The trapped regime of a free-electron laser is considered in terms of the relativistic quantum-mechanical Klein-Gordon equation in the presence of the undulator and the laser field. The electron which is trapped in the wells of the ponderomotive potential occupies discrete equidistant levels. Transitions between these quantum-mechanical levels are shown to lead to the well-known classical sidebands. As a new feature in spontaneous emission we obtain a low frequency δω emitted slightly off axis, where δω denotes the shift between the first sideband and the small-signal laser frequency. The low frequency is again classical and constitutes a sideband of the zeroth harmonic ω=0. Under current experimental conditions this low-frequency spontaneous emission is at the borderline of detectability.

The interference pattern from a light source containing a single excited atom was observed with an interferometer 45 m in length. The visibility of the single-photon interference pattern was the same as that obtained with a high-intensity light source to within the experimental uncertainty of ±5%.

Analytic and numerical solutions are obtained for the equations describing the propagation of several pulses of different frequencies through a Raman medium. The transient case is treated, and the analysis includes Stokes, pump, and anti-Stokes frequency components. The effect of phase mismatch Δk between these waves is investigated. An analytic solution is found that describes the phenomenon of transient Stokes–anti-Stokes gain suppression in the limit Δk=0. For nonzero values of Δk, the behavior of the transient gain coefficient is found to follow a scaling rule that is the analog of a similar result known from the steady-state limit. Calculations are performed to identify conditions that enhance conversion to anti-Stokes radiation. It is found that there is an optimum strength of the Stokes seed, and that proper phase matching of the initial waves is essential.

Repeated measurements of the atomic inversion are incorporated in the theory of the micromaser. Two examples of measurements-induced dynamics are presented which display (a) quantum diffusion above a potential barrier and (b) an instability in the form of quantum-mechanical relaxation oscillations. Implications of these results on the study of the quantum-classical interface are briefly discussed.

A nonequilibrium generalization of the density-functional theory of freezing is proposed to investigate the shear-induced first-order phase transition in colloidal suspensions. It is assumed that the main effect of a steady shear is to break the symmetry of the structure factor of the liquid and that for small shear rate, the phenomenon of a shear-induced order-disorder transition may be viewed as an equilibrium phase transition. The theory predicts that the effective density at which freezing takes place increases with shear rate. The solid (which is assumed to be a bcc lattice) formed upon freezing is distorted and specifically there is less order in one plane compared with the order in the other two perpendicular planes. It is shown that there exists a critical shear rate above which the colloidal liquid does not undergo a transition to an ordered (or partially ordered) state no matter how large the density is. Conversely, above the critical shear rate an initially formed bcc solid always melts into an amorphous or liquidlike state. Several of these predictions are in qualitative agreement with the light-scattering experiments of Ackerson and Clark. The limitations as well as possible extensions of the theory are also discussed.

We have measured the coefficient for recombination of ${\mathrm{O}}_4^{+}$ ions with electrons as a function of electron temperature by analyzing electron- and ion-density decays in microwave-generated afterglow plasmas in neon-oxygen mixtures. Electron temperatures $T_e$ in the afterglow were elevated above those of the neutral species and ions by continuous application of microwave power. The data analysis included effects on the electron temperatures arising from inelastic collisions of electrons with the minority oxygen molecules and spatial nonuniformities of $T_e$ due to the spatially nonuniform microwave heating field. Over the temperature range 143 K<$T_e$<5500 K the recombination coefficients were found to vary as α(${\mathrm{O}}_4^{+}$) (${\mathrm{cm}}^3$/s)=(4.2±0.4)×${10}^{\mathrm{-}6}$[${\mathrm{T}}_{\mathrm{e}}$(K)/300${]}^{\mathrm{-}\mathrm{z}}$, where z${=0.48\mathrm{}}_{\mathrm{-}0.05}^{+0.1\mathrm{}}$. While the values of the recombination coefficients for this dimer ion are an order of magnitude larger than those of the monomer ions, the temperature dependence is close to the $T_e^{\mathrm{-}0.5}$ dependence predicted and often observed for diatomic ions.

A microwave-afterglow mass-spectrometer apparatus employing microwave heating of the electrons has been used to determine the dependence on electron temperature $T_e$ of the recombination coefficient of electrons with ${\mathrm{HCO}}^{+}$ ions. By comparison of the observed electron-density decays to the computed behavior of a recombination- and ambipolar-diffusion-controlled afterglow, it is found that the electron-temperature dependence of the recombination coefficients follows a power law of the form α(${\mathrm{HCO}}^{+}$) (${\mathrm{cm}}^3$/s)=(2.4±0.4)×${10}^{\mathrm{-}7}$[${\mathrm{T}}_{\mathrm{e}}$ (K)/300${]}^{\mathrm{-}}$0.69±0.07 over the range 293 K<$T_e$<5500 K. The magnitude of the recombination coefficient is similar to that observed and calculated for simple diatomic ions, while the temperature dependence is somewhat stronger than the $T_e^{\mathrm{-}0.5}$ dependence predicted by a simplified theory for diatomic ions.

