Cooperative effects in a system of three-level atoms in cascade configuration interacting with intense resonant fields are investigated. Analytical expressions for atomic populations in the excited levels, fluorescence intensities, and normalized intensity correlations are presented. The intensity correlations are used to test the violation of the Cauchy-Schwarz inequalities. The analytical results predict in the cooperative limit N→∞, a discontinuous behavior of all atomic observables with respect to a parameter related to the field amplitudes and the atomic decay coefficients. This discontinuous behavior is analogous to a typical nonequilibrium first-order phase transition.

According to the standard Karplus-Schwinger theory of saturation broadening, saturated line shapes are Lorentzians with linewidths that increase linearly with the perturbing field strength. This, however, is not what is observed experimentally when the saturating field is inhomogeneous. If the saturating field strength varies significantly over the experimental signal volume, we find that the saturated line shapes are strikingly non-Lorentzian. The ‘‘sharpness’’ of the experimental line shapes is quantified by an ‘‘effective linewidth,’’ which is the half width at half maximum of a Lorentzian that approximates the experimental line shape near line center. For certain classes of inhomogeneous fields, we find that this effective linewidth increases approximately as the square root of the saturating field strength, rather than linearly. We show that this class of inhomogeneous fields is distinguished by the presence of a node in the field geometry, and that the effect arises because the line shape near line center is dominated by the atomic population in the vicinity of the node. These results indicate the importance of understanding and accounting for inhomogeneous field effects when extracting physical information from experimental line shapes.

We present an analysis of a quantum nondemolition (QND) measurement, which determines which of the two possible paths a photon follows through a Mach-Zehnder interferometer. The measurement is effected by the nonlinear Kerr effect. If a photon traverses the arm of the interferometer containing the Kerr medium, it shifts the phase of a probe beam and then continues through to the interferometer output. The measurement does not destroy the photon but does disturb its phase. Using various probe states, we show how such phase disturbances reduce fringe visibility and enforce a principle of complementarity; the more accurately the QND measurement determines the path of the photon, the lower is the fringe visibility. We determine the appropriate parameters to optimize the observation of the two complementary quantities.

We compare theoretical predictions and experimental data for the multimode instability of optical bistability, which arises from the coherent dynamics of a system of two-level molecules contained in an optical cavity and driven by an external stationary laser field. Considerable insight into this phenomenon is provided by two ‘‘rules of thumb’’ that govern the behavior of the self-pulsing frequency, and establish its relation with the Rabi frequency of the intracavity field. We describe in detail the experimental apparatus and the main features of the experimental findings. The theoretical results are based on the Maxwell-Bloch equations for a ring cavity in the plane-wave approximation. Despite the crudeness of this model, the numerical data display a satisfactory qualitative agreement with the experimental results. Additional period-doubling and chaotic phenomena, predicted by the theory and not observed in the experiment, are presumably washed out by the longitudinal and radial variation of the electric field in the cavity.

In this paper we consider the nonlinear development of the plasma Rayleigh-Taylor instability, also known as the Kruskal-Schwarzschild instability. Numerical calculations suggest that the plasma-vacuum interface, which initially takes the shape of an exponentially growing cosine function, will become multivalued after a while. Bubbles are seen to develop and to tend to at least partially detach themselves from the plasma. This paper gives a simple model of the process on the interface of a plasma layer with a vacuum. Profiles obtained are very similar to those found numerically by other authors. These multivalued profiles acquire a new symmetry in the semi-infinite plasma limit.

In this paper we extend the previous study of flow profiles in cylindrical Couette flow of a Lennard-Jones fluid so as to include the effects of normal stresses neglected in the previous work. The flow is subject to a temperature gradient and thermoviscous effects are taken into consideration. We apply the generalized hydrodynamic equations which are provided by the modified moment method for the Boltzmann equation reported previously. The results of calculation are in good agreement with the Monte Carlo direct simulation results of K. Nanbu [Phys. Fluids 27, 2632 (1984)] and experimental data for all Knudsen numbers. The inclusion of normal stresses also brings about a new aspect to the flow properties which has not been seen before, since the flow profiles exhibit a phase-transition-like behavior as the Knudsen number increases beyond a critical value. There also appear slips in velocity at the inner cylinder wall in the supercritical regime of Knudsen number. At the critical Knudsen number the entropy production for the flow process also exhibits a singular behavior which is reminiscent of a second-order phase transition in thermodynamic systems.

