We present the concept of dynamic symmetry of the Gell-Mann type to the dynamical evolution of an arbitrary quantum system of N levels involving generally time-dependent interaction parameters which are of arbitrary strengths and which need not be precisely known. The most important consequence of the dynamic symmetry is the existence of a characteristic set of constants of motion which resembles the existence of a set of quantum numbers of various flavors in high-energy particle physics, and which implies various types of population trapping in the coherent excitation of atoms by lasers in intense-field electrodynamics.

We examine phase conjugation via degenerate four-wave mixing in liquid suspensions of microellipsoids in the small-field limit, where saturation effects can be ignored. For these media, electro- strictive torques rotate the microellipsoids in such a way that two orthogonal orientational gratings are created. Furthermore, electrostrictive forces modulate the microparticle density, which gives rise to the formation of two orthogonal spatial gratings that are superimposed on the orientational ones. Coherent scattering of pump radiation from these four gratings generates the conjugate wave and, in the low-loss limit, amplifies the probe wave. We discuss the steady-state and transient characteristics of the probe and conjugate waves in this limit where microparticle dynamics are governed by diffusion.

The nonlinearly induced nonreciprocity of counterpropagating waves caused by an index grating in a Kerr medium can be used to nonlinearly enhance the Sagnac effect in a ring resonator. A specific discussion of this effect in the case of a fiber-optic rotation sensor is presented. Our theory, which holds for any value of the cavity finesse, includes transverse effects explicitly, but neglects stimulated scattering. Special emphasis is given to pure cavity effects which always occur simultaneously with the nonlinear Sagnac effect.

The incoherent emission from an undulating electron beam in the presence of metallic boundaries is analyzed. A general method of solving Maxwell’s equations is used to express the field of a single particle in terms of vector waveguide modes. It is shown that the radiation characteristics depend upon a parameter involving the energy, wiggler wavelength, and the waveguide transverse dimension. At some values of this parameter the energy spectrum and angular distribution will differ significantly from the analogous free-space results. The amount of energy emitted into resonator modes is also analyzed in terms of a similar expansion.

The operation of a free-electron laser with an electromagnetic pump in the presence of a guide magnetic field is considered. It is shown that several different steady-state helical equilibria are allowed in a given configuration of the pump and guide fields. The study of the dynamics of the beam shows that the helical equilibrium is an exception rather than the rule. Thus only special initial conditions and careful tapering of the transition region at the entrance into the laser allow launching the beam on one of the stable steady states. The small signal gain in the laser is also derived. It is shown that the gain can be substantially enhanced when the beam approaches the orbital instability regime. Numerical examples demonstrate that the strength of the pump field in these conditions can be greatly reduced while still providing enhanced gain in the laser.

The squeezing spectra for the output fields of several intracavity nonlinear optical systems are obtained. It is shown that at critical points, e.g., the turning points for optical bistability, the threshold for parametric oscillation, and the self-pulsing instability in second-harmonic generation, perfect squeezing in the output field is, in principle, possible.

A Monte Carlo method is used to generate trajectories for a nonlinear stochastic model. A set of initial conditions distributed according to the equilibrium distribution function of the system is considered. Then, after averaging, the equilibrium time correlation function can be computed. The numerical results are compared with those obtained by means of the van Kampen expansion method and also by the local equilibrium approximation. The latter is shown to give a good description of the behavior over a wide range of values of the parameters.

Plasmas produced from cylindrical and planar targets by line-focused 30-ps-duration, high-intensity (∼${10}^{14}$ W/${\mathrm{cm}}^2$), 1064-nm laser pulses have been characterized with a number of diagnostics. Detailed measurements of the morphology and expansion of the electron-density profile were made with picosecond interferometry and compared with predictions of a two-dimensional Eulerian hydrodynamic code. Microscopic filamentation structure in the center regions of the corona, and the generation of a density plateau at $n_c$/4, were features consistently observed which lack quantitative explanations. The implications of these observations for the production of optimum plasma conditions suitable for recombination or collisionally excited x-ray laser schemes are discussed.

Starting from an exact expression for the Helmholtz free-energy functional of an inhomogeneous classical liquid, an approximate functional is presented which depends on a weighted average of the physical density. It retains the nonlocal character of the exact expression, but requires only the properties of the homogeneous liquid. A physical choice of the weighting function used to construct the weighted density is made by appealing to the structure of the homogeneous liquid. The resulting weighted-density approximation (WDA) corresponds to an approximation for some of the third- and higher-order terms in a density-functional expansion of the true free energy, the first-, second-, and a subset of higher-order terms being retained exactly. In this respect the theory differs crucially from earlier functionals based on weighted-density ideas. As an application of the WDA, the freezing of simple liquids is considered within the framework of mean-field theory and is briefly compared to previous theories. In particular, the freezing transition of the hard-sphere system is studied using the WDA formalism, the resulting freezing parameters and the equation of state for the solid being in good agreement with computer-simulation studies.

We present data with an accuracy of 1 part in ${10}^4$ for the equation of state of the classical hard-disk fluid obtained by a Monte Carlo–molecular-dynamics method for a system of as many as 5822 particles when τ=${\rho }_0$/ρ ranges from τ=30 to 1.4, where ${\rho }_0$ is the value of the number density ρ for closest packing. The data are in excellent agreement with those obtained using a Levin approximant applied to the first six terms of the virial series.

We show that the formal results of many-body, isothermal response theory can be generated from thermodynamic extremum principles. It is shown that this method yields the correct time-dependent response to a perturbing external field.

