This paper presents new results for the steady states of a detuned ring laser with a saturable absorber. We employ a semiclassical model which assumes homogeneously broadened two-level atoms. We proceed by solving the Maxwell-Bloch equations for the longitudinal dependence of the steady states of this system, and then simplify our solution by use of the uniform-field approximation. We present uniform-field results for squared electric field versus operating frequency, and for each of these versus cavity tuning and laser excitation. Various cavity linewidths and both resonant and nonresonant amplifier and absorber line-center frequencies are considered. The most notable finding is that cavity detuning breaks the degeneracies found in the steady-state solutions of the fully tuned case. This leads to the prediction that an actual system will bifurcate from the zero-intensity solution to a steady-state solution as laser excitation increases from zero, rather than to the small-amplitude pulsations found for the model with exactly resonant tuning of the cavity and the media line centers. Other phenomena suggested by the steady-state results include tuning-dependent hysteresis and bistability, and instability in both intensity and frequency due to the appearance of one or more new steady-state solutions as tuning is varied. These effects of detuning are being tested by a linearized stability analysis whose results will be reported separately.

We have observed a collisionally induced rotation of the polarization of a linearly polarized probe beam interacting with a nonresonant circularly polarized pump beam in sodium vapor. We interpret this Faraday effect of a new kind both by a nonlinear-susceptibility calculation and by an optical-pumping calculation, and we show the close connection between the two approaches.

We investigate numerically the photon statistics and squeezing properties of the free-electron laser. In one model we assume the initial distribution of photons to be thermal (Bose-Einstein distribution). Our results for this model indicate no photon antibunching. We obtain similar results for another model, where we have started from an initial distribution which is nearly a pure state (the α-β model). However, both these models exhibit squeezing.

We demonstrate the use of so-called essential states in relativistic electron theory, in a case where free-free matrix elements are not factorable in energy.

We consider the polarization dynamics of a pulse propagating through an arbitrary nonlinear medium, in the limit of small nonlinearities, anisotropies, and dispersion, using the full SO(3) covariance of the Stokes parameters. The invariants of the motion are discovered and physically interpreted, a complete analogy with the ‘‘airplane-and-rotor’’ problem of rigid-body dynamics is established, and a full classification of the solutions for parity-invariant and non-parity-invariant media, with all propagation-axis rotation symmetries, is presented. In all cases, the problem is reduced to quadrature; in most cases, we find analytic solutions in terms of well-known functions.

A Stokes-vector formalism is used to describe the nonlinear polarization dynamics of counterpropagating beams. We prove the existence of a new general invariant, and the full SO(3) covariance of the Stokes parameters is applied to investigate the form the equations take for parity-invariant and non-parity-invariant media, with a rotational symmetry $C_n$, n≥1 about the propagation axis. As long as n≠1, 2, or 4, the equations are found to be integrable. Otherwise, chaotic behavior is possible. A host of new, simple analytic solutions are found.

Dynamical cross-correlation functions are reported for the diffusion of spherical-top molecules, exemplified by the $T_d$-symmetry molecule carbon tetrachloride in the liquid state at 296 K. These are novel types of cross-correlation functions which exist directly in the laboratory frame of reference, (x,y,z), and involve rotational and translational motion simultaneously. Contemporary analytical theories for the diffusion of the spherical top are not able to account for these results, which were obtained by computer simulation.

We present a novel spectroscopic diagnostic that provides a detailed picture of a radio-frequency discharge’s response to photodetachment of electrons from negative ions. Spatially and temporally resolved changes in the local electric field of a 50-kHz discharge through ${\mathrm{BCl}}_3$ are monitored using Stark-mixing spectroscopy. These local measurements are also compared to current transients that appear simultaneously in the external circuit (optogalvanic effect). Both the external current and the local field exhibit oscillations at frequencies characteristic of ion motion; however, the local measurements provide a more detailed picture of the changes in sheath structure. Near the momentary anode, the sudden increase in negative charge mobility causes a reduction in the sheath field magnitude but an overall increase in sheath thickness. Initially, the plasma potential floats up toward the anode potential because of the loss of negative charge but subsequently decreases below the initial level as the system relaxes back to steady state in an oscillatory manner.

