We develop a theory of optical absorption of a diatomic molecule in a simple monatomic liquid. Using approximations appropriate to the case of a light molecule like ${\mathrm{H}}_2$, we show that the absorption spectrum near an infrared-inactive vibrational transition of the molecule can be interpreted to give information about collective effects in the fluid. We show that some features of existing experimental results on ${\mathrm{H}}_2$-Ar mixtures are consistent with the theory, although no direct evidence of collective effects is seen in these experiments.

Investigations concerning the behavior of the $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ population in active-discharge and after-glow helium plasmas are described. Good quantitative agreement is obtained between measured $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ densities in active discharges and predicted values based on the solution of a nonlinear rate equation. The rate coefficient for ionizing triplet-metastable-metastable collisions is measured in afterglow helium plasmas for the pressure range 10-40 Torr; close agreement is obtained with the value reported by Phelps and Molnar, though consideration of effects due to electrons suggests a downward revision of about 20%. The electron temperature decay in the afterglow is measured and found to agree closely with the decay expected on the basis of calculated energy source and loss processes which affect the electron gas. In this work, measurement of the $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ metastable density is accomplished by the novel use of a He-Ne laser operating at 1. 0798 $\mu$ in an interferometer as well as by the conventional optical-absorption method. Advantages and disadvantages of this interferometer technique are discussed.

We study the space-time-dependent correlation functions of density and velocity in a dilute gas using classical scattering theory. A density expansion of correlation functions is discussed. The effect of two-body interaction is analyzed in detail for the case where the relevant wave-length is long compared to the atomic dimension but small compared to the mean free path. Explicit formulas for the correlation functions in terms of the impact parameter and the time delay are obtained. The equivalent quantum-mechanical analysis has been carried out elsewhere. The classical and quantum formulas are nearly identical. A main purpose of this paper is to make the results of the (difficult) quantum-mechanical treatment more accessible.

Experiments are reported on the dissipative steady-state flow regime of liquid helium II. These were done with a view to examining the theoretical assertion that the chemical potential gradient $\nabla \mu$ is related to the superfluid-flow speed $v_s$, by the equation $-\nabla \mu =G\exp \left(\frac{1-v_c\mathrm{}\left(T\right)\mathrm{}}{v_s}\right]$. Our experiments showed good qualitative agreement with this equation. Other assertions about the magnitude of the parameters in this equation and their dependence upon the superfluid fraction $\frac{{\rho }_s}{\rho }$ and temperature $T$ were also explored experimentally.

The contribution of order-parameter fluctuations to the static and dynamic properties of a weakly interacting Bose gas near the Bose-Einstein condensation temperature $T_c$ is investigated via a novel approach. Self-consistent approximations for the propagator of order-parameter fluctuations $G$ are generated in successive temperature ranges closer and closer to $T_c$. Mean-field theory corresponds to assuming that the correlation of fluctuations $G_2$ is given by ${G_2}^{\mathrm{}\left(1\right)\mathrm{}}=GG$. This first approximation is valid in the range ${\tau }_1<\tau =\frac{(T-T_c)}{T_c}<1\mathrm{}$, where at $\tau ={\tau }_1$ the neglected terms are comparable to those included. In this paper we consider the second approximation ${G_2}^{\mathrm{}\left(2\right)\mathrm{}}=GGVGG$, which involves the first-order interaction between the fluctuations. Two independent criteria for the range of validity ${\tau }_2<\tau <{\tau }_1$ of the second approximation are established. It is conjectured that the qualitative results of the present model calculation are applicable to liquid helium in the presently accessible temperature range. The predicted temperature dependences of the specific heat, superfluid density, and fourth sound are in agreement with the scaling hypothesis and available experiments in helium. The condensate density is predicted to vanish linearly with $\tau$. It is shown that the contribution of order-parameter fluctuations to the thermal conductivity diverges as ${\tau }^{\frac{-1\mathrm{}}{3}}$ above $T_c$, and it is suggested that the absence of logarithmic factors is due to the inconsistent treatment of entropy fluctuations.

