in terms of the linked translational and rotational Langevin equations both written in the moving frame of reference. The terms appearing in these equations suggest the existence of cross-correlation tensors in the moving frame (1,2,3) and in the laboratory frame (x,y,z). Their existence has been confirmed by molecular-dynamics computer simulation both in the absence and presence of a strong external electric field of force. The symmetry group to which the cross-correlation tensors belong depends on the variables being correlated, and changes when the field is applied. The latter is capable of generating cross-correlations which otherwise have no existence, and may therefore be used experimentally to isolate the cross-correlation functions from the ever-present autocorrelation functions which form the ‘‘background’’ to the ensemble molecular dynamics. It is shown that some off-diagonal elements exist in frame (x,y,z) in the absence of the field, thus invalidating the basic hypothesis of the theory of rotational diffusion.

We consider dissipative systems where the contraction in phase space corresponds asymptotically to the center-manifold-functional dependence of the fast-relaxing variables $X_f$’s on the order parameters given by the slow variables $X_s$’s. We derive analytically the Green-function sensitivity matrix to calculate the response on the subordinated variables to instantaneous perturbations on $X_f$ or on $X_s$. We thus show how these perturbations propagate along the center manifold. This information is obtained from sensitivity measurements on the experimentally relevant variables $X_s$’s using also the center-manifold expansion. The results are applied to a randomly driven damped anharmonic oscillator. The spectral density is found by Fourier transforming the sum of the different contributions to the equilibrium correlation: The $X_s$$X_s$, $X_s$$X_f$, and $X_f$$X_f$ terms. The average local attractivity of the center manifold is calculated and used in this computation. The sensitivity functions involving only the subordinated degrees of freedom are used as fundamental propagators to calculate the $X_f$$X_f$ term. The results are tested against an analog computer simulation and vis-à-vis plots obtained from statistical linearization methods. A very good agreement is observed.

Binary phase-separation dynamics in liquid mixtures of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ has been investigated near the tricritical point with laser-light scattering techniques. Rapid decompression of the mixtures results in quenches into the miscibility gap so that both the metastable and unstable (spinodal) regions can be probed. Quenches into the unstable region allowed measurements of the normalized dynamic structure factor S(k,t) that confirm the dynamical scaling hypotheses for spinodal decomposition. Measurements made for concentrations well away from the tricritical value show different behavior and suggest the presence of a spinodal boundary. Forward scattering intensities for shallow quenches probe nucleation phenomena and permit quantitative measurements of anomolous supercooling as a function of quench rate. Comparisons with data in organic binary mixtures are given.

The relations between the various frequency-moment sum rules of electron liquids, which include even-power moments, are systematically examined by using the Cauchy-Schwarz and Hölder inequalities. A relation involving the isothermal sound velocity and the kinetic and potential energies is obtained from one of the inequalities in the long-wavelength limit, and is generalized to arbitrary spatial dimensions.

On fluid interfaces in finite-size systems, capillary waves longer than the system size are cut off, and the interfacial tension is higher than its infinite-system value σ. We quantify this increase using capillary-wave theory to calculate ${\sigma }_{2\pi /l}$, the surface tension of an interface with no capillary waves longer than l. The effect is small for a liquid-vapor interface near a triple point unless l is on the order of 10 molecular diameters. In contrast, ${\sigma }_{2\pi /l}$/σ near a critical point can be significantly larger than unity for reasonably large values of l. We find that ${\sigma }_{2\pi /l}$/σ=1.6 for l=20ξ, with ξ the bulk correlation length in either coexisting phase. Because systems on the order of 20ξ are physically realizable, this result has important implications for surface tension in confined geometries. Our normalization of the capillary-wave partition function implies that ${\sigma }_{2\pi /l}$ also obeys finite-size scaling: ${\sigma }_{2\pi /l}$/σ=F(l/ξ), where F(x) depends on the shape of the confined geometry but is otherwise universal. The implications of these and other predictions are discussed in light of recent developments involving surface tension and confined geometries.

