This paper discusses the connection between the atomic-momentum distribution due to photon recoil and photon statistics. A new formulation is presented based on a Fourier transform with respect to momentum. The asymptotic approximation that is equivalent to a Fokker-Planck treatment is found. Resonance fluorescence is treated in detail. The anomalous diffusion contribution recently found by Ashkin, Gordon, and Cook is separated, and its physical significance is discussed. In particular, it is pointed out that it signifies the coherence between successive photon recoil events. It follows that to obtain the correct diffusion expression one must perform the adiabatic elimination of internal atomic degrees of freedom in the frame moving with the atom, including the deflection caused by light-pressure force. Connections to earlier work are discussed.

The coherent superposition of oppositely polarized neutron beams of equal amplitude results in a final beam polarization perpendicular to the polarization of both initial beams. This polarization can be rotated by purely scalar interaction applied to the beams before superposition, which is equivalent to an additional Larmor precession applied to the beam after superposition. We have directly observed these effects in an experiment performed using the perfect-crystal neutron interferometer at the high-flux reactor at Grenoble. This paper gives the experimental results and discusses their theoretical foundation.

Radiative lifetimes of six $\mathrm{Ne}2p^{5}3p$ states have been measured with uncertainties lower than 1.5% by means of a pulsed electron excitation laser-induced fluorescence technique. This method allows one to obtain fluorescence signals by exciting from resonant as well as from metastable levels at low pressures. The lifetime results are 14.0±0.1, 17.9±0.1, 16.9±0.2, 20.2±0.1, 19.0±0.2, and 20.6±0.2 nsec for the $2p_1$, $2p_2$, $2p_3$, $2p_4$, $2p_5$, and $2p_6$ levels, respectively.

The billiard-ball echo model is expanded to include the effects of using sub-Doppler-linewidth lasers in photon-echo experiments. The simple heuristic model which emerges explains such echo phenomena in gases as the echo time width and the degradation of echo intensity with angling of the excitation pulses. We derive simple results in the small-pulsearea limit and give formal expressions for excitation pulses of arbitrary area.

We use an effective bimodal velocity distribution in a five-level model to analytically examine the problem of laser-driven gas transport in mixtures of an absorbing gas and a buffer gas. Analytic expressions expressions are given for the steady-state active-gas density distribution in a closed tube for a uniform excitation profile. The model also predicts that laser-induced transport may occur without a buffer gas if collisions favoring simultaneous vibrational deactivation and velocity change occur. Profiles are given for C${\mathrm{H}}_3$F:He mixtures when a C${\mathrm{O}}_2$ laser is used to excite the $Q_{12,2}$, ${\nu }_3$ band absorption.

Glauber's definition of quantum coherence is used for neutron fields under the assumption that the complete occupation number space is a direct product of Fermi subspaces. As a result, completely coherent microfields are obtained which define a density operator in full analogy to Glauber's $P$ representation of boson fields. For better physical significance, a transformation from the $P$ representation to a momentum representation is performed. It is proved that the second-order coherence function in this representation is equivalent to Wolf's second-order coherence function of a classical Dirac field. Finally, the results of the theory are used to calculate explicitly the second-order coherence function and the coherence time of an ideally collimated neutron beam.

The semiclassical impact-parameter method is used to calculate shifts of ionized helium lines in the first three spectral series caused by electrons in a plasma. These shifts together with opposite and smaller shifts due to ion quadrupole interactions are in agreement with observed shifts of lines corresponding to the Paschen series of hydrogen. Adding plasma polarization shifts according to the linearized Debye model to the shifts calculated here results in overestimates by a factor of 2 for the shifts of these lines. For lines corresponding to the Balmer series such addition may be consistent with measurements, while for the Lyman series all present theoretical models are found inadequate.

We derive an equation of motion for the instantaneous position of a planar liquid surface using fluctuating hydrodynamics. For the fluid constrained to be in a nonequilibrium steady state by a small temperature gradient, we then obtain the dynamic structure factor $S_{\mathrm{ss}}(q,\omega )$, which represents the spectrum of thermal ripplons (capillary waves) on the liquid surface. Our analysis is done for both classical and quantum fluids. We find that there is an asymmetry in the heights of the two ripplon peaks in $S_{\mathrm{ss}}(q,\omega )$ due to broken time-reversal symmetry. Our numerical estimates of the effect for liquid helium II, suggest that it could be measurable. We have undertaken a moment analysis of $S_{\mathrm{ss}}(q,\omega )$; the first frequency moment is long ranged ($\sim \frac{1}{q^2}$) in the steady state, though it vanishes in equilibrium. From the zeroth frequency moment we recover the familiar result for the infrared logarithmic divergence of the mean-square displacement of the interface; the analysis explicitly involves the coupling of the surface to the bulk fluid. We modify the so-called capillary-wave model by including the surface-bulk coupling, and thereby make it consistent with the capillary-wave dispersion.