We analyze the derivation of boundary-layer models for dendritic growth and investigate the extent to which they yield information about the existence of a continuous family of steady-state needle crystal solutions. Although recent work has established that there exists only a discrete set of solutions for viscous fingering in a Hele-Shaw cell, side walls play an important role in this system, and we argue on physical grounds that the same mechanism may not apply to free dendrites. After a discussion highlighting the physical differences in these two systems, we analyze the model equations for dendritic growth, which first suggested the breakup of the family. We develop a systematic, and in principle exact, boundary-layer formalism for diffusion-controlled dendritic growth starting from the full heat-conduction equation. A consistent application of the formalism generates an expansion of the smooth steady-state solutions in powers of (1-Δ), where Δ is the dimensionless undercooling, but gives no indication as to whether or not a family of such solutions exist. Different physically motivated approximations yield different model equations, including the boundary-layer model of Ben-Jacob and co-workers, with very different properties. Steady-state predictions of all such models are arbitrary. We show that a proper phase-space description requires an infinite-dimensional phase space, in which there are stable directions not found in the boundary-layer model.

Taking the excitation 1s→2s of a hydrogenlike ion as an example, the authors have examined the effect of plasma electrons on the resonance contribution 1s→3pnl→2s to the excitation cross section, where 3pnl stands for the doubly excited ion produced by dielectronic capture of the 1s ion. They adopt an approximation method in which it is assumed that all the dielectronic capture into the doubly excited levels lying higher than a certain critical level is lost from the doubly excited levels through the ladderlike excitation ‘‘ionization.’’ The part of the resonance cross section corresponding to these levels accordingly disappears. They follow the same procedure to obtain the effect on the resonance contributions from 1s→3snl→2s and 1s→3dnl→2s. It is found that for the ${\mathrm{Ne}}^{9+}$ ion taken as an example the plasma electron effect is appreciable for densities higher than ${10}^{19}$ ${\mathrm{cm}}^{\mathrm{-}3}$.

The conductivity of water-AOT-undecane microemulsions has been studied with respect to the molar ratio ω=[water]/[AOT], temperature, and salinity. [Here AOT is an abbreviation for sodium bis(2-ethylhexyl)sulfosuccinate.] The use of a percolation model gives an excellent agreement between experimental and calculated values. We have determined for three temperatures (T=15, 25, 35?deC) the positions of the percolation thresholds in the phase diagram. The influence of salinity shows the important role of the interactions between particles.

Spectra of the complete series of ground-state transitions in heliumlike ${\mathrm{Ar}}^{16+}$ (1snp-1$s^2$, for 2≤n<50) have been obtained from the Alcator-C tokamak with use of a compact x-ray crystal spectrometer. Radial profiles of these transitions have been measured and have been compared with the results of a transport model which includes the basic atomic processes. In the plasma center, collisional excitation is the most important population mechanism for the upper levels. For the outer regions of the plasma (r/$a_L$>0.5), recombination of ${\mathrm{Ar}}^{17+}$ is the dominant population process for upper levels of most transitions, and preferentially populates the n=2 triplet levels. Impurity transport provides sufficient amounts of hydrogenlike argon at the cooler, outer radii. For the high-n transitions 1s9p-1$s^2$ and 1s10p-1$s^2$, charge-exchange recombination is the dominant population mechanism at the plasma edge under certain operating conditions. The intensities of these lines have been used to determine neutral-hydrogen density profiles. For ground-state transitions with n>13, charge transfer from excited neutral hydrogen is the only important population process for r/$a_L$>0.5.

