The ground-state energy of solid ${\mathrm{He}}^3$ is evaluated by means of a perturbation expansion. The unperturbed Hamiltonian chosen localizes each atom at a given site. As such, the formalism is one of distinguishable particles. No a priori self-consistency of the single-particle potential is assumed. Two-particle diagrams are summed to all orders by means of a set of Bethe-Goldstone equations.

The response of a system of coherently pumped atoms to weak electromagnetic perturbing fields is discussed in general terms. The pump field is prescribed, and is assumed to propagate unattenuated through the medium which the (identical) atoms comprise, exciting a particular transition through either electric or magnetic dipole coupling. The perturbing field, which is assumed to act through electric dipole coupling, is allowed to be the (resonant) field emitted by the atoms, a weak external field absorbed by the atoms under resonant conditions, or a resonant or nonresonant wave propagating through the pumped medium. All of these cases are conveniently described within the same general framework, based on an analysis of the (single-atom) two-time dipole-moment correlation function. This function contains nonstationary components as well as stationary ones, owing to the time dependence imposed by the pump field. We are accordingly led to introduce a time-dependent linear susceptibility, which is inhomogeneous and anisotropic, due, respectively, to the variation of the pump phase within the medium and the preferred direction established by the pump-field polarization. Such disparate effects as parametric frequency conversion, emission- and absorption-line splitting, and time-dependent modulation of resonant emission and absorption functions in optical-pumping experiments emerge naturally from a single unified formalism.

The Penning-ionization cross sections for He, Ne, Ar, and Kr metastable atoms with Zn and Cd have been measured in a pulsed afterglow. Within the framework of existing theories we have determined those parameters which are of importance in collisions of this type. We find that our data are internally consistent if the cross sections are proportional to the cube of the "hard-sphere" radii and the effects of selection rules are included. A theoretical basis for this dependence is suggested.

It is shown that first- and second-sound resonance can lead to the appearance of spurious stable states and pumping phenomena in the Richards-Anderson experiment on the Josephson effect in superfluid helium, and proposals are made for their elimination.

Considering the elementary excitation spectrum of ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures to be of the form proposed by Landau and Pomeranchuk, we calculate the scattering cross section for roton and ${\mathrm{He}}^3$ quasiparticle collisions, taking final-state interactions into account. Our theory demonstrates the importance of final-state interactions in renormalizing the roton energy and lifetime. Previous theories based on the Born approximation are shown to give unreliable results for the change of the energy and lifetime for rotons in dilute ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures owing to roton-${\mathrm{He}}^3$ scattering. We obtain upper bounds on the changes in the energy and lifetime of a roton as a function of the roton-${\mathrm{He}}^3$ coupling strength, using a simplified model for the coupling. These bounds give an insignificant change of the roton energy with the ${\mathrm{He}}^3$ concentration and thus explain recent neutron-scattering and Raman data on the mixtures. Effects of level repulsion between rotons and the ${\mathrm{He}}^3$ quasiparticle-hole continuum are calculated, and estimated to be small on the basis of recent Raman data. However, decay of a roton into a ${\mathrm{He}}^3$ quasiparticle-hole pair may give rise to an interesting concentration dependence of the roton linewidth. Further experimental studies of the mixtures are suggested, which may check the detailed predictions of the theory and provide insight into the momentum dependence of the coupling parameters. The present analysis represents an essential link between microscopic theories of the quasiparticle coupling and related experiments on dilute ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures.

The normal-fluid viscosity of superfluid ${\mathrm{He}}^4$ has been calculated for temperatures below about 0.6 °K. The calculation assumes that the dominant scattering mechanism is the three-phonon process in the first order of perturbation theory. This contrasts with the previous calculation of Landau and Khalatnikov, who assumed a second-order process involving four phonons. The theory is compared with the experiments of Whitworth on heat flow through tubes. Good agreement is obtained, as regards both the magnitude of the viscosity and its temperature dependence.

Acoustoelectric amplification in piezoelectric semiconductors can be profitably treated as the acoustic analog of a classical laser. The nonlinear acoustic gain and frequency pulling can be found by combining Maxwell's equations with the piezoelectric equations of state and solving the resulting system to third order in a perturbation expansion. Recent experimental findings (acoustic mode locking, etc.) encourage the use of such methods, which produce results analogous to those of the Lamb theory of a classical laser. We here present solutions for the case of a single acoustic mode. Diffusion effects are found to be important, especially near threshold.

Wegner's paradigm for constructing renormalization groups in statistical mechanics is applied to fluids. The coordinates of the fraction ($1-y$) of the molecules are integrated over and a system of interactions describing the remaining fraction $y$ is constructed with the aid of the McMillan-Mayer solution theory. Renormalized Ursell functions are defined in terms of which the group operations are shown to be linear. The group operations commute with a scaling operation and it is found that a series of renormalization groups depending on a parameter $x$ can be constructed by combining the operation of integrating over coordinates with the scaling operation. By comparing the renormalized cluster functions with the form of the critical cluster functions given by scaling it is shown that a fixed point of one of the series of groups corresponds to the critical point. The parameter $x$ turns out to be the scaling exponent for the chemical potential. The question of the universality of critical phenomena is expressed as the question of the discreteness or continuity of the spectrum of values of the parameter $x$ for which the linear fixed-point equations have a nontrivial solution. It is suggested that this question can be answered definitively only when a precise formulation is made of the function space in which the sequence of renormalized Ursell functions must lie.