Complete hydrodynamic theory of the dynamics of equilibrium fluctuations in one-component fluid layers confined by rigid solid boundaries is presented. The dynamic structure factor for such a fluid layer is shown to have both diagonal and off-diagonal elements which depend on the layer height $L$ and on the transport of energy and tangential momentum across the fluid-solid interfaces. The effects of interfacial energy transport have been analyzed in the limits of maximum or vanishing tangential momentum transport ("stick" or "slip" boundary conditions on the velocity field). In the presence of interfacial transport, two new propagating modes have been found for each distinct interface. In the limit of maximum energy and/or tangential momentum transport, the new modes differ from the bulk sound modes only by an increased attenuation coefficient. Additional dissipation is in part due to shear created by the boundaries, and in part, since the sound is not isothermal, to heat conduction between the fluid and solid. In the dynamic structure factor, the new modes appear as additional peaks in the vicinity of the Brillouin peaks of the unbounded fluid; for wave vectors typical of light scattering experiments these peaks are found to be significant for $L\sim 100$ μm. Since the positions and line shapes of these peaks are very sensitive to interfacial transport, their study may provide a useful experimental probe of transport across the fluid-solid interfaces.

Tagged-particle motion in fluids is studied as a function of size and mass via variational solutions of the repeated-ring and self-consistent repeated-ring equations. For a massive particle, the transition from Boltzmann to Stokes-Einstein behavior is found as the particle radius varies from small to large with respect to the mean free path. New and more complicated effects are found for light particles. The theory appears to provide an explanation of the results of the computer simulation of Alder and Alley on size and mass dependence.

Monte Carlo simulations have been carried out to investigate the deposition of particles on surfaces and fibers under conditions where the deposition is diffusion controlled. Deposits prepared under diffusion-controlled conditions have a completely different morphology from deposits prepared under conditions where diffusion is not important. For the case of deposition on thin fibers we find that the radius of gyration of the deposit is related to the number of particles in the deposit ($N$) by $R_g\sim N^{\delta }$ ($\delta =0.665\mathrm{}\pm 0.030$) in the limit of large $N$ and long fibers. Consequently, deposits formed on fibers under diffusion-controlled conditions have fractal characteristics similar to those associated with clusters formed under diffusion-controlled conditions. Similar, but less quantitative, results are presented for surface deposits. For two-dimensional deposits grown on a one-dimensional "surface" under diffusion-controlled conditions, the root-mean-square thickness ($T$) of the deposit is related to the number of particles by $T\sim N^{\epsilon }$ ($N\to \infty$). The exponent $\epsilon$ has the value 1.30±0.075. Similar results were obtained in three-dimensional simulations of diffusion-controlled deposition on a surface $T\sim N^{\epsilon }$, with ($\epsilon =1.70\mathrm{}\pm 0.2$). All of the results reported in this paper were obtained using two- and three-dimensional lattice models. Our results suggest that the structural characteristics of systems grown by diffusion-controlled processes are determined mainly by the dimensionality of the space in which the growth is occurring and are insensitive to geometric variables such as "surface" curvature.

High-resolution ac calorimetric measurements have been made on $\mathrm{azoxy}-4,4^{\prime }-\mathrm{di}-\mathrm{undecyl}-\alpha -\mathrm{methylcinnamate}$ (AMC-11), butyloxybenzylidene heptylaniline (4O.7), heptyloxybenzylidene hexylaniline (7O.6), and heptyloxybenzylidene butylaniline (7O.4). The heat capacity $C_P$ exhibits a sharp, asymmetric peak near the second-order smectic-$A$—smectic-$C$ transition. The $C_P$ values increase in the smectic-$C$ phase as the transition temperature $T_c$ is approached and then decrease abruptly at $T_c$. These data are well described by a mean-field Landau model and are not consistent with the heliumlike critical behavior expected from the de Gennes model. It is also shown that it is very difficult to distinguish between meanfield and $\mathrm{XY}$ critical behavior on the basis of data obtained only in the smectic-$C$ phase.

