It is shown that Haller's interpretation of the unitary transformation from the minimalcoupling to the multipolar form of the Hamiltonian in nonrelativistic quantum electrodynamics not only conflicts with the Maxwell-Lorentz equations but also ascribes a special status to the minimal-coupling Hamiltonian which is not warranted by the general method of canonical quantization. The correct interpretation of the transformation as the quantum analog of a classical canonical transformation is reiterated. It is also shown that the transformation is equivalent to a gauge transformation of the electromagnetic potentials.

An explicit derivation of Maxwell's equations from the mutlipolar Hamiltonian is presented.

Recent computations of complex-energy resonance poles by Rittby, Elander, and Brändas for a $V\left(x\right)=(\frac{1}{2}{x}^2-J)e^{-\lambda x^2}+J$ model potential are compared with results found by a recently developed alternative technique using Milne's method. Differences in the resulting behavior of the pole string are discussed.

Discrepancies in two different computations of complex-energy resonances for the potential $V\left(x\right)=(\frac{1}{2}{x}^2-J)e^{-\lambda x^2}+J$ are investigated. The difference is shown to be related to the existence of a critical rotation angle ${\theta }_{\mathrm{crit}}$ for which the asymptotic characteristics of the potential undergo a fundamental change.

We have used magnetically induced birefringence to determine the divergence of the susceptibility for the smectic-$C$ order parameter in butoxybenzylidene heptylaniline (40.7). The critical exponent $\gamma$ was 0.98 ± 0.04, consistent with a mean-field model and the Ginzburg criterion.

Fluctuating hydrodynamics is used to show that in fluids with large temperature gradients the shear mode couples to the heat mode in a resonant manner that results in a very large increase in the amplitude of the central peak of the spectrum of scattered light, in agreement with the results of Kirkpatrick et al. [Phys. Rev. A 26, 995 (1982)].

The hydrocarbon part of ${\mathrm{C}}_{10}$${\mathrm{H}}_{21}$N${\mathrm{H}}_3$Cl represents at room temperature an intercalated smectic lipid bilayer. With increasing temperature the effective chain diameter increases due to a partial melting of the chains. When the effective chain diameter becomes larger than half the lattice distance, a first-order reconstructive transition to a nonintercalated structure takes place. A Landau theory describing this transition has been constructed.

A technique is proposed to measure the surface tension of nonfluid materials by monitoring the resonance frequencies of drumhead vibrations of freely suspended films. It has been applied to the smectic-$A$ and -$B$ phases of a liquid-crystal BBOA (butyloxybenzylidene octylaniline). The anomalous temperature dependence of the surface tension is in accordance with that previously suggested surface ordering above the bulk $A-B$ transition temperature.

We present a theory of spinodal decomposition which is based on the linearized hydrodynamic equations including the stochastic fluctuations in stress tensor and heat flux and which accounts for nonlocal driving force through pressure gradient. The equation of state is obtained using liquid-state perturbation theory, and the transport coefficients are obtained from the Enskog theory of dense fluids. The theory thus has no adjustable parameters. The time-dependent structure factor calculated from the theory is in good quantitative agreement with molecular-dynamics experiments for early times. An effective amplification factor extracted from the experimental results also agrees well with the theoretical dispersion of the growing mode. Extension of our theory to binary-fluid mixtures shows that, within the linear regime, hydrodynamic flow effects are negligible and the Cahn-Cook description is adequate.

Formulas have been obtained for the degree of linear polarization of recombination radiation from a homogeneous plasma having an anisotropic electron velocity distribution $f\left(\overrightarrow{\mathrm{v}}\right)$ characterized by an axis of symmetry. Polarization measurements are described which utilize these formulas to determine aspects of the anisotropy such as the symmetry axis direction and the lowest-order even angular moments of $f\left(\overrightarrow{\mathrm{v}}\right)$. As a special case, if the plasma conforms to a distribution such as a "bi-Maxwellian with drift," we determine the quantities $\frac{u_D}{T_{\parallel }}$ and ($\frac{1}{T_{\parallel }}-\frac{1}{T_{\perp }}$) which involve the electron drift speed, and the "perpendicular" and "parallel" electron temperatures.

The use of free-electron-gas (FEG) motivated theories, proposed by Lindhard and colleagues, has proved extremely successful in treating the stopping power of neutral targets, and their relatively modest requirements of computational effort has led to their recent application to the stopping by electrons bound to target ions in plasmas. The FEG approximation for the average-excitation-energy Bethe-Born parameter is shown, for hydrogenic targets with nuclear charge $Z$, to be $Z^{\frac{3}{2}}$ times the neutral hydrogen value instead of having the correct $Z^2$ proportionality constant. Numerical data are presented for ${\mathrm{Al}}^{q+}$ that show the FEG error obeys this rule and, while the error approaches zero for $q=0\mathrm{}$, it is substantial for all $q>\mathrm{}0\mathrm{}$. An empirical adjustment of the FEG theory is found that reproduces the accurate ${\mathrm{Al}}^{q+}$ average-excitation-energy data. Two empirical rules now in use are observed to differ markedly from each other and from the accurate ${\mathrm{Al}}^{q+}$ results. The use of the standard FEG theory for all incident projectile energies is questioned on the basis of these results and the augmented theory proposed here requires further testing.

The electronic structure of a neon impurity in jellium as a function of temperature is studied. The self-consistent density profile is calculated within "density-functional formalism." It is shown how the pair interaction between ionized atoms in a neon plasma can be deduced from these calculations.

Several methods for deriving invariants for time-dependent systems have been developed. Four of these methods are as follows: (1) dynamical algebra, (2) Noether's theorem, (3) transformation group, and (4) Ermakov's method. These four methods are related by their use in deriving invariants for the forced, time-dependent oscillator. For this system the methods give the same results. We also discuss forced, nonlinear oscillators possessing analogous invariants. The nonlinear superposition laws for the forced oscillator are derived and discussed.