In computer simulations of the molecular dynamics of liquid water from 1 bar, 293 K to 200 kbar, 1043 K, direct statistical correlation has been observed in the laboratory frame of reference between the molecular linear center of mass velocity v and (i) the dipole unit vector μ, and (ii) its time derivative. These results imply that dielectric relaxation and far-infrared absorption spectra are incompletely understood with theories which neglect cross correlations.

In a molecular-dynamics computer simulation of liquid water, a circular field of force is applied to a central region of about 250 molecules out of a total of 500 molecules. This is achieved by dividing the molecular-dynamics sample into an outer cube subject to periodic boundary conditions, and an inner cube, whose side is 0.75 of that of the outer cube. The inner cube (containing roughly half the molecules on average) can therefore be seen as subject to natural or thermal boundary conditions for the circular flow set up there. The effect of this circular flow on the molecular dynamics of all 500 molecules is then studied by means of autocorrelation and cross-correlation functions in the laboratory frame, and in the moving frame defined by the principal moment of inertia axes of the water molecule. The results are compared with equivalents in 500 molecules of liquid water at equilibrium, and the effects of rotational flow on the symmetry of various single-molecule cross-mode coupling tensors are discussed in detail.

An innovative method for determining the thermal-accommodation coefficients of gases by means of monitoring the Mie scattering from a single suspended water droplet is described. The heat exchange between the gas molecules and the suspended droplet is analyzed by considering the simultaneous mass- and heat-transfer processes during droplet growth by condensation in a gas–water-vapor environment. Measurements have been carried out for helium with water-vapor-to-helium ratios in the range of 1:0.5 to 1:2.5. The thermal conductivity of this mixture is found to be best represented by its reciprocal average. The thermal-accommodation coefficient of helium on water surfaces is determined to be 0.65±0.05, as compared to unity for water vapor on water surfaces.

Molecular dynamics (MD), where the equations of motion of up to thousands of interacting atoms are solved on the computer, has proven to be a powerful tool for investigating a wide variety of nonequilibrium processes from the atomistic viewpoint. Simulations of shock waves in three-dimensional (3D) solids and fluids have shown conclusively that shear-stress relaxation is achieved through atomic rearrangement. In the case of fluids, the transverse motion is viscous, and the constitutive model of Navier-Stokes hydrodynamics has been shown to be accurate—even on the time and distance scales of MD experiments. For strong shocks in solids, the plastic flow that leads to shear-stress relaxation in MD is highly localized near the shock front, involving slippage along close-packed planes. For shocks of intermediate strength, MD calculations exhibit an elastic precursor running out in front of the steady plastic wave, where slippage similar in character to that in the very strong shocks leads to shear-stress relaxation. An interesting correlation between the maximum shear stress and the Hugoniot pressure jump is observed for both 3D solid and fluid shock-wave calculations, which may have some utility in modeling applications. At low shock strengths, the MD simulations show only elastic compression, with no permanent transverse atomic strains. This result for perfect 3D crystals is also seen in calculations for 1D chains. We speculate that, if it were practical, a very large MD system containing dislocations could be expected to exhibit more realistic plastic flow for weak shock waves too.

Measurements of drift velocity and electron density in electron-beam-irradiated Ar-${\mathrm{F}}_2$ gas mixtures which have been subjected to an externally applied electric field are reported. The electron density was measured by time-resolved infrared interferometry. The drift velocity was derived from discharge-current-density measurements. Experiments were performed for gas mixtures with various fluorine concentrations between 0.025% and 2% and total mixture pressures between 0.5 and 2 atm. The electron-beam current density was varied between 10 mA/${\mathrm{cm}}^2$ and 6 A/${\mathrm{cm}}^2$ and the field strength was between 0 and 10 Td (1 Td${=10\mathrm{}}^{\mathrm{-}17}$ V ${\mathrm{cm}}^2$). The experimental results were analyzed using two coupled kinetic codes. One code calculated the secondary-electron energy distribution and the second code calculated the density of the different atomic and molecular ionic and neutral species. The two codes were run in cyclic order until a self-consistent solution was obtained. The experimental results for the drift velocity and electron density were compared with the theoretical predictions. From the dependence of the electron density on the fluorine concentration, the rate constant for dissociative attachment of electrons to fluorine has been obtained. The dependence of the drift velocity and the attachment rate constant for fluorine on experimental parameters such as electric field strength, fluorine concentration, and electron-beam current density are discussed in detail. It is shown that these dependencies can be explained by accounting for the mutual effect of these experimental parameters on the secondary-electron distribution function.

