It is shown that Prony’s method of exponential interpolation provides a simple technique for the construction of effective oscillator-strength distributions from a set of moments of the actual distribution. These effective oscillator-strength distributions may then be inserted into second-order perturbation expressions to yield upper and lower bounds on properties of atoms and molecules. Extensive calculations have been performed on the ground state of atomic hydrogen and bounds on the logarithmic mean excitation energies and the van der Waals coefficient are obtained.

The effects of finite laser bandwidth on resonant degenerate four-wave mixing (DFWM) are calculated with use of a model in which the intense, counterpropagating pump beams are characterized by a chaotic field, the probe beam is weak and monochromatic, and the medium consists of a gas of two-level atoms. We present a steady-state solution in the limit where the pump-laser bandwidth exceeds all other atomic relaxation rates. Although the mean intensity due to the fluctuating fields is spatially independent (no steady-state standing-wave pattern is established), the analytic results indicate that, for intensities above the saturation intensity $I_{\mathrm{sat}}$, spatially periodic saturation effects are important. Increasing bandwidth is shown to lead to an increase in the effective saturation intensity resulting in lower phase-conjugate reflectivity for I<$I_{\mathrm{sat}}$ than for coherent pump fields, in contrast to the results for narrow-bandwidth chaotic fields. The resonant DFWM line shape is also calculated and compared to the coherent result. We comment on the application of the model to other four-wave-mixing processes employing broad-bandwidth lasers.

The gain of the klystron free-electron laser is calculated with use of the coupled, self-consistent Lorentz-Maxwell equations. For high gain, the objective of the klystron configuration, the gain spectrum is found to be modified from the previously known low-gain result. This is caused by the shifting of the optical phase during the gain process. The klystron saturation in strong nonlinear optical fields is also discussed.

We propose an equation to calculate the intensity correlation function of a dye-laser model with a pump parameter subject to finite-bandwidth fluctuations. The equation is valid, in the weak-noise limit, for all times. It incorporates novel non-Markovian features. Results are given for the short-time behavior of the correlation function. It exhibits a characteristic initial plateau. Our findings are supported by a numerical simulation of the model.

Driven stimulated Brillouin rescattering, obtained by a multiline laser light, each satellite line downshifted by twice the acoustic frequency, is an efficient way to reduce stimulated Brillouin reflection [C. Montes, Phys. Rev. Lett. 50, 1129 (1983)]. An explicit reflection formula for two input lines depleting in a finite, homogeneous plasma slab—in the heavy ion-damping limit—is obtained which generalizes Tang’s formula for one single input line. Finite spectral interaction of narrow input lines with broad backscattered spectra are considered by solving numerically the nonlinear integro-differential ion-Compton equations. The results are compared to those obtained by a single wide-bandwidth input spectrum.

We examine phase conjugation via degenerate four-wave mixing in liquid suspensions of microspheres in the small-field limit, where saturation effects can be ignored. For these media, electro- strictive forces modulate the microparticle density in such a way that two orthogonal spatial gratings are created. Coherent scattering of the pump radiation from these two gratings gives rise to the formation of a conjugate wave, as well as amplification of the probe wave. We discuss the steady-state and transient characteristics of the probe and conjugate waves in this regime where the dynamics of the microparticles is governed by diffusion.

An analysis of the experimental self-oscillation spectra of an acousto-optic bistable device is presented in relation to a theoretical model developed recently by Gao and co-workers. The main feature of the spectra is the superposition of a modulated noisy background to a discrete structure composed of a fundamental oscillation and its harmonics. A shift of this fundamental oscillation in the route to chaos is measured and discussed in terms of the modes of the theoretical model.

The use of pulse sequences offers a solution to the conflicting requirements of spectral selectivity and high peak intensities needed to study multiphoton processes. In addition, it is shown that random—rather than regular—pulse sequences can provide unique information on the influence of coherence on a resonant multiphoton process, because the coherence can be adjusted independently of the resonance condition.

The effect of dissipation on a macroscopic superposition of quantum states is studied with use of a Markovian master-equation approach. It is shown that a superposition of two states is reduced to a mixture at a rate proportional to the separation between the two states. This underlines the difficulty of observing a superposition of macroscopic quantum states in practice.

A theoretical study is made of the process in which incident pump photons that interact with a nonlinear medium (such as a crystal lacking inversion symmetry) are spontaneously split into lower-frequency signal and idler photons. The down-converted fields are quantized and described by a continuum of modes, a subset of which interacts with each photodetector. It is shown that when two ideal photodetectors are appropriately located so that they receive the conjugate signal and idler photons, then the joint probability of two-photon detection by the two detectors can equal the single-photon detection probability. The time correlation between the two detected photons is shown to be limited either by the resolving time of the detectors, or by the bandwidth of the down-converted light, and to be independent of the coherence time of the pump field or of the length of the nonlinear medium. These conclusions are compared with the results of recent experiments.

Anisotropic Gaussian Schell-model (AGSM) fields and their transformation by first-order optical systems (FOS’s) forming Sp(4,R) are studied using the generalized pencils of rays. The fact that Sp(4,R), rather than the larger group SL(4,R), is the relevant group is emphasized. A convenient geometrical picture wherein AGSM fields and FOS’s are represented, respectively, by antisymmetric second-rank tensors and de Sitter transformations in a (3+2)-dimensional space is developed. These fields are shown to separate into two qualitatively different families of orbits and the invariants over each orbit, two in number, are worked out. We also develop another geometrical picture in a (2+1)-dimensional Minkowski space suitable for the description of the action of axially symmetric FOS’s on AGSM fields, and the invariants, now seven in number, are derived. Interesting limiting cases forming coherent and quasihomogeneous fields are analyzed.

