We report measurements of the static properties of laser-cooled non-neutral ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{+}{}_{}{}^{}$-ion plasmas stored in Penning traps under a variety of experimental conditions. We have measured the shape, rotation frequency, density, and temperature of the ions as functions of the Penning-trap potential and laser-cooling configuration. Two different traps were used. In one trap, we were able to measure the ion temperature in directions both perpendicular and parallel to the trap magnetic field. In the other trap, ${}_{}{}^{198}{}_{}{}^{}\mathrm{Hg}_{}^{+}{}_{}{}^{}$ ions were stored simultaneously with the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{+}{}_{}{}^{}$ ions and their effect on the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}_{}^{+}{}_{}{}^{}$ ions was measured. The experimental measurements are compared with theoretical predictions. Within experimental error, the ion plasmas rotate without shear and exhibit approximate thermal equilibrium. For a single stored species, a static model of the ion plasmas, based on thermal equilibrium, is formulated. When the ion-plasma dimensions are small compared to the trap dimensions, this model predicts that the ion plasmas are spheroidal and have an aspect ratio which is a function of the plasma rotation frequency, and the single-particle cyclotron and axial frequencies. This is verified by measurement. The ion densities and temperatures measured in our experiments show that the plasmas are strongly coupled and should exhibit liquid and solid properties.

The homodyne scattering function, F(q,t), for a turbulent fluid is computed using a renormalization-group analysis of the stochastic Navier-Stokes equations subjected to Gaussian forcing with $k^{\mathrm{-}y}$ correlations (k is the wave vector) [D. Ronis, Phys. Rev. A 36, 3322 (1987)]. Scaling forms for F(q,t) in the long- and short-time limits are obtained for large Reynolds number. Corrections to scaling are analyzed in light of the recent experiments of Tong et al. [Phys. Rev. A 37, 2125 (1988)].

A procedure is presented for the calculation of the intensity of light doubly scattered by a critically opalescent fluid. The procedure is valid for general scattering angles and fully incorporates the effect of turbidity on the double-scattered light. The intensity and depolarization ratio of double-scattered light is evaluated as a function of temperature, angle, and sample-cell dimensions for some representative liquid mixtures near the critical point of mixing. A comparison with experimental multiple-scattering data is also included.

We study the Couette-Taylor instability for a large class of Maxwell models. We find that for a wide range of parameters the basic equations do not have an axisymmetric Couette-like solution. Furthermore, we show that from Maxwell-type models oscillatory instability is not to be expected at threshold. We calculate the critical Reynolds number and the critical wave vector by integrating the perturbation equations numerically for the cases of small and large gap.

Dielectric relaxation of water/AOT/oil (iso-octane, undecane, dodecane, cyclohexane) microemulsions was studied by means of time-domain spectroscopy. [Here AOT is an abbreviation for sodium bis(2-ethylhexyl)sulfosuccinate.] The experiments were carried out for several values of the volume fraction φ (water + AOT) and of the molar ratio n= [water]/[AOT]. They showed the presence of a maximum of static permittivity ${\epsilon }_s$ associated with a minimum of the relaxation frequency ${\nu }_R$ and a maximum of the frequency-spread parameter α. The influence of the salt content was also considered. The results are discussed with reference to the theory of percolation, and were found to be in close agreement with the theoretical predictions. By analogy with previous results on conductivity [M. Moha-Ouchane, J. Peyrelasse, and C. Boned, Phys. Rev. A 35, 3027 (1987)], the influence of temperature is discussed. The important part played by interactions and the phenomenon of ‘‘hopping’’ are demonstrated in connection with an already existing model (an off-lattice simulation). Finally, the results show the importance of the notion of ‘‘percolation threshold lines’’ introduced previously (Moha-Ouchane, Peyrelasse, and Boned).

On the basis of the maximum-entropy principle, the usual definition of temperature is extended to quantal systems. Entropy, specific heats, and state equations are evaluated for bounded (i.e., spinorial systems) and unbounded operators (i.e., electromagnetic field systems).