Inelastic-neutron-scattering spectroscopy is utilized to probe single-particle excitations as a function of temperature in light and heavy water over an energy range of 50 to 600 meV, covering the librational, bending, and stretch vibrational regions of molecular motion. A computer molecular-dynamics simulation of liquid water based on a simple point-charge model is also carried out to compute the Q-dependent proton density of states $G_s$(Q,E) for direct comparison with the equivalent quantity deduced from experimental measurements on an absolute scale. The calculated classical density of states is lower than the measured one by a factor of 2, indicating the importance of quantum-mechanical corrections at high-energy transfers. The classical simulation fails to predict a combination band at 525 meV which we attribute to a quantum-mechanical process of simultaneous excitation of the stretch vibrational mode and breaking of the adjacent H-O...H hydrogen bond. The temperature dependence of this band is predicted correctly by a quantum-mechanical calculation using a one-dimensional hydrogen-bond model.

Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.

Dielectronic-recombination rate coefficients of selected hydrogenlike ions (Z=10, 14, 18, 20, 22, 26, and 28) have been calculated at various plasma temperatures (${\mathrm{kT}}_e$=0.6–10 keV) using the Hartree-Fock-Slater atomic model and assuming a Maxwellian velocity distribution for the free electrons. The effects of configuration interaction and spin-orbit coupling are included in all intermediate resonance states ‖2lnl’SLJ〉 for n≤4. Configuration average rates have been used to calculate dielectronic-recombination rate coefficients for n=5–8, and 1/$n^3$ scaling law for all higher-lying states. The results from the present calculations are compared with available theoretical and experimental values of dielectronic-recombination rate coefficients.

We obtain the long-wavelength energy excitations for a system of interacting charged particles confined to a plane perpendicular to a constant magnetic field. The results are derived by generalizing the Bogoliubov approximation used for liquid helium.

We propose a two-component soliton model for proton storage and transport in hydrogen-bonded quasi-one-dimensional chains. The model is investigated both analytically and by molecular-dynamics simulations. At 310 K we find that in certain regions of the parameter space it is possible, from realistic initial conditions, to excite a kink in the proton sublattice. For certain parameter values and initial conditions the kink is excited just to be annihilated shortly after. For other parameter values the kink continues to travel for much longer times. Therefore the presented model can explain the essential physics of proton storage as well as proton transport in hydrogen-bonded substances.

The diffusion of a pair of bound particles in a two-dimensional triangular periodic potential is studied by computer simulation. Well-defined diffusion coefficients are found for various energies of the system. The dependence of the diffusion coefficient on the energy of the particles and on the range of their mutual interaction is discussed. In particular, interaction between the particles reduces the diffusion coefficient compared with the one-particle noninteracting case.

The transport of dynamically neutral tracer in flow through a random network of tubes with percolation disorder is investigated. For each bond of the system, the tracer motion is governed by a convection-diffusion equation, with the drift term accounting for the local bond velocity. This represents an extension of random walks in disordered media to the important case of finite macroscopic flow rates. A calculational technique is developed which provides, for a given configuration of the disorder, the exact moments of the distribution of transit times for the tracer to traverse the system. This approach is implemented numerically for L×L random networks at the bond percolation threshold. When the total fluid flux Q vanishes, the kth moment of the transit time is found to scale with sample size as $L^{k(2+\theta )}$, where θ=t-β/ν is the exponent describing the scale dependence of the diffusion coefficient of the ‘‘ant in the labyrinth,’’ $D_{\mathrm{ant}}$. By contrast, when Q becomes large, the kth moment is found to scale as $Q^{\mathrm{-}1}$$L^{2\mathrm{-}\beta /\nu +\left(k\mathrm{-}1\right)(2+\theta )}$. This behavior of the moments at large Q is explained on the basis of a simple heuristic argument and from a more detailed analytical calculation. Furthermore, a scaling ansatz for the transit-time moments is postulated which describes our data for all flow rates. The large-Q behavior of the moments leads to a longitudinal dispersion coefficient which scales as $U^2$$L^2$/$D_{\mathrm{ant}}$, where U is the average flow velocity, in agreement with a prediction of de Gennes.

We have investigated the elastic and the optical properties of nematic and smectic side chain polymer liquid crystals at hypersonic frequencies. In contrast to classical liquid crystals, the polymer materials show a significant coupling between the static order parameter and the square of the elastic strain ${\epsilon }_3$. The inverse shear stiffness constants do not diverge. All elastic constants behave continuously at the nematic-isotropic transition ($T_{\mathrm{ni}}$). From certain optoacoustic properties and the refractive index functions, it follows that order-parameter fluctuations play no role at $T_{\mathrm{ni}}$, but that the glass transition dominates the dynamic elastic properties at hypersonic frequencies.