It is shown that intense collisionless Rayleigh-type extraresonant signals in degenerate four-wave mixing (DFWM) can be obtained when the $| a 〉\to | b 〉$ transition which produces the DFWM signal is coupled to another transition ($| a 〉\to | d 〉$) which is excited near-resonantly by an additional laser beam. Two effects contribute to the Rayleigh-type extraresonant signal at ${\omega }_2={\omega }_1$. The first effect is resonance-enhanced three-photon scattering (TPS), which leads to the population of state $| b 〉$ and consequently contributes a term in ${\rho }_{\mathrm{ba}}$, the off-diagonal density-matrix element, which is characterized by the linewidth ${\left(\frac{1}{T_1}\right)}_{\mathrm{ba}}$, the inverse lifetime of the state $| b 〉$. The second effect derives from the effective lifetime acquired by the ground state $| a 〉$ due to its strong coupling to state $| d 〉$. This leads to a term in ${\rho }_{\mathrm{ba}}$ characterized by a linewidth $\frac{1}{2}{\left(\frac{1}{T_1}\right)}_{\mathrm{da}}$, which is half the inverse lifetime of the state $| d 〉$. When ${\left(\frac{1}{T_1}\right)}_{\mathrm{da}}\gg {\left(\frac{1}{T_1}\right)}_{\mathrm{ba}}$, the TPS effect dominates and the extraresonant DFWM signal is narrow and intense. When ${\left(\frac{1}{T_1}\right)}_{\mathrm{da}}\simeq {\left(\frac{1}{T_1}\right)}_{\mathrm{ba}}$, the signal is less intense and interference between the two effects is evident.

A general input-output theory for quantum dissipative systems is developed in which it is possible to relate output to input via the internal dynamics of a system. This is applied to the problem of computing the squeezing produced by a degenerate parametric amplifier located inside a cavity. The results for the internal modes are identical with those of Milburn and Walls [Opt. Commun. 39, 401 (1981)]. The output field is also found to have only 50% of maximal squeezing. However, by taking the output for a degenerate parametric amplifier inside a single-ended cavity and feeding this into an empty single-ended cavity, one can produce a maximally squeezed state inside this second cavity.

We have formulated the quantum theory of formation of the superfluorescence pulse from a pencil-like amplifier. The coupled system of the linearized Bloch equations for two-level atoms and the three-dimensional wave equation for the electric field has been solved in the geometrical-optics approximation for Fresnel numbers $F \ge 1$. Several properties of the superfluorescence pulse are discussed. The spatial coherence function of the pulse has been found as a function of the Fresnel number. This function provides a precise formulation of the concept of "diffraction modes." The delay-time distribution function for various Fresnel numbers has been found. The results are consistent with experimental data and numerical simulations.

A simple model of a one-dimensional optical cavity having output coupling is used to develop a fully quantized linear laser theory. The present model and procedure, which work directly within the continuous spectrum, allow us to find a simple treatment that leads to explicit solutions for the field inside and outside the laser cavity. The threshold condition for laser light onset is obtained by assuming the field operating in a single collective mode and the usual adiabatic hypothesis. A development that removes this later restriction is also discussed and outlined.

A detailed investigation is presented of the use of soft x rays, emitted from a laser-produced plasma, for the excitation of highly energetic ions. The emphasis is on the excitation of ${\mathrm{Li}}^{+}\left(1s2s\right)$ metastable levels with energies of approximately 60 eV. The experiments were made possible by the use of a geometry in which the laser beam was focused through the Li vapor onto a massive target placed inside the vapor. Populations of ${\mathrm{Li}}^{+}\left(1s2s\right)$ ions in excess of ${10}^{15}$ ${\mathrm{cm}}^{-3\mathrm{}}$ have been measured and the effect of varying parameters such as laser energy, distance from the target, Li density, and time delay after the initial excitation has been examined. In this work the plasma emission can be considered as radiation from a blackbody with a temperature of 10-100 eV, and the conversion efficiency from 1.06-μm radiation to blackbody radiation was estimated to be in excess of 5%. A comparison has been made of the effect of using $Q$-switched ($\tau \sim 10$ ns, $E\sim 200$ mJ) and actively modelocked ($\tau \sim 0.6$ ns, $E\sim 50$ mJ) neodymium-doped yttrium aluminum garnet (Nd: YAG) lasers to make the soft-x-ray—emitting plasma. ${\mathrm{Li}}^{+}\left(1s2s\right)$ population measurements have been made for the cases of Ta, Fe, Ni, and Li target materials, and the populations excited by photoelectrons into the $\mathrm{Li}\left(1\mathrm{}{s}^{2}2p\right)$ and ${\mathrm{Li}}^{+}\left(1\mathrm{}{s}^2\right)$ levels have been measured. The applications of these experiments to various proposed extreme-ultraviolet laser systems are discussed.