For random walks on finite lattices with multiple (completely adsorbing) traps, one is interested in the mean walk length until trapping and in the probability of capture for the various traps (either for a walk with a specific starting site, or for an average over all nontrap sites). We develop the formulation of Montroll to enable determination of the large-lattice-size asymptotic behavior of these quantities. (Only the case of a single trap has been analyzed in detail previously.) Explicit results are given for the case of symmetric nearest-neighbor random walks on two-dimensional (2D) square and triangular lattices. Procedures for exact calculation of walk lengths on a finite lattice with a single trap are extended to the multiple-trap case to determine all the above quantities. We examine convergence to asymptotic behavior as the lattice size increases. Connection with Witten-Sander irreversible particle-cluster aggregation is made by noting that this process corresponds to designating all sites adjacent to the cluster as traps. Thus capture probabilities for different traps determine the proportions of the various shaped clusters formed. (Reciprocals of) associated average walk lengths relate to rates for various irreversible aggregation processes involving a gas of walkers and clusters. Results are also presented for some of these quantities.

A theory is presented for the anomalous light scattering which has been observed at the surface of a growing ice crystal. The theory is based on a model for the production and distribution of defects at and near the growing interface. Analysis of this model shows under appropriate conditions that the surface distribution exhibits multiple uniform or nonuniform stationary states. Connected with the occurrence of the multiple stationary states is a critical growth velocity at which the surface undergoes a transition from a state of low average defect density to a state of high average defect density. Using hydrodynamic fluctuation theory, we calculate the structure factor for quasielastic light scattering from defects in the surface layer. The model accounts for the following qualitative observations: a threshold for anomalous scattering, the change in spectrum of scattered light, hysteresis, and spreading in time of the scattering region. Using the measured spectral linewidth, the measured critical velocity, and the experimental estimate of the scattering layer, we deduce from the model that the scattering region will spread with a constant velocity of 5 μm ${\sec }^{\mathrm{-}1}$. This number falls within a factor of 2 of the experimental value. On the basis of the model suggestions are made for further experiments.

High-electron-density, low-temperature plasmas have been produced with a minimum of 1 electron per Debye sphere by high-power, short-pulse resonant laser pumping of dense (${10}^{16}$–4×${10}^{17}$ ${\mathrm{cm}}^{\mathrm{-}3}$) sodium vapor. The recombining plasmas were diagnosed by time-resolved emission spectroscopy. Electron densities between 0.5×${10}^{16}$ and 2.2×${10}^{16}$ ${\mathrm{cm}}^{\mathrm{-}3}$ were inferred from widths and shifts of allowed lines and intensities of forbidden components. Electron temperatures between 0.2 and 0.3 eV were calculated from relative line intensities, since all states above 3d were shown to be in partial local thermodynamic equilibrium. Such low temperatures coupled with other experimental evidence suggested that laser-induced associative ionization involving atoms in the 3p state was the dominant ionization mechanism.

Cool, dense plasmas were produced by two-photon resonant (3s→3d) three-photon ionization of sodium vapor by a 0.5-MW pulsed dye laser operating at λ=6854 Å. Electron densities were deduced from the width and shift of the 3p-4d line shape observed in emission and from the intensity of the dipole-forbidden component 3p-4f. Electron temperatures were calculated from ratios of line intensities by assuming partial local thermodynamic equilibrium. A minimum of 1 electron per Debye sphere was achieved and the degree of nonideality shown to be limited by collisional recombination.

The motion of atomic ions in a rare-gas cathode fall is limited by symmetric charge exchange. Nonequilibrium solutions of the Boltzmann equation for this problem are presented. The distance required for the average ion velocity to approach within 10% of the equilibrium drift velocity is calculated for constant and for linearly increasing fields, with a plane ionization source and with a uniform source. The equilibration distances range from two-thirds to six mean free paths. A rare-gas cathode fall is typically 50–100 mean free paths thick; hence the ion motion may be accurately described by the equilibrium drift velocity throughout most of the cathode fall.

From mode-coupling theory, we obtain the complete long-time behavior of kinetic, potential, and cross terms of the Green-Kubo integrands for the transport coefficients in a classical electron gas. The results for the kinetic parts are in agreement with those derived recently with use of kinetic theory. The differences between the long-time tails in the electron gas and those in neutral fluids are discussed in detail. The theory suggests that the frequency-dependent heat conductivity diverges as the plasma frequency is approached.

Two previously unreported phenomena, a period-2 window and band splitting, are observed in an LRC circuit, and a model with the same characteristics is presented.

The transition from Hamiltonian to dissipative systems is studied. In the dissipative standard map the area-preserving map becomes dissipative as the dissipation parameter is varied and ultimately turns into a one-dimensional circle map. All periodic orbits on the Hamiltonian map go over smoothly into orbits in the circle map. Many-piece strange attractors on the one-dimensional map are gradually wiped out as the dissipation disappears.

Wavelengths and atomic parameters for the satellite spectrum of the 1$s^2$-1s2p parent lines of heliumlike ions from ${\mathrm{Ar}}^{16+}$ to ${\mathrm{Mn}}^{23+}$ have been calculated using a multiconfiguration intermediate-coupling scheme with a statistical Thomas-Fermi potential. The results are compared to high-resolution x-ray spectra of ${\mathrm{Ar}}^{16+}$, ${\mathrm{Sc}}^{19+}$, ${\mathrm{V}}^{21+}$, ${\mathrm{Cr}}^{22+}$, and ${\mathrm{Mn}}^{23+}$ obtained from plasmas generated at the Tokamak de Fontenay-aux-Roses.