The nonlinear evolution of a Rayleigh-Taylor (RT) unstable free surface is studied by three independent approaches. (i) The method of least-squares approximation (LSA) is critically examined and applied to the general RT initial-value problem. It extends previous results of perturbation theories to higher orders and describes the appearance of bubbles and spikes for both single- and multiple-wavelength surface perturbations. Computational limitations, however, are found for the steady-state bubble regime where the number of harmonics becomes exceedingly large. (ii) A mathematically consistent sinusoidal flow model is developed valid for certain nonuniform gravitational accelerations. Its general properties are discussed, including a spike singularity and a unique steady-state bubble shape. As a special case, Layzer’s model is obtained and compared with the LSA calculations. (iii) Steady-state bubbles are described more generally in terms of source potentials. A one-parameter family of possible bubble shapes and corresponding gravitational potentials can be derived. It includes the steady-state sinusoidal flow model and yields improved analytic expressions for the constant-acceleration bubble parameters. From this model it is also concluded that flow singularities can limit the general applicability of Fourier analyses to free-boundary flows.

The aim of the present work is to perform an in-depth analysis of neutron scattering data on liquid metals and to extend previous types of comparisons between experimental scattering functions and various model theories. The kinematic viscosity ν(q) for some liquid metals—liquid lead at 623 and 1173 K, liquid bismuth at 578 K, and liquid rubidium at 315 K—is derived, based on the dynamical scattering functions S(q,ω), and compared to molecular dynamics data for hard spheres. The general behavior of the ν(q) curve is traced. With use of an analytical form of pair potential with several free parameters, a form of V(r) for liquid lead at 623 K is derived. Finally, the short-time interaction part of the experimental memory function ${\Phi }_l$(q,t) for the longitudinal current correlation function is directly compared to the corresponding result calculated from kinetic theory in the mode-coupling version. This comparison is based upon the derived form of the interatomic potential for Pb at 623 K and upon other known potential data for Rb at 315 K.

Diffusion-limited surface deposition has been studied in the limit of high anisotropy using two-dimensional computer simulations. In this model the diffusion of particles is isotropic but growth is allowed to occur only in the direction away from the surface. This model results in the formation of an irregular distribution of needles perpendicular to the surface. The mean density profile and the distribution of needle lengths can be described, to a good approximation, by a power law with exponential cutoffs. The structures produced in these simulations resemble those observed in some systems undergoing unstable dendritic growth.

The relationship between the two different ordering procedures taking place in an ideal charged relativistic Bose gas in the presence of a uniform external magnetic field B is investigated in an arbitrary number of spatial dimensions d. In particular the analytical form of the charge-density condensate $q_c$ and the magnetization density ρ are calculated as a function of B and the inverse temperature β for relativistic bosons without spin. In the small-field limit (B→0) this system exhibits the complete restoration of the symmetry of the ideal relativistic Bose gas for all d at any finite temperature.

Procaccia and Gitterman have suggested that the reaction rates of chemically reacting binary mixtures are drastically reduced near their thermodynamic critical points and that this reduction is responsible for anomalies observed in a series of experiments performed more than 15 years ago. A more detailed analysis shows that this suggestion is untenable, that spatially uniform composition fluctuations are not drastically retarded at thermodynamic critical points, and that spatially varying composition fluctuations are at best slowed down over a small range of wavenumbers that will be difficult to detect experimentally. A qualitative picture is provided by mean-field and Van Hove theory. Quantitative corrections are obtained with use of renormalization-group techniques. At small and large wavenumbers, the hydrodynamic modes most affected near the critical point are, respectively, thermal and particle diffusion. The mode-couplings relevant in these regimes differ from the mode couplings relevant at intermediate wavelengths where the critical slowing of a reaction might be observable.