The effects of amplitude and phase fluctuations of the pump laser on the resonance fluorescence under two-photon resonant excitation are studied. The averaging of the stochastic Bloch equations is carried out within the approximation scheme that has recently been applied to the case of one-photon resonant excitation. In the case of two-photon resonant excitation the stochastic pump field gives rise to multiplicative nonlinear Gaussian fluctuation effects. The phase fluctuations are treated in the phase-diffusion model, and the averaging over the amplitude fluctuations is performed by means of generating-function methods. Both the intensity and the intensity correlation of the fluorescent light are studied. When the amplitude fluctuations are weak, the cases of one- and two-photon resonant excitations are similar. The difference between both cases consists of a modification of the Rabi frequency and a faster damping of the Rabi oscillations in the two-photon case. For sufficiently fast correlation decay of the amplitude fluctuations their effect can simply be described by a rate. In the general case of n-photon resonant excitation this rate is larger by a factor of $n^2$ than that in the case of one-photon resonant excitation. When the amplitude fluctuations are sufficiently strong, the Rabi oscillations are ‘‘washed out.’’ In the case of one-photon resonant excitation both the intensity and the intensity correlation function of the scattered light develop into step functions over time. In the two-photon case the dynamics of both quantities is determined by a new time constant which acts as both the oscillation time and the damping time. Consequently an overshoot peak occurs in both the intensity and the intensity correlation instead of the tendency to become step functions.

We study, theoretically and numerically, domain formation and growth in a one-dimensional system with nonconserved order parameter, which evolves from an initial unstable state, through the field model equation of Ginzburg and Landau. We are able to distinguish two time regimes and to give an estimate of the separation time, associated with early-stage domain formation and their final slow growth related to domain-wall interaction.

Autoignition phenomena in combustion problems exhibit a remarkable random behavior. We show on a simple model of an exothermic reaction that the phenomena has strong analogies with the transient behavior of a chemical explosion (Malthus model). These analogies lead to the construction of a simple theory of fluctuations. This theory is a natural extension of the theory already developed for the transient behavior associated with the Malthus-Verhulst problem and laser instability. Although we study only a very simple model, the approach that we propose is expected to be valid also in more complicated and realistic cases.

Glass microballoons filled with mixtures of argon and neon were imploded using the University of Rochester 24-beam Ω laser system. Experimentally observed Lyman-series x-ray lines were analyzed to determine plasma core parameters and the effects of opacity on spectroscopic diagnostics. The analysis produced results which were at odds with some previous assumptions.

Molecular-lattice-theory results reveal that the steric (hard-repulsive) packing of rigid cores and partially flexible tails can explain the relative stabilities of the smectic-$A_1$, smectic-$A_d$, and higher-temperature and lower-temperature nematic (including reentrant-nematic) liquid-crystalline phases, and the isotropic liquid phase. These phases and transitions between them are presented as a function of temperature, pressure, tail-chain length and flexibility, and orientational and positional order of the molecules for different systems. Critical exponents calculated at the smectic-$A_d$ to nematic transitions are consistent with an identification of the fraction of one-dimensional positional alignment (i.e., the fraction of segregated packing of cores with cores and thus of tails with tails) of the molecules in the smectic-$A_d$ phase as an order parameter.

Quantum-mechanical propagators of regular and chaotic systems are qualitatively different. The rms time average of a chaotic propagator is uniformly spread over the entire Hilbert space, while that of a regular propagator is large in some domains and small in others. Moreover, the instantaneous (complex) value of the propagator appears to follow a regular pattern for regular systems and is ‘‘random’’ for chaotic systems.

A self-contained Ornstein-Zernike approximation scheme for calculating the structural and thermodynamic properties of a hard-sphere fluid is proposed within a simple functional ansatz for the tail function d(r) and without resorting to any a priori availability of numerical simulation data. This is done by adopting a complete thermodynamic closure on the solution of the model by means of internal-consistency constraints which arise from demanding, through the knowledge of the structural correlations in the fluid, a unique estimate for the equation of state whatever route is followed for its evaluation.

The quantum mechanics of nonlinear Hamiltonians whose classical limit is of the form H=${\mathrm{Kq}}^2$$p^2$ is studied in several dimensions. Such Hamiltonians arise in the canonical formulation of the hydrodynamics of an ideal, incompressible fluid, where the canonical variables are Clebsch potentials. They also appear in the study of the propagation of electromagnetic radiation through an optically active medium. Despite the nonlinearity, exact solutions are obtained in both the classical and quantum-mechanical formulations. The relevant Heisenberg operators for the dynamical behavior of the system are found and compared to their corresponding classical counterparts.

Analytical and numerical methods are used to study the linear stability of spatially periodic solutions for various two-dimensional equations which model thermal convection in fluids. This analysis suggests new model equations that will be useful for investigating questions such as wave-number selection, pattern formation, and the onset of turbulence in large-aspect-ratio Rayleigh-Bénard systems. In particular, we construct a nonrelaxational model that has stability boundaries similar to those calculated for intermediate Prandtl-number fluids.