It is predicted that, at sufficiently high laser intensity, the recently observed Raman-type extra-resonant enhancement of four-wave mixing [Y. Prior, A. R. Bogdan, M. Dagenais, and N. Bloembergen, Phys. Rev. Lett. 46, 111 (1981)] should not vanish in the absence of collisions. The collisionless contribution to the extra resonance is associated with a three-photon scattering process which produces an extra-resonant signal intensity which is fourth order in the laser intensity.

A nonlinear, one-dimensional formulation of the free-electron laser with an axial magnetic field is presented. The problem is formulated in the cold-fluid approximation for the electron beam, and is reduced to a system of the first-order, nonlinear, coupled, ordinary differential equations. Nonlinear effects due to the departure of the electrons in the beam from the conventional helical orbits are considered and illustrated in numerical examples. The formalism also allows the study of the initial phase of saturation in the laser. In the presence of the axial magnetic field the saturation is shown to be mainly due to the development of undesirable large radial excursion of the electron trajectories.

Periodic phase matching is used to enhance the dc electric-field-induced secondharmonic generation by gases illuminated with a low-power laser beam. The theory of periodic phase matching is discussed and experiments for measuring molecular hyperpolarizabilities are described.

The propagation of a step-function light pulse in a nondamping resonant medium is studied. Numerical analysis and conservation laws show that the asymptotic solution cannot be described by a single solition-lattice-type solution. As the pulses propagate in space they become narrower and with larger amplitude, but the time separation between pulses remains constant. This result is explained by an asymptotic area theorem which restricts the time average of the electric field to be equal to that of the imput field.

We introduce a method to derive expressions for the distribution $\rho$ of large fluctuations about a stable oscillatory steady state and for the transition rate from that state into another stable state. Our method is based on a WKB-type expansion of the solution of the Fokker-Planck equation. The expression for $\rho$ has a form similar to the Boltzmann distribution with the energy replaced by a function $W$, which is the solution of a Hamilton-Jacobi-type equation. For the case of small dissipation, a simple analytical approximation to $W$, in terms of an action increment, is derived. Our results are employed to predict various measurable quantities in physical systems. Specifically we consider the problems of the physical pendulum, the shunted Josephson junction, and the transport of charge-density-wave excitations.

The time evolution of an isolated, spatially homogeneous system, with an isotropic distribution of velocities and with particles interacting via a Lennard-Jones potential, has been analyzed by means of molecular dynamics. The initial velocity distribution is assumed to be zero except for two given speeds $v_{\alpha }$ and $v_{\beta }$. We have found an overpopulation phenomenon for high speeds, analogous to the one observed in the theoretical studies of model Boltzmann equations. The influence of $v_{\alpha }$ and $v_{\beta }$ on this effect has been analyzed. A qualitative comparison with theoretical results is presented. Furthermore, we have observed a similar, less intense, overpopulation effect for low speeds.

Results from experimental studies of x-ray emission during gas discharges are reported. They confirm experimentally the presence of runaway electrons in short, high-pressure discharges under highly overvolted conditions. These electrons, when stopped at the anode, produce x-ray radiation. A high-energy component above 3 keV was measured. The effects of the type of gas, its pressure, electrode separation, and applied voltage are presented. The results are analyzed with respect to breakdown development described by a model based on two groups of electrons present in the discharge.

The ground state of a charged Bose gas is studied throughout a large range of densities in a self-consistent-field approximation formalism which includes the short-range correlations between bosons through a local-field correction. Numerical self-consistent calculations have been carried out in order to determine the static structure factor $S\left(\overrightarrow{\mathrm{q}}\right)$. Hence, from $S\left(\overrightarrow{\mathrm{q}}\right)$ we have obtained the pair-correlation functions, the ground-state energy which essentially is the correlation energy, the pressure of the gas, and, from Feynman's relation, the energy spectrum of elementary excitations. The response of the system to a static impurity charge has also been investigated. In the high-density limit our calculations show the same results as those given by Bogoliubov's perturbation theory. In the intermediate-density region, corresponding to the strongly coupled system, our results are in very good agreement with recent calculations based on the hypernetted-chain integral equation as well as Monte Carlo computations.

Nematic—to—smectic-$A$ transitions in liquid crystals with director fluctuations confined to an easy plane are studied via a scaling analysis and an expansion in $\epsilon =4-d$. The lower critical dimension for these systems is $d^{*}=2.5\mathrm{}$. In three dimensions, scaling predicts anisotropically diverging correlation lengths, with exponents in the ratio 3:2. The $\epsilon$ expansion suggests a fluctuation-driven first-order phase transition for an $n$-component generalized model, provided $n<\mathrm{}110.8\mathrm{}$. For $n>\mathrm{}110.8\mathrm{}$, we find a stable, anisotropic fixed point with, however, a much weaker anisotropy than that predicted by scaling. Two sets of lengths are then necessary to describe order-parameter correlations below the transition. The constraint of planar director fluctuations can, in principle, be imposed experimentally by applying electric fields to nematics with a large transverse dielectric constant. The theory may also be applicable to transitions from smectic-$C$ liquid crystals to bismectics.