Time-periodic Taylor vortex flow between two concentric cylinders is studied. With the outer cylinder at rest and the inner one rotating with angular velocity Ω(t)=Ω(1+Δ cosωt), the stability boundary of circular Couette flow and the fully nonlinear Taylor vortices are investigated. Results are obtained by a finite-difference numerical simulation of the full Navier-Stokes equations for a radius ratio η=0.65 and by an analytical Galerkin approximation with four modes for arbitrary gap width. Data obtained by both methods agree very well. Modulation is found to destabilize the basic flow in agreement with earlier theoretical results. The time dependence of Taylor vortices is determined in detail and compared with recent experiments. Their response to the modulated driving is elucidated and explained by investigating various limiting behaviors and by comparison with the amplitude equation. Subharmonic response is found for large modulation amplitudes when the driving Ω(t) becomes supercritical in both rotation directions during one period. Differences and similarities of linear and nonlinear flow properties with modulated convection in Rayleigh-Bénard systems are discussed in detail. That low-frequency small-amplitude modulation stabilizes the basic conductive state in the latter system while it destabilizes circular Couette flow is shown to be caused by the different coupling of the driving to the secondary flow field.

The linear stability of viscous flow between two rotating coaxial horizontal cylinders with a partially filled gap is investigated. It is shown that, for a range of values of the rotation ratio μ, the stability diagram for stationary modes consists of two separate curves connected by an oscillatory branch. For 0.26<μ<0.61 the critical point is on the oscillatory branch. Therefore it can be expected that, at onset, the instability will set in as an oscillatory mode. We have established the existence of codimension-2 points for two particular values of the rotation ratio μ=0.26 and 0.61, where the onset of instability for stationary as well as oscillatory modes occurs for the same value of the Taylor number.

The curvature dependence of the interfacial tension in binary nucleation was formulated by employing Tolman’s [J. Chem. Phys. 16, 758 (1948)] idea for the variation of state and the thermodynamics of inhomogeneous systems due to Cahn and Hilliard [J. Chem. Phys. 28, 258 (1958); 30, 1121 (1959); 31, 688 (1959)] and Hart [Phys. Rev. 113, 412 (1959)]. To investigate the numerical significance of the curvature dependence, the inhomogeneous regular solution model due to Cahn and Hilliard was employed. The interfacial tension was found to decrease with curvature and to be about 20% smaller than the value of the flat interface at a radius of 3 or 6 intermolecular distance for T=0.5$T_c$ or 0.8656$T_c$, respectively. The reversible work to form a critical nucleus predicted by the present theory is significantly lower than that obtained by neglecting the curvature dependence of the interfacial tension. Thus, neglect of the curvature dependence may severely underestimate the nucleation rate.

We have extended our previous analysis of diatom laser-induced excitation transfer, illustrated by several examples, to include modifications due to laser-induced resonances. Compact and rigorous final results have been obtained through the use of a projection-operator scheme in combination with the ‘‘symmetric-top’’ basis set and a full quantal treatment of the radiation field. The principal limitations on our analysis are a neglect of fine-structure coupling and a simplifying assumption that the ground electronic manifold supports no bound nuclear states. Simple order-of-magnitude estimates of the predicted resonant cross sections also are provided.

Local phase separation at the growth front of a spherulite has been found during crystallization in a polymer mixture of poly(ε-caprolactone) and polystyrene. The phenomenon can be qualitatively explained by the coupling between the preferential rejection of impurities (polystyrene) during crystallization and the existence of a phase diagram. This unusual phase separation clearly shows that there is an impurity-rich layer on the growth front of the spherulite. A nonlinear growth of spherulite and a shape instability have also been found in this system. They are discussed on the basis of the formation of an impurity-rich layer at the growing interface. We also discuss the relation between our results on spherulitic growth and the current theories on dense branching morphology in diffusion-controlled growth.

The complex shear viscosity of sterically stabilized colloidal dispersions of different-sized silica particles (radius a=28–76 nm) was measured with torsion resonators and a nickel-tube resonator between 80 Hz and 200 kHz. The volume fraction of the samples was varied from 0.10 to 0.60. In the intermediate-frequency region, the real and the imaginary parts of the complex shear viscosity decay as ${\omega }^{\mathrm{-}1/2}$ to their limiting values. The viscoelastic behavior can be described in terms of one relaxation strength $G_1$ and a series of relaxation times with ${\tau }_p$=${\tau }_1$ $p^{\mathrm{-}2}$. The complex shear viscosity scales with the dimensionless relaxation strength $a^2$$G_1$/$D_0$${\eta }_s$, the dimensionless relaxation time $D_0$${\tau }_1$/$a^2$, and the dimensionless angular frequency $a^2$ω/$D_0$. The dimensionless groups $a^2$$G_1$/$D_0$${\eta }_s$ and $D_0$${\tau }_1$/$a^2$ are a function of the volume fraction only. At higher volume fractions the high-frequency limiting values of the real part of the complex shear viscosity, ${\eta }_{\infty }^{\mathcal{’}}$, corroborate values calculated by Beenakker [Physica 128A, 48 (1984)].

We have used five-frame photography to investigate plasma-jet formation and its evolution in line-focused laser-produced plasmas. Small-scale plasma jets have been observed in low-Z and high-Z plasmas. We have also observed relatively large-scale plasma jets, which are similar in appearance to ‘‘tips of oxhorns’’ and always appear at the boundaries between hot plasma and cold target material or between two different-Z (e.g., high-Z and low-Z) plasmas. It is also shown that the plasma-jet structure is more pronounced for the short-wavelength-laser–irradiated targets. The causes of plasma jets and their influence on x-ray–laser schemes using a line-focused laser-produced plasma as a gain medium are discussed.