A multistate molecular expansion is developed to describe the charge transfer of ${\mathrm{O}}^{3+}$ ions with neutral hydrogen atoms in which the individual fine-structure levels of the initial ${\mathrm{O}}^{3+}$ ion and the product ${\mathrm{O}}^{2+}$ states are taken into account. The coupled scattering equations are solved and cross sections are obtained for charge transfer excitation at energies near 1 eV.

Fractal boundaries can occur for certain situations involving chaotic Hamiltonian systems. In particular, situations are considered in which an orbit can exit from the system in one of several different ways, and the question is asked which of these ways applies for a given initial condition. As an illustration, specific examples are considered for which there are two possible ways in which a particle can exit from the system. We examine the space of initial conditions to see which of the two exit possibilities applies for each initial condition. It is found that the regions of initial-condition state space corresponding to the two exit modes are separated by a boundary that has both fractal and smooth (nonfractal) regions, for one example, and by a fractal boundary for the other example. Furthermore, it is found for the example where the boundary has fractal and smooth regions that these regions are intertwined on arbitrarily fine scale. The existence of fractal boundaries is conjectured to be a typical property of chaotic Hamiltonian dynamics with multiple exit modes. Two situations in space physics where our results may be relevant are discussed.

The Hartree-Fock potential surface of a stacked formamide dimer is fitted with a Taylor series of sixth order in three geometrical degrees of freedom. Using this potential, molecular dynamics in formamide stacks are studied. The existence of solitary waves is numerically shown. Furthermore, it is shown that the phenomenon is due to the nonlinear part of the forces. These waves are produced by distortions of the geometry at the chain ends as well as in the middle of the chain. In the latter case two waves traveling in opposite directions are formed. Two solitary waves survive collisions without considerable perturbations. The velocities of the different kinds of waves are intrinsic properties of the system, being independent of the kinetic energy transported. The kinetic mass of the waves is rather high (up to 900 electron masses) depending on the energy carried by the waves. A lower limit of the excitation energy for creating a solitary wave could not be found.

A percolation model of critical-cluster scaling is studied. The model allows the generation of configurations of strongly self-similar clusters by stochastic decimation on a tree. Tree traversal is controlled by a probability parameter p. At p=0 or 1, the configuration is deterministic, but, for 0<p<1, it is random. The decimation algorithm uses the Sierpinski carpet and Vicsek snowflake generators, so that the treelike character (connectedness) of the clusters can be changed continuously. Various dimensions of the (fractal) percolation cluster are calculated using boundary conditions that give correct values at the deterministic limits. The usual cluster distribution law, $n_s$∝$s^{\mathrm{-}\tau }$ with τ=d/D+1, is obeyed for stationary p in (0,1), although τ=d/D, the deterministic value at p=0 or 1. Here d is the space dimension, and D the fractal dimension of the percolation cluster. The sensitivity of τ to changes in p near p=0 or 1 allows anomalous cluster scaling, so that τ may be fixed between d/D and d/D+1, without affecting D. Possible applications of the model are discussed.

We explicitly show that analytic continuations in the number n of components in n-component cubic models usually break down at finite values of the field at low temperatures due to phase transitions in n. We also consider the replica system and show that replica symmetry must be broken, not only when n→0, but also when n is a positive integer.

A formalism which allows perturbative renormalization-group calculations for self-avoiding polymers and flexible membranes of a fixed internal connectivity is presented in detail. Upon considering general D-dimensional elastic manifolds embedded in a d-dimensional space, we expand about a line in the (d,D) plane separating ideal ‘‘phantom manifold’’ behavior from a region where self-avoiding interactions are important. When d is fixed at 3, this procedure leads to a (6/7+ε expansion for the radius of gyration exponent ν, where ε=D-(6/7. Although we obtain consistent results for ν to lowest order in ε, the generalized polymer exponent γ displays an anomalous dependence on the shape of the manifold boundary.

A variational approach is applied to collisions of a particle having a mass m with a harmonic oscillator having a mass M in one dimension. We have used trial functions which become exact in the limit of either m/M≫1 or m/M≪1. We have derived exact expressions in the limit m/M→0 for inelastic as well as elastic collisions to leading order in the parameter m/M for any impenetrable interaction potential.