In the presence of self-generated magnetic fields in laser-produced plasmas, the mode-converted plasma waves near the critical layer decay parametrically into electron Bernstein waves and Langmuir sidebands. The threshold for this instability is easily exceeded at the currently employed power densities and the growth rate above the threshold ${\gamma }_0\simeq 0.06{\omega }_c\frac{v_0}{v_e}$ for typical plasmas; $v_0$ and $v_e$ are the oscillatory and thermal speeds of electrons and ${\omega }_c$ is the cyclotron frequency. The electron cyclotron turbulence thus generated may have significant consequences on the energy deposition rate.

Molecular dynamics has been used to investigate the properties of supercooled liquid states for a model of liquid rubidium. The energy-temperature relation for the reduced density $n^{*}=0.95\mathrm{}$ for liquid, amorphous solid, and bcc crystal phases is presented along with the pair-correlation function, the self-diffusion coefficient, and the transverse-current correlation as functions of temperature for the liquid. The self-diffusion coefficient is found to vary with temperature in a way which correlates with the temperature evolution of the pair-correlation function. The power spectra of the transverse-current correlation function are used to determine the minimum length required for the decay of fluctuations to be describable by linearized hydrodynamics. This length grows rapidly as the amount of supercooling increases and becomes significantly larger than the dimensions of the cube to which periodic boundary conditions are applied.

Photon correlation spectroscopy was performed on a dilute bcc colloidal crystal in a thin-film cell to measure its response to thermal fluctuations with wave vectors along lattice symmetry directions. The phonon dispersion curves show a definite harmonic-lattice behavior for longitudinal and transverse modes. We present a Langevin treatment of the lattice dynamics, based on harmonic potentials and a theory of hydrodynamic interactions which is exact to lowest order in sphere volume fraction and includes important unsteady flow effects. The model takes into consideration the discreteness of the lattice, which is important near the Brillouin-zone boundary, and has the correct behavior for long-wavelength fluctuations as well (underdamped transverse modes, overdamped longitudinal modes). The mass renormalization of propagating transverse lattice modes is discussed, along with the effects of the thin-film configuration on their propagation. The role of backflow in overdamping longitudinal modes is made clear. From the measured dispersion curves for longitudinal wave vectors, we obtained the following elastic constants: $c_{11}=6.96\mathrm{}$ dyn/${\mathrm{cm}}^2$ and $c_{12}=c_{44}=2.43\mathrm{}$ dyn/${\mathrm{cm}}^2$.

The cluster expansion of the Helmholtz free energy is based on two-body interactions through a central potential $\phi \mathrm{}\left(r\right)\mathrm{}$. For a fluid at fixed density, it is shown that the cluster expansion provides a convergent high-temperature expansion of the free energy. Because $\phi \mathrm{}\left(r\right)\mathrm{}$ for a liquid metal depends explicitly on the density, the corresponding cluster expansion of the pressure differs from the ordinary virial series. For a physically realistic interaction, $\phi \mathrm{}\left(r\right)\mathrm{}$ is integrable at small $r$. From this it follows that the two-body-interaction contributions to thermodynamic functions for realistic fluids are bounded at high temperatures. In contrast, for potentials such as Lennard-Jones which are not integrable at small $r$, these thermodynamic contributions increase without limit as the temperature increases.

An adiabatic scanning calorimeter has been used to study the thermal behavior of the liquid-crystal octylcyanobiphenyl (8CB) in the temperature range between 10 and 50°C. The solid—to—smectic-$A$ ($\mathrm{KA}$), the smectic-$A$—to—nematic ($\mathrm{AN}$), as well as the nematic-to-isotropic (NI) phase transitions, which fall in this temperature range, have been investigated in great detail. From our measuring procedure the enthalpy behavior (including latent heats) as well as the heat capacity have been obtained. For the KA transition the latent heat was 25.7±1.0 kJ/mol and for the NI transition it was 612±5 J/mol. Within the resolution of our experiment we find that the $\mathrm{AN}$ transition is a continuous one. For the latent heat, if any, we arrive at an upper limit of 0.4 J/mol (or 1.4×${10}^{-3\mathrm{}}$ J/g). The observed anomaly in the heat capacity for the $\mathrm{AN}$ transition is not consistent with a nearly logarithmic singularity as predicted by the $\mathrm{XY}$ model, instead we obtain a critical exponent $\alpha ={\alpha }^{\prime }=0.31\mathrm{}\pm 0.03$. This result is consistent with the anisotropic scaling relation ${\nu }_{\parallel }+2\mathrm{}{\nu }_{\perp }=2-\alpha$. The pretransitional effects near the NI transition are in qualitative agreement with the hypothesis of quasitricritical behavior.