The wave number for one-dimensional maps is introduced. For unimodal maps the wave number as a function of the tuning parameter displays a complicated plateau structure. The wave number for every superstable orbit can be calculated from the Metropolis-Stein-Stein (MSS) [J. Comb. Theor., Ser. A 15, 25 (1973)] dynamic word. The smallest tuning parameter value corresponding to a superstable orbit with given wave number defines a sequence of superstable orbits, called the left sequence. The general expression for the MSS words of the left sequence is obtained. The left sequence of the plateau then forms a Farey staircase. The parameter dependence of the wave number, and in particular its scaling behavior, is discussed. In addition, introduction of higher-level wave numbers provides a more precise characterization for the long periodic and chaotic motion. The connection between the wave number and the power spectrum is also considered. Explicit results for the logistic map are presented.

The thermodynamic properties of a d-dimensional relativistic Bose gas mixture of particles and antiparticles are studied. The anomaly in the specific heat of the relativistic gas is removed by the pair-creation mechanism. The crossover from the nonrelativistic limit to the ultrarelativistic limit is also analyzed.

Experimental data are presented for the refractive-index behavior in the homogeneous phase below the cloud-point temperature of a critical microemulsion composed of sodium di-2-ethylhexylsulfosuccinate (AOT), water, and decane. The pressure dependence of the critical temperature (${\mathrm{dT}}_c$/dP) is also reported. Fitting the refractive-index data as a function of temperature, we find a (1-α) power-law singularity with an α value consistent with the Ising value ${\alpha }_I$=0.11. It is shown that the refractive-index anomaly observed in this microemulsion is an intrinsic effect, most likely related to the electric field dependence of the critical temperature (${\mathrm{dT}}_c$/${\mathrm{dE}}^2$). Further, using two-scale-factor universality and experimental values for ${\mathrm{dT}}_c$/dP and the correlation-length critical amplitude ${\xi }_0$, we also found that the density contribution to the refractive-index anomaly is negligibly small.

Several sources of error in the calculation of attractor dimension from time series by the Grassberger and Procaccia or similar algorithms can be avoided or minimized by appropriate choice of algorithm and of criteria for selection of parameter values. Some problems and means of avoiding them are demonstrated, and statistical results are presented for dimension calculated from many independent sets of each of a wide range of data set size, to show that sets of a few hundred vectors or even less are useful for dimension calculation. This method with small data sets is shown to be effective in following changes in attractor dimension of a nonstationary dynamical system.

A generalization of the McMillan-Kobayashi mean-field theory of smectic-A liquid crystals to explicitly include anisotropic hard-core interactions is described. Hard-core effects are incorporated using perturbation arguments on a reference system of aligned parallel ellipsoids with effective shape parameters, which is treated by a nonlocal-density-functional approach. The results reveal the necessity of including both anisotropic repulsions and certain ‘‘symmetry-breaking’’ attractive interactions, usually omitted from McMillan-Kobayashi treatments, for obtaining stable smectic-A phases. The theory shows explicitly how the interlayer distance in a smectic phase results, variationally, from incompressibility of the hard cores. Phase diagrams that include nematic, smectic, as well as isotropic liquid and vapor phases are presented, using both temperature and density (or pressure) as independent variables.

Feynman path integrals offer a convenient and elegant tool for dealing with the statistical physics of quantum-mechanical systems. By using the Trotter product formula, one can evaluate directly the propagation of many-body quantum systems in imaginary time. The idea of an influence functional arises when one wishes to consider division of the physical system into a primary system and a bath. We present a general approach to the problem of constructing influence functionals, one that is capable of dealing both with Boltzmann baths (classical oscillators) and quantum baths of bosons or fermions. The fermion bath of special interest is generally a submanifold of the electronic state such as the bridge structure connecting chromophores or electron localization subunits which are common in problems of mixed valency and superexchange. The fermion bath is treated by a general rewriting of the influence phase S as a sum of an eigenvalue part $S_{\mathrm{EV}}$ and a remainder, $S^0$, that describes transitions. Reduction of the original Hamiltonian leads to a reduced Hamiltonian with effective off-diagonal matrix elements and influence functionals which can include memory effects. We present a general formalism for construction of influence functionals, and discuss particular applications to systems of interest, especially in electronic-structure problems. The following paper presents a variational technique for finding effective Hamiltonians.

A powerful numerical procedure is developed for calculating temperature-dependent quantities, such as partition functions for quantum systems coupled to thermal or other baths. A variational procedure is worked out to construct model Hamiltonians starting from the general results of the previous paper for influence functionals. Explicit, though intricate, formulas for all relevant quantities are presented. The methods developed are applied to a generalized model for a boson-bath interaction.