A two-photon dichroism measurement is used for the first time to deduce the second nontrivial moment $〈 P_4 〉$ of the orientational distribution of 4-cyano-4′-pentylbiphenyl (5CB) in the nematic phase. An anisotropic local-field model is developed for the data analysis. The resultant temperature variation of $〈 P_4 〉$ is in fair agreement with that deduced from Raman depolarization measurements. The negative $〈 P_4 〉$ near the nematic-isotropic transition temperature is believed to be due to a strong ordering in the local structure of the medium.

We treat the master equation in one dimension for the Rayleigh-piston problem of hard rods, i.e., a single heavy tagged particle with finite mass $m_A$ moving in an ensemble of light bath particles with mass $m_B$ and a time-independent velocity distribution. The backward form of the master equation is used to obtain a transport equation for a conditional average of a time-dependent physical quantity. It is shown how this integro-differential equation can be solved successively by transforming it into a closed set of first-order linear partial differential equations. The solution of the $l$th linear partial differential equation is completely determined by the solutions of the $l-1\mathrm{}$ linear partial differential equations, meaning that higher approximations do not change lower ones. It is shown how the motion of the tagged particle can be separated into a deterministic (nonfluctuating) part and into fluctuating contributions. It turns out that the $l=0\mathrm{}$ term in the successive approximation scheme satisfies a homogeneous linear partial differential equation and describes the nonfluctuating motion, whereas the higher approximations ($l\ge 1$), which are solutions of nonhomogeneous linear partial differential equations, describe the fluctuating contributions. The calculations for arbitrary time-dependent conditional averages are performed explicitly up to order 2 in the expansion parameter ${\Omega }^{-1\mathrm{}}=\frac{m_B}{(m_A+m_B)}$. This new method is employed to calculate the conditional averages for the time-dependent mean velocity, the mean-square velocity, the velocity-autocorrelation function, and the self-diffusion coefficient. In addition, the results show that conditional averages calculated via a Gaussian distribution function deviate considerably from the exact results obtained for mass ratios of order 1.

Linear and circular complexities and entropies of periodic series are defined. These concepts are then used to discuss the transition to turbulence in the infinite cascade of subharmonic bifurcations of the logistic map. When the stochasticity parameter increases from a critical value to the next critical value, the entropies are constant, or nearly constant. However, they undergo a discontinuity equal to In2 at each transition, increasing by steps. For chaotic orbits in the chaotic domain, a trivial extension of the concepts leads to infinite entropies.

Stark-width measurements are reported for lines in the $ns-4p \mathrm{}(n=7-10\mathrm{})\mathrm{}$ and $nd-4p \mathrm{}(n=5-8\mathrm{})\mathrm{}$ series in neutral potassium (Ki). These measurements were made by observing the end-on emission from a low pressure (20 Torr) potassium-argon wall-stabilized arc source. The on-axis electron density and temperature in the 20-A arc were (2.0±0.2) × ${10}^{15}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and 2955±100 K, respectively. The experimentally determined Stark widths were compared with the theoretical values calculated by Griem. The measured Stark widths agreed with theory to within 30% for lines in the $ns-4p$ series; while the measured Stark widths of the $nd-4p$ series lines were only one-third of the theoretical values.

Transient molecular reorientation induced in a liquid crystal by a giant laser pulse was observed for the first time in a nematic substance 4′-$n$-pentyl-4-cyanobiphenyl (5CB). Even though the response time of molecular reorientation was several orders of magnitude longer than the laser pulsewidth, the effect on the refractive indices was still large enough to be easily detectable by a Mach-Zehnder interferometer. Transient laser heating of the medium also affected the refractive indices, but with proper geometric and polarization arrangement, it could be decoupled from molecular reorientation and measured separately. Theoretical calculations using the Ericksen-Leslie theory for molecular reorientation in liquid crystals and the heat-diffusion theory for the laser heating effect were able to explain the experimental observations quantitatively.

The Tolman law, $T{[-g_{\mathrm{tt}}\mathrm{}(r\left)\right]}^{\frac{1}{2}}=\mathrm{const}$ is generalized to thermal nonequilibrium in the case of spherically symmetric and stationary heat conduction in a given spherically symmetric and static gravitational field. This is achieved by establishing the general relativistic equation of thermal conduction. An exact solution is found, which generalizes the Tolman law. We explore some nonequilibrium properties for the heat flux in a given static gravitational field by investigating the idea that heat energy has weight in the theory of relativity.