Stochastic processes with a special class of time-dependent transition rates (TDTR) that can be related to time-independent transition rates (TITR) by time-scale transformations are considered. A proper subclass of TDTR processes are those which have their associated relaxation function depending only on the ratio $\frac{t}{\tau }$, where $\tau$ is a constant characteristic time. In the transformed time frame $\theta$ this process simulates one with TITR and the relaxation function is $\exp (-\frac{\theta }{{\tau }_s})$, where ${\tau }_s$ is a constant. It is shown that the only time-scale transformation that has the property $\theta \left(\tau \right)={\tau }_s$ and which converts a TDTR into a TITR is a monomial $\theta \mathrm{}\left(t\right)=a{t}^b$. Equivalently the TDTR is $t^{b-1\mathrm{}}$. This class of processes has a relaxation function of the form $\exp (-a{t}^b)$. This model is widely applicable in the description of measured relaxation behavior and leads naturally to Ngai's renormalization relation for activation energies.

Accurate static structure factors, which take into account short-ranged (diffraction and symmetry) quantum effects in a strongly magnetized electron-ion plasma, are introduced in a guiding-center formulation. Quantum and classical analytic expressions are, respectively, obtained for the hydrodynamic (Bohm) (${\beta }_{\mathrm{cl}}+{\beta }_{\mathrm{qu}}\sim \frac{1}{B}$) and the kinetic (${\alpha }_{\mathrm{cl}}+{\alpha }_{\mathrm{qu}}\sim \frac{1}{B^2}$) contributions to the complete hybrid diffusion. ($B$ denotes the magnetic fields strength.) In a certain range of ($B$,$T$) parameters, one obtains ${\beta }_{\mathrm{qu}}\sim {\alpha }_{\mathrm{cl}}$. Large $B$ values are shown to extend the validity of a classical calculation.

In this paper we discuss a theory of light reflection from a liquid in equilibrium with its vapor. We take into account the fluctuations of the Gibbs surface between the two phases and generalize the planar formula given by Drude for the ellipsometric coefficient. At the same time, by considering a finite width of the metastable region, we go beyond the capillary-wave model which assumes a sharp step discontinuity between the two phases. The two effects cannot be treated separately since they give rise to a strong interference. We show also that the capillary-wave model is inadequate to explain light measurements and leads to wrong conclusions. Throughout the paper we focus on recent experimental measurements of the coefficient of ellipticity, which constitute the motivation of the present work.

The rotational viscosity ${\gamma }_1\mathrm{}\left(T\right)\mathrm{}$ of a nematic is of dominant importance for wide operating temperature display applications. In this paper we show that ${\gamma }_1\mathrm{}\left(T\right)\mathrm{}$ is, except for a small prefactor variation, a universal function of $T-T_g$ where $T_g$ is the glass transition temperature. In a mixture $T_g$ is a linear function of the component mole fractions and $T_g$ of a component can be predicted from molecular structure by a simple phenomenological model. ${\gamma }_1\mathrm{}\left(T\right)\mathrm{}$ of a mixture can thus be predicted from the molecular structures and concentrations of the components.

We study the effects of noise on the dynamics of a weakly damped van der Pol—Duffing oscillator. In the case of additive white noise, maxima in the stationary probability density correspond to stable stationary points of the unperturbed oscillator, and ridges correspond to stable limit cycles. Multiplicative white noise differs in the possibility of a noise-induced bifurcation for some parameter values. Our results are widely applicable because the oscillator we study also describes the dynamics near a common codimension-2 bifurcation.

The analysis of the physical basis of the power conversion of the reversible energy fluctuations (REF) converter is extended to include the effect of particle interactions in localized submicron regions on the performance. By use of a model for which electron barrier crossing occurs between equilibrium states for the REF circuit, the performance of the circuit is derived as a function of the effect of the particle interactions on the barrier-crossing rates. The performance of the model is shown to be consistent with the essential repeated randomness assumption of the master equation and to be consistent with physical laws and experimental data for the interacting-particle effects. It is also shown using an idealized physical model that the theorem of the closed cycle of corresponding collisions that is fundamental to the derivation of the $H$ theorem does not impose a limitation on the performance of the power conversion of energy fluctuations. The computed performance of the power conversion of energy fluctuations as a function of the interacting particles show that efficiencies can be achieved as high as 100% over a wide temperature range. Circuit designs are given for experiments to test these theoretical results.