We report homogeneous-nucleation-temperature measurements in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ over a bath-temperature range $2.31<\mathrm{}{T}_b<4.62\mathrm{}$ K. These measurements were performed with the use of a transient superheating technique. The nucleation data constitute a demonstration of the quantitative accuracy of the Becker-Döring nucleation theory in describing the first-order transition kinetics in a quantum liquid, such as liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, in a region far from the critical point. A simple empirical form is presented for estimating the homogeneous-nucleation temperatures for any liquid with a spherically symmetric interatomic potential. The ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ data are compared with nucleation data for Ar, Kr, Xe, and ${\mathrm{H}}_2$; theoretical predictions for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are given in terms of reduced quantities. It is shown that the nucleation data for both quantum and classical liquids obey a quantum law of corresponding states (QCS). On the basis of this QCS analysis, predictions of homogeneous-nucleation temperatures are made for hydrogen isotopes such as HD, DT, HT, and ${\mathrm{T}}_2$.

The one-dimensional harmonic liquid, subject to a temperature gradient, is studied using the Fokker-Planck (FP) equation. A formalism is set up for solution of the FP equation and calculation of (1) the phase-space distribution function for the nonequilibrium steady state (NESS), (2) the conditional probability for evolution through phase space in the NESS, (3) phase-function averages in the NESS, (4) the correlation of phase functions in the NESS, etc. For the harmonic liquid this formalism can be implemented without approximation. Some properties of the harmonic liquid in equilibrium are examined to illustrate use of the formalism; so are some phase-function averages in the NESS. The displacement-displacement correlation function $D(k,\omega )$ in the NESS is calculated and found to have the well-established, interesting amplitude and frequency dependence. The completeness of the Fokker-Planck description makes it possible to identify the physical processes responsible for the behavior of $D(k,\omega )$ and the dynamic structure factor $S(k,\omega )$. The interesting features of light scattering from a liquid subject to a temperature gradient, seen in $S(k,\omega )$ or $D(k,\omega )$, are due to light scattering from width fluctuations induced by the gradient; the interesting features in light scattering from a liquid-supporting shear are due to an attenuation mechanism that arises because of the velocity field induced by the shear. The results in this paper constitute a partial demonstration of the usefulness of the method employed in handling the Fokker-Planck equation.

Recent experimental results on the intermittent generation of shear turbulence raise questions about the significance of Reynolds averaging. In this paper, statistical equations are derived by progressively averaging the Navier-Stokes equation over a series of increasing time periods. Averaging over the shortest time smooths out part of the field (which corresponds to the highest-frequency fluctuations). The mean effect of these fluctuations may be calculated from the time-averaged equation of motion, and so eliminated from the equation describing the rest of the velocity field (that is, the unaveraged part). An iterative process leads to equations for the mean and covariance of the fluctuating field, in which the Reynolds stresses do not appear explicitly. They are represented in each cycle of the iteration by the sum of the following: (1) a constitutive relation, expressing the mean-square fluctuation in terms of the mean rate of strain, and (2) the unaveraged portion of the nonlinear term. The method resembles the renormalization group (it differs insofar as the averaging process is the defining operation). A renormalization-group analysis is used to investigate the iteration process. With some simplifying assumptions (e.g., the fluctuations are taken to be isotropic and the spectrum to be a power law), a recursion relation for the viscosity is found to reach a fixed point. In the limit of long averaging times, the mean-field equation reduces to the Reynolds equation, with the turbulent stresses replaced by an effective viscosity.

Through cumulant expansions of the free energy and the susceptibility, a new variational procedure is proposed with the purpose of improving the standard variational method in equilibrium statistical mechanics. The procedure is tested for two types of classical anharmonic single oscillators, namely, those whose elastic potential is proportional to $x^{2n}(n=1,2,\dots )$ and those of the type $a{x}^2+b{x}^4$, whose exact free energy, specific heat, and susceptibility are herein established. Although convergence problems (similar to those appearing in the asymptotic series) exist (at least for the free energy) in the limit of high perturbative orders, great improvement (typically of the order of 40) with respect to the standard variational method is obtained in all the physically meaningful situations, and a quite satisfactory description is provided (with a "single shot") for both limits $T\to 0$ and $T\to \infty$ simultaneously.

Exact second Born amplitudes for $1s-1s$ electron capture are presented and interpreted in terms of contributions from intermediate states off the energy shell and on the energy shell. The classical model of Thomas corresponds to two-step scattering via one particular on-shell intermediate state. In the high-velocity limit for $1s-1s$ capture, this on-shell intermediate state of the Thomas model accounts for one-half of the total cross section, i.e., the second Born cross section. The other half comes from off-energy-shell intermediate states near the on-shell Thomas state. Above 5 MeV both the off-shell and on-shell amplitudes have a simple structure near the Thomas peak. Below 1 MeV, contributions from a broader range of intermediate states are evident in the amplitudes. Although the contribution from the Thomas state is not large below 1 MeV, other second Born effects are significant.

Experimental verification of reduced stimulated Brillouin scattering (SBS) is reported for multiline ${\mathrm{CO}}_2$ laser radiation interacting with high-density plasma. For long-pulse (40-nsec) irradiation SBS was observed to decrease from 15% to a negligible level when the spectrum of the incident laser pulse was changed from 1 to 2 or more well-separated frequencies. Results for both long- and short-pulse multiline laser conditions are in general accord with the expected behavior for varying $\frac{\Delta \omega }{{\gamma }_0}$, where $\Delta \omega$ is the frequency separation and ${\gamma }_0$ is the homogeneous growth rate.