The non-Markovian Brownian motion was studied by photon correlation spectroscopy on spherical particles suspended in viscous fluid. The non-Markovian property has been expected to give rise to a long-time tail proportional to $t^{-\frac{3}{2}}$ in the velocity correlation function and, correspondingly, a term of the form $p_{\frac{1}{2}}{t}^{\frac{1}{2}}$ in the argument of the exponential function of the photon correlation spectroscopy. Measurements were done on polystyrene latex spheres of 0.804-μm diameter suspended in pure water. Results of the experimental determination of the coefficient $p_{\frac{1}{2}}$ at three different temperatures were 0.397±0.035 ${\mathrm{s}}^{-1/2\mathrm{}}$ at 32.8°C, 0.326±0.029 ${\mathrm{s}}^{-1/2\mathrm{}}$ at 28.0°C, and 0.267±0.027 ${\mathrm{s}}^{-1/2\mathrm{}}$ at 23.5°C, the corresponding theoretical values being 0.409, 0.346, and 0.293 ${\mathrm{s}}^{-1/2\mathrm{}}$, respectively. Thus there is good agreement between the experimental values and the theoretical predictions.

The two-dimensional Gaussian core model in the high-temperature regime has been examined by two means: (1) exact high-temperature series, and (2) molecular-dynamics simulation. The former diverge but can be summed by Borel transforms. Evidence is offered that in the case of the mean potential energy per particle and the excess pressure that the Borel transforms are analytic throughout the complex plane. Furthermore, these transforms grow exponentially along the positive real axis at a rate which determines the fluid's freezing-point temperature. Approximate Borel transforms have been constructed which fit the simulation data adequately.

A systematic method is given to compute the semiclassical Wigner-Kirkwood expansion of the off-diagonal thermal kernel of an $N$-body quantum system.

Calorimetric investigations of the lateral flow of energy away from C${\mathrm{O}}_2$-laser-irradiated regions of disk targets are reported. The fraction of energy reaching the rear surface is shown to decrease with increasing target diameter, but does not depend on target thickness. Most of the plasma blow-off energy in front of the target is due to fast ions, but these account for less than 20% of the rear blow-off energy. The rear surface is heated preferentially at the edges, in the plane of laser polarization. These observations are consistent with energy being transported laterally by hot electrons inside the corona which expands at a speed of ∼ ${10}^8$ cm/s.

A numerical method, based on the path-integral formalism, is presented to solve non-linear Fokker-Planck equations with natural boundary conditions. For one-dimensional stochastic processes, several specific examples possessing exact analytic solutions are evaluated numerically for purposes of comparison. Various discretization prescriptions are investigated and found to be equivalent as expected. The numerical method is shown to give accurate results provided the spatial discretization and the time step satisfy certain relationships determined by the drift and the diffusion functions of the nonlinear Fokker-Planck equations.

A manifestly covariant extension of the Low-Sturrock Lagrangian is formulated and its invariance properties are investigated. In particular we clarify the meaning of particle displacements which play the role of the configuration variables of the variational principle in general relativity. As a consequence of the variational principle we derive a conservation law for Whitham's wave-vector action in the WKB approximation.

We report on measurements of the x-ray line emission in the wavelength region $\lambda =4.3-5.3\mathrm{}$ Å from molybdenum in charge states between 28+ and 32+. The experimental results were compared with calculated line spectra (also presented) which facilitated the identification of many of the principal $2p-3d$, $2s-3p$, and $2p-3s$ transitions. Some indications of weaker satellite-line contributions were also found. The principal $2p-3d$ transitions were found to be the dominant ones. In particular, ${\mathrm{Mo}}^{32+}$ gave stronger contributions than other charge states for our plasma condition of $T_e=1.0-1.5\mathrm{}$ keV while available calculations of relative ion abundances have predicted ${\mathrm{Mo}}^{32+}$ to be relatively strongest at $T_e=2.5-3.0\mathrm{}$ keV.

In continuation of an earlier paper [F. Schlögl and R. S. Berry, Phys. Rev. A 21, 2078 (1980)] (referred to as I), small fluctuations in the interface between two phases will be discussed and with this an error in I will be corrected. The dynamics of the fluctuations is connected with the quantum mechanics of the modified Pöschl-Teller potential. Moreover, the fluctuations in the solitary solution of a moving surface are studied and also brought into connection with a quantum-mechanical system. The regression spectrum of these fluctuations is discussed in dependence on the velocity of the interface. If this velocity exceeds a certain value, the character of the regression to the kink profile changes qualitatively.