Bose-Einstein condensation and the atomic momentum distribution are investigated for a simplified liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ground state obtained by antisymmetrization, with respect to the electron variables, of a product of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$-atom wave functions, each in its individual electronic and translational ground state. The momentum distribution is defined and evaluated by the method of redundant modes and generalized Tani transformation. Bose-Einstein condensation is found, with a condensate depletion of 6% owing to the purely kinematical repulsion arising from the Pauli exclusion principle. The noncondensed atoms are spread in momentum space by an amount of a few inverse Bohr radii. Dynamical correlations would increase the depletion in a more realistic ground state.

The fluctuations in a generalized version of Lubensky's spin model for cholesterics are shown to still diverge (for an infinite system). The generalization consists in allowing the skew term of the interaction Hamiltonian to include a dependence on the directions of the "short" molecular axes. Some such dependence is expected in molecules of real cholesterics.

The scattering of electromagnetic radiation by a fully ionized, collision-dominated plasma in a magnetic field is investigated using a stochastic approach. The stochastic equations for the density-fluctuation operators are modified to include particle collisions through a Bhatnagar-Gross-Krook collision model. The equations of this model are constructed to conserve particle number, energy, and momentum. Explicit numerical results are obtained in the absence of magnetic fields and compared to experimental values and other theories. The analytical results are assumed valid for plasmas which can be characterized by Maxwellian velocity distributions for electrons and ions at the same or different temperatures.

An improved version of the theory of amplified spontaneous emission (ASE) is presented and shown to be satisfied by experimental data obtained using the 3.39-μm transition of He-Ne. The new approach allows the effect of an external signal injected at one end of the system to be investigated and its influence on both the positive-going and negative-going waves to be calculated for He-Ne. A special case occurs when the injected signal is replaced by a mirror which reflects the negative-going wave back into the medium and the theory of this commonly occurring laboratory system is experimentally verified at 3.39 μm. The treatment allows the importance of the interaction between spontaneous and stimulated emission to be considered. The beam divergence predicted by the theory is evaluated and compared with experiment. The spectral distribution for a pure ASE system is considered, as is the distribution of inversion which results from the positive- and negative-going waves and which is shown to have minima at the medium extremities. Finally the implications of this work for the problem of interstellar OH emission is considered.

Formally exact equations of motion satisfied by the gross variables of a macroscopic system valid far from thermal equilibrium are obtained with the aid of the new projection operator in nonequilibrium statistical mechanics. These equations are used to study nonlinear shear viscosity and normal stress effects of a model incompressible fluid in the presence of a shear flow which is not necessarily small. We find that the mode-coupling mechanism responsible for the long-time tails in time-correlation functions becomes very important here also and that a simple power-series expansion in the rate of shear $D$ therefore fails. The part of shear viscosity dependent upon the rate of shear and the normal stress effect are found to vary as ${\mathrm{}\left|D\right|\mathrm{}}^{\frac{1}{2}}$ and ${\mathrm{}\left|D\right|\mathrm{}}^{\frac{3}{2}}$, respectively.

Below the critical point the liquid-vapor interface of a simple fluid is characterized by a thin transition layer across which the values of density vary between the two phases. This transition layer can be described by a density profile characterized by an effective interface thickness $L$. As the temperature $T$ approaches the critical temperature $T_c$, $L$ diverges as ${\epsilon }^{-{\nu }^{\prime }}$, where $\epsilon =1-\frac{T}{T_c}$. From the measurement of optical reflectivity of the liquid-vapor interface of sulfur hexafluoride, we have deduced the interface thickness and the critical index $\beta$ for the coexistence curve. In the temperature range $9.73\times {10}^{-5\mathrm{}}\le \epsilon \le 5.33\times {10}^{-2\mathrm{}}$ we find ${\nu }^{\prime }=0.620\mathrm{}\pm 0.01$ if an error-function profile is assumed as proposed by Buff, Lovett, and Stillinger, or ${\nu }^{\prime }=0.663\mathrm{}\pm 0.02$ if the density profile proposed by Fisk and Widom is used. For both profiles $\beta$ is found equal to 0.333 ± 0.008. These indices, when combined with the critical index ${\gamma }^{\prime }$ for the isothermal compressibility and $\mu$ for the surface tension, are used to test various scaling relations.

We have measured the spectrum of the light that is quasielastically scattered at angles close to the direction of reflection by the thermal excitations of the liquid-vapor interface of sulfur hexafluoride near its critical temperature $T_c$. The surface tension $\sigma$ and an average shear viscosity $\overline{\eta }$ have been deduced from the experiments using hydrodynamic theories of the propagation of damped surface waves. The recent theory of Bouchiat and Meunier, which takes into account the retardation of the dissipative bulk flows, is confirmed. In the temperature range $1.22\times {10}^{-4\mathrm{}}\le \epsilon \le 6.90\times {10}^{-2\mathrm{}}$ the data can be fitted to $\sigma \mathrm{}\left(t\right)={\sigma }_o{(1\mathrm{}-\frac{T