Diffusion of a tagged particle in a fluid with uniform shear flow is described. An expression for the diffusion tensor is obtained in a form similar to the Green-Kubo result for the equilibrium self-diffusion coefficient, but which is applicable even far from equilibrium. In one form the diffusion tensor is determined from a type of Einstein relationship to the nonequilibrium mean-square displacement in the Lagrangian frame for the fluid. Alternatively, the diffusion tensor is expressed as a time integral of the autocorrelation function for the velocity of the tagged particle in a local rest frame. A frequency- and shear-rate-dependent diffusion tensor is defined from these results and evaluated in two limits. The first case is the Boltzmann limit for a low-density gas, and the diffusion tensor is found to be an analytic function of both frequency and shear rate. Consequently, nonlinear transport coefficients of arbitrary order are well defined and finite. In the second case the mode-coupling contributions for a general fluid are obtained by an extension of the equilibrium mode-coupling phenomenology to shear flow. The hydrodynamic modes are obtained as a function of time and shear rate and lead to a nonanalytic dependence of the diffusion tensor on both frequency and shear rate. A universal function is obtained to describe the crossover from asymptotic frequency to asymptotic shear-rate dependence. This function is compared with a similar result predicted by a phenomenological model from nonlinear continuum mechanics.

A practical approach to the description of time evolution via the mean values of a set of a few relevant observables is discussed. The mean values determine, in a self-consistent way, the time propagation of the system. The procedure yields variational formulation, through which closedform equations of motion of Hamiltonian form are derived for the relevant mean values. The approximation can provide an exact description under well-defined conditions. The time evolution is reversible in that the entropy does not increase and that it can be described by a unitary evolution operator. A special case of both practical and formal importance is when the relevant observables form a Lie algebra. The self-consistency conditions can then be explicitly implemented and a symplectic structure can be provided for the reduced phase space. Time displacements (of either the state or the observables) can then be described by a self-consistent Hamiltonian, linear in the generators. An example corresponding to the evolution of a Morse-type oscillator under a time-dependent external perturbation is discussed in detail.

It is first shown that the propagator of a charged particle in a constant external magnetic field is related to the propagator of a one-dimensional driven harmonic oscillator with memory. The memory term can be removed by introducing the auxiliary force term and then by integrating it out. By using this new formula for a driven harmonic oscillator, a generalization of Horváthy-Feynman formula, we finally evaluate exactly the propagator beyond and at caustics of our dynamical system.

In treating a many-body system, the concept of correlation has been used by various authors to calculate the interacting ground state. In particular, in the Wong-Fung theory, the interacting ground state is expressed in terms of the correlation operators and the noninteracting ground state. Including pair ($u_2$) and three-particle ($u_3$) correlations, the wave function can be written as explicit algebraic functions of $u_2$ and $u_3$ and the noninteracting wave function [K. W. Wong et al., Phys. Rev. A. 22, 1272 (1980)]. On the other hand, the authors of the present paper have recently developed a $U$-matrix theory [Phys. Rev. A. 27, 1760 (1983)] to study general quantum-mechanical problems. For a time-independent problem, we can use this theory to find an analytic solution for the interacting wave function in terms of the potential functions of the system. A bridge between the correlation functions and the potential functions is built by identifying the interacting wave functions of the stated two theories to be the same quantity. Using the above idea, we are able to express the two-particle potential function $v_2$ as a simple function of the pair correlation $u_2$ and a "switching integral" $I$, which determines how the interaction Hamiltonian is switched on, to the lowest order to approximation. Instead of using a model for $u_2$, we obtain the explicit form of $u_2$ through the neutron scattering data of Henshaw and the concept of radial distribution function $g_2$. It is interesting to note that this $u_2$ is not divergent at any point and is Fourier transformable. Then we proceed to deduce the resulting two-particle potential function. The deduced two-particle potential is shown to be similar in form to the Lenard-Jones potential, with the same depth, a smaller hard-core radius, and a softer core.

It is shown that the Schrödinger equation for the helium atom does not have a Frobenius-type solution in the variables $r_1$, $r_2$, and $r_{12}$.

In a recent paper [W. Rösner et al., Phys. Rev. A 28, 2071 (1983)] a simple analytical potential was introduced for the H atom in strong magnetic fields, and its usefulness in calculating bound states was demonstrated. In this Brief Report we show that this potential is also excellently suited for computing—fast and accurately—continuum wave functions. As an application photoionization cross sections are evaluated with use of the approximate continuum functions, and are compared with previous calculations.

Differential cross sections for Compton scattering on Cu, Zn, Cd, Sn, W, Pt, Pb, and U were measured for scattering angles between 5° to 60°. The measurements are in agreement with values of the incoherent-scattering-factor theory, and for small scattering angles deviations from the free-electron Klein-Nishina value occur.

The absolute ($e$, $2e$) triply differential cross sections measured in coplanar nonsymmetric conditions are reported for the intermediate $2p$ orbital of Ar, at an incident energy of 8.4 keV. The data are made absolute by integrating over all ejection directions and comparing with the corresponding doubly differential cross section. The latter is also measured in a separate experiment and is made absolute by use of the Bethe sum rule. Preliminary calculations using first-order theories indicate very large discrepancies between experiment and theory, at the relatively low energy of the outgoing electron: 150 eV.

Asymptotic solution of equations of motion of particles in a planar channel of a magnetic crystal is used to determine the emission rate of $\gamma$ rays due to the longitudinal variation of crystal fields, and to assess the prospects for stimulated gain and laser operation.