The numerical analysis of stochastic relaxation in bistable periodic potentials driven by colored external noise is carried out by employing a numerical algorithm based on a well-established continued-fraction expansion. The present investigation is aimed to sort out conflicting theoretical predictions by providing a detailed and accurate numerical description of the phenomenon. Some of the perturbation theories reported in the literature are shown to reproduce, each to a different extent, the stationary probability distribution of the problem, whereas a nonperturbative approach is required to approximate the relevant relaxation time (mean first-passage time). Our numerical analysis exhibits the lack of a comprehensive theory of bistability in the presence of colored noise. A new finding of the study herein is the extension of the property of isospectrality of the Fokker-Planck equation under potential inversion (from bistable to metastable). Such a property is proved to hold for Fokker-Planck equations describing one-dimensional systems also driven by colored external noise.

Simulations of ballistic deposition onto an inclined surface (deposition at non-normal incidence) have been carried out using two-dimensional lattice and off-lattice models and three-dimensional off-lattice models. For most of these models the relationship between the angle of incidence (θ) and the angle of growth (φ) is given by φ=$C_1$θ for small angles of incidence and φ=θ-$C_2$ for large angles of incidence. The constant parameters $C_1$ and $C_2$ are sensitive to model details. All of our results deviate strongly from the tangent rule (tanφ=(1/2tanθ). For small (near-normal) angles of incidence the thickness of the deposit surface (ξ) is related to the mean height of the surface (h¯) by ξ∼h${¯}^{\beta }$ where the exponent β has a value of about (1/3. As θ is increased β increases and approaches a limiting value of about (1/2 for θ→π/2. Similarly, the exponents ${\nu }_{?}$ and τ which describe the internal substructure of these compact deposits change from values of 0.6 and 1.4 for normal incidence to values of about (2/3 and (4/3 for grazing incidence.

The three-photon-annihilation contribution to the positronium hyperfine interval is obtained in analytic form. This contribution is of order m${\alpha }^6$, and has the value -0.969 MHz. The result of a previous calculation of this contribution is shown to be incomplete because of a subtlety in the regularization of infrared divergences.

Asymptotic formulas for the resonances of the cubic anharmonic oscillator in both the regimes of small and large coupling constant g are derived. In addition, a numerical calculation is carried out to give a complete graphical picture of the behavior of the resonance eigenvalues over the whole range of g.

A sum rule for the so-called quantum phases is established, without assuming adiabatic evolution. By considering two interacting quantum systems, conventionally designated as a boson and a fermionic one, we evaluate the effective bosonic action after integrating out the fermionic variables. This effective action contains a nontrivial topological part, which has the same origin as the quantum adiabatic phase. However, the derivation does not rely on any adiabatic assumption.

A theoretical procedure based on the configuration-interaction approach of Fano [Phys. Rev. 124, 1866 (1961)] is presented for the photoionization between states dominated by strong configuration interaction. By correctly identifying the main contributing interaction between the dominating bound configurations, the effectiveness of this procedure is demonstrated by its application to photoionization from the Mg 3s3${\mathit{p}}^1$P excited state to the ${}_{}{}^1{}_{}{}^{}\mathrm{S}$ continuum dominated by the 3$p^2$ ${}_{}{}^1{}_{}{}^{}S$ doubly excited autoionization state above the first ionization threshold. In addition to the good agreement with the experimental data, the individual contributions from different physical processes are also examined in detail.

A Coulomb-Born distorted-wave approximation, in which allowance is made for the distortion of partial waves by direct multipole potentials, has been used to evaluate the excitation cross section of ${\mathrm{Mg}}^{+}$ by electron impact. The calculations have been carried out using a unitarized four-state approximation (3s-3p-4s-3d) for the incident energy range 4–135 eV. The problem has been formulated in the LS coupling scheme, with the target ion being represented by a core plus atomic electron (frozen-core approximation) and exchange between the atomic and the incident electron being neglected. For the optically forbidden 3s-3d and 4s-3d transitions a simple analytic formula has been derived to estimate the contribution to the total collision strength from large values of angular momentum.