We present the results of a study of models of controlled aggregation on a square lattice. The purpose is to provide insight into the geometry of aggregates formed during diffusion-controlled growth. The probability of particle appendage at each surface site is solved for exactly, and the particles sited according to physically motivated algorithms. The resulting aggregates are compared to a paradigm for such growth: Witten-Sander diffusion-limited aggregates (DLA). The importance of noise in producing the DLA geometry is studied by introducing randomness in a controlled way. We find that for strictly deterministic models in which particles are sited according to the relative strength of the diffusion field, the resulting aggregates show DLA-like scaling over 2 orders of magnitude in mass N, but tend to a dense structure with a morphology distinct from DLA. By contrast, the controlled-randomness aggregates display DLA-like scaling, morphology, and a skin depth which scales linearly with the size of the aggregate. From this we conclude that the open structure of DLA simulations results from the stochastic nature of its growth and, conversely, that experimental realization of DLA is due to fluctuations.

We apply renormalization-group and Monte Carlo methods to study the equilibrium conformations and dynamics of two-dimensional surfaces of fixed connectivity embedded in d dimensions, as exemplified by hard spheres tethered together by strings into a triangular net. A continuum description of the surfaces is obtained. Without self-avoidance, the radius of gyration increases as √lnL , where L is the linear size of the uncrumpled surface. The upper critical dimension of self-avoiding surfaces is infinite. Their radius of gyration grows as $L^{\nu }$, where Flory theory predicts ν=4/(d+2), in agreement with our Monte Carlo result ν=0.80±0.05 in d=3. The Rouse relaxation time of a self-avoiding surface grows as $L^{3.6}$.

Connections between the static density-functional theory of the glass transition and the dynamic mode-coupling theory of the glass transition are discussed. In three dimensions, some approximate equivalences are established. These equivalences are made more precise by examining high-dimensionality liquids and glasses. The similarities with early static and dynamic mean-field theories of the spin-glass transition are emphasized. Some speculations on the relationship between structural glasses and Potts glasses are also included.

We present an appraisal of differential-equation models for anomalous diffusion, in which the time evolution of the mean-square displacement is 〈$r^2$(t)〉∼$t^{\gamma }$ with γ≠1. By comparison, continuous-time random walks lead via generalized master equations to an integro-differential picture. Using Lévy walks and a kernel which couples time and space, we obtain a generalized picture for anomalous transport, which provides a unified framework both for dispersive (γ<1) and for enhanced diffusion (γ>1).

Herein we present a calculation of the mean first-passage time for a bistable one-dimensional system driven by Gaussian colored noise of strength D and correlation time ${\tau }_c$. We obtain quantitative agreement with experimental analog-computer simulations of this system. We disagree with some of the conclusions reached by previous investigators. In particular, we demonstrate that all available approximations that lead to a state-dependent diffusion coefficient lead to the same result for small D${\tau }_c$.

The occurrence of smectic order in a system of perfectly aligned hard cylinders is studied with use of a bifurcation analysis of the free-energy functional in the second virial coefficient approximation. This approximation is shown to yield a second-order transition of mean-field type towards a smectic phase. The influence of higher-order terms in the density expansion of the free-energy functional is considered by calculating the shift in the location of the bifurcation point associated with the transition, when the third- and fourth-order terms in the one-particle density are taken into account.

The problem of finding the probability density function of the output of an oscillator (a filter of order higher than the first) driven by dichotomous Markov noise (the random telegraph signal) is considered. No known theoretical methods are available for completely solving problems of this type. A somewhat general expression is derived for the output moments and an exact formulation for the probability density is presented in terms of Fokker-Planck–type equations. However, partly because of irregularly shaped boundaries, the Fokker-Planck equations are complicated and remain unsolved except in the first-order case. The paper concludes with some Monte Carlo results for a second-order Butterworth filter.

The phase diagram of a two-dimensional system consisting of colloids is investigated within the Kosterlitz-Thouless-Halperin-Nelson-Young theory of dislocation-mediated two-dimensional melting. We also present results for the interaction energy, the phonon spectrum, and the longitudinal and transverse sound velocity for different values of the screening length.