Integral equations of the Watson-Faddeev type, developed in the context of few-body nonrelativistic scattering theory, are shown to play an important role in the structure analysis of many-body Green's functions and in variational techniques for the approximate determination of these Green's functions. Such equations sum up an infinite chain of few-body correlations. Those correlations which are not of this form, i.e., the intrinsic many-body correlations, are accounted for by the appearance of an effective (or "renormalized") interaction, as can be seen by direct transformation of the exact Martin-Schwinger equations for the Green's functions. For a given choice of effective interaction, the few-body correlation functions must be determined self-consistently. The Schwinger variational principle, originally developed for linear integral equations, is nevertheless the key element in a variational formulation of the nonlinear equations encountered here. For simplicity we confine our attention to equations which determine the two-body Green's function, although the entire procedure can be generalized to higher orders.

The theory of Brownian motion of a quantum oscillator is developed. The Brownian motion is described by a model Hamiltonian which is taken to be the one describing the interaction between this oscillator and a reservoir. Use is made of the master equation recently derived by the author, to obtain the equation of motion for the various reduced phase-space distribution functions that are obtained by mapping the density operator onto $c$-number functions. The equations of motion for the reduced phase-space distribution functions are found to be of the Fokker-Planck type. On transforming the Fokker-Planck equation to real variables, it is found to have the same form as the Fokker-Planck equation obtained by Wang and Uhlenbeck to describe the Brownian motion of a classical oscillator. The Fokker-Planck equation is solved for the conditional probability (Green's function) which is found to be in the form of a two-dimensional Gaussian distribution. This solution is then used to obtain various time-dependent quantum statistical properties of the oscillator. Next, the entropy for a quantum oscillator undergoing Brownian motion is calculated and we show that this system approaches equilibrium as $t\to \infty$. Finally we show that in the weak-coupling limit the Fokker-Planck equation reduces to the one obtained by making the usual rotating-wave approximation.

The well-known variational (maximum-entropy) property of the Maxwellian velocity distribution is used to shed some light on the range of validity of the Boltzmann transport equation. It permits a characterization of the initial states for which the Boltzmann $H$ theorem is violated. In particular, it is shown that: (a) Any monatomic system for which the equilibrium potential energy exceeds the minimum possible value possesses a continuum of initial states for which the approach to equilibrium takes place through an increase, rather than a decrease, in Boltzmann's $H$. (b) If the initial distribution of particles is spatially homogeneous and Maxwellian, the approach to equilibrium will take place through an increase (decrease) in the Boltzmann $H$, according as the initial potential energy is less (greater) than the equilibrium value. (c) A necessary condition for the $H$-theorem-violating phenomenon is that the approach to equilibrium takes place through a conversion of kinetic energy into potential energy; a sufficient condition requires also that the initial velocity distribution be sufficiently close to Maxwellian. (d) These $H$-theorem-violating conditions are readily attained experimentally; for example, the free expansion of oxygen gas at 160 °K and 45-atm pressure produces an experimentally realizable violation of the Boltzmann $H$ theorem.

The generator-coordinate method, well known in nuclear physics, is employed to derive the Bogoliubov theory of superfluidity of a boson system. The treatment is fully number conserving. Analogies to a normal Fermi system (especially to the random-phase approximation for that system) are pointed out, and some further insight into the nature of superfluidity is gained. Possible generalizations are mentioned.

The Kubo-Zwanzig-Fano relaxation method is extended to the problem of a homogeneous dilute system interacting with arbitrarily strong fields composed of several monochromatic modes, neglecting breakdown and spatial correlations. The Von Neumann equation for the density matrix is solved for classical fields, using a procedure in which the harmonics numbers are treated as the classical analog (in Liouville space) of the quantum fields occupation-number representation. This solution is adapted to the case where memory effects during the absorption or emission of a photon can be neglected. Two examples illustrate the method, which is generally applicable in such problems as saturation, double resonance, and frequency mixing involving the nonlinear response of independent molecules.

The theory of scattered light waves with exponential temporal and spatial gain is investigated in the linearized approximation for a number of different cases of material excitation. Regions of weakly coupled gain (the rate-equation approximation) and strongly coupled gain are found. A group velocity for the scattered wave is introduced to facilitate the analysis. Gain is found for the case where the material excitations lose their uncoupled character.

The momentum distributions of electron pairs in superconductors and of helium atoms in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ are defined by summing the pair or atomic state occupation probability over all internal states of the pair or ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atom corresponding to a given value of total translational momentum. By use of the closure relation for internal wave functions, the momentum distribution of electron pairs is expressed in terms of the two-electron density matrix ${\rho }_2(x_1{x}_2,x_1^{\prime }{x}_2^{\prime })$ of the $2n$-electron system. Similarly, for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atoms, the momentum distribution is expressed in terms of the single-atom density matrix ${\rho }_3(x_1{x}_2\overrightarrow{\mathrm{R}},x_1^{\prime }{x}_2^{\prime }{\overrightarrow{\mathrm{R}}}^{\prime })$ of the $n$-atom system, where $x_1$, $x_2$, and $\overrightarrow{\mathrm{R}}$ are the coordinates of two electrons and an $\alpha$ particle. The equivalence of this definition of the momentum distribution with two other plausible definitions is demonstrated. It is shown that exchange and the exclusion principle produce a strong spreading of the momentum distribution both for a superconductor and for liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, completely suppressing Bose-Einstein condensation in the strong sense of macroscopic occupation of the zero-momentum state. However, a much weaker singularity at zero momentum, characteristic of the off-diagonal long-range order (ODLRO) of ${\rho }_2$ for a superconductor and of ${\rho }_3$ for liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, does occur. By comparison with the hypothetical case of pairs of bosons, it is shown that the exclusion principle (not merely exchange) plays an essential role in broadening the momentum distribution in superconductors and liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.

The transport coefficients of ${}_{}{}^3{}_{}{}^{}\Sigma$ molecular oxygen in magnetic fields show large deviations from an $\frac{H}{p}$ law, even at moderate pressures and fields. This complex behavior is explained by the effect of a quadratic Zeeman splitting of the $\sigma =0\mathrm{}$ multiplets, superimposed on the normal linear splitting. Because the normal linear splitting is very small for $\sigma =0\mathrm{}$, the anomalous effects occur at fields far below the true Paschen-Back region. Collisionally uncoupled model calculations give the transverse viscosity coefficients in quite detailed agreement with experiment. The distinct behavior of the single- and double-frequency viscosity coefficients reflects distinct selections from the internal-state frequency spectrum, determined by weight factors ${\left|Y^{2\mu }\right(\theta ,\phi \left)\right|}^2$ in the orientation of $\overrightarrow{\mathrm{J}}$. The anomalous behavior of the even coefficients is predicted to be quite complex. In particular the $\frac{H}{p}$ curves of ${\eta }_1^{+}$ at about 4 Torr should show three steps, instead of the usual two, and the behavior of ${\lambda }_{\parallel }$ should be similar.

The general form of the density operator for unpolarized radiation is obtained. It is shown that if two orthogonally polarized components of unpolarized radiation are statistically independent, the radiation is necessarily chaotic. It is also shown that the procedure currently being used for studying interactions of unpolarized radiation is not correct, and that Stokes's parameters do not correctly specify the unpolarized state of radiation.

Drachman's and Oberoi and Callaway's variational polarized-orbital equations for low-energy particle-atom scattering can be rewritten without any approximation in a central-potential form.

The compressibility of solutions of several alkali metals in liquid ammonia has been calculated using a hard-sphere model. The constituents are solvated ions and free ammonia molecules. The calculation requires solvation numbers for the ions consistent with expectations based on chemical experience.

We have attempted to measure the depression of the superfluid transition temperature $T_{\lambda }$ in liquid helium by a heat current $Q$, and found that within our precision, $T_{\lambda }$ is independent of $Q$ for $0.2\le Q\le 2$ ${\mathrm{W}/\mathrm{c}\mathrm{m}}^2$. An effect of the size $\frac{\Delta T_{\lambda }}{Q}\cong 3\times {10}^{-3\mathrm{}}$ K ${\mathrm{cm}}^2$/W would have been observable. This upper limit is inconsistent with the value 59 × ${10}^{-3\mathrm{}}$ K ${\mathrm{cm}}^2$/W reported recently by Bhagat and Lasken for ${10}^{-3\mathrm{}}\le Q\le {10}^{-1\mathrm{}}$ ${\mathrm{W}/\mathrm{c}\mathrm{m}}^2$.

Monte Carlo studies of the reference fluid used by Chandler, Weeks, and Andersen (CWA) are reported. Although the CWA theory gives good values for the total thermodynamic properties, in its original form it gives less satisfactory values for the individual terms in their perturbation expansion. This results in part from the use of the Percus-Yevick theory in the CWA calculation of the radial distribution function.

For not-too-strong field strengths, the one- and two-photon resonant fields are shown to obey together an area theorem. The generated one-photon resonant (harmonic) field is discussed in the steady-state and superradiant regions.