Measurements are reported of the radiative decay rate of the Hg 6 ${\mathrm{}}^1$$P_1$ population under conditions of strong radiation trapping at the 184.9-nm resonance line. The experiments were made in the afterglow of a low-pressure Hg discharge with a dye-laser absorption method. The radiative decay rate as a function of the Hg pressure shows a pronounced minimum. The value at minimum is lower than the limiting value at higher Hg densities by a factor of 2. Furthermore, the experimental rates are up to a factor of 8 lower than those calculated from theory with the usual assumption of complete redistribution. Indeed, complete redistribution is not expected in the present case, where the optical thickness is large and elastic collision rates are smaller than the single atom spontaneous emission rate. We derived an analytical expression for the fundamental-mode radiative decay rate in a homogeneous medium from a theory based on partial redistribution in frequency. A condition for the existence of a fundamental mode is discussed and is shown to be largely satisfied in our experiments. The expression for the decay rate was obtained for a resonance line with a hyperfine structure, and was elaborated for a cylindrical geometry. The resulting calculated decay rates agree with the experimental ones within 25%.

Measurements are reported of the fundamental mode radiative decay rate of the Hg 6 ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ population under conditions of low collision rate and large optical thickness of the 184.9-nm resonance line. The measured data extend over a wide range of experimental conditions. The measurements were made using two different experimental methods, both employing low-pressure mercury–noble-gas discharges. In the first method the decay rate of the 6 ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ population was measured in the afterglow of the discharge using a dye-laser absorption technique. In the second one the decay was measured of the laser-induced fluorescence at the 184.9-nm line created by pulsed optical pumping. Radiative decay rates obtained with the two independent experimental methods for nominally the same conditions agreed within the experimental error of 5%. For zero perturber gas density the radiative decay rate as a function of the Hg density shows a pronounced minimum. This minimum disappears with the addition of an argon density of more than about 3×${10}^{22}$ ${\mathrm{m}}^{\mathrm{-}3}$, which corresponds with an extra collisional broadening of ∼15 MHz. The experimental decay rates differ largely from rates calculated with a complete frequency redistribution theory. Comparison with rates calculated from the partial redistribution theory described in paper I (preceding paper) shows agreement within 25%. The behavior of the experimental rates at the lowest mercury densities could be interpreted as due to a deviation from the natural abundance in the 6 ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ excited-state population.

We study the analytic properties of the hypernetted-chain (HNC) and soft-mean-spherical (SMSA) theories in the asymptotic high-density limit (AHDL). The scaling properties of the inverse power potentials lead to the introduction of the SMSA-Ewald functions, which correspond to the ‘‘overlap-volume’’ functions for hard spheres. The HNC and SMSA theories for soft interactions, as well as the Percus-Yevick theory for hard spheres, feature the same AHDL analytic structure of the pair correlation functions, which is dictated by the hard-sphere Ewald functions. The general discussion is supplemented by detailed results for the one-component plasma. Implications to the analysis of the density-functional theory, of dense matter, near its exact Thomas-Fermi limit are pointed out.

A kinetic theory is presented for the thermal conductivity of a strongly coupled, fully ionized hydrogen plasma of typical temperature and density 10≤T≤${10}^4$ eV, ${10}^{20}$≤n≤${10}^{27}$ ${\mathrm{cm}}^{\mathrm{-}3}$. This theory gives results in good agreement with molecular dynamics and recovers weak-coupling-theory values at high temperature. The theory has then been generalized to a three-component hydrogen plasma made up of protons and electrons of spin up and spin down. It is found that the ionic part of the thermal conductivity cannot be neglected in the high-temperature high-density domain of the parameters.

We present a computer simulation on a lattice of a long charged polymer diffusing in a topologically restricted environment in the presence of an electric field. The problem is related to that of a set of self-attracting particles diffusing in a random environment. For strong fields the polymer gets trapped in metastable configurations, so that the relaxation time of the polymer has an exponential dependence on chain length. Various correlation functions such as the mean square displacement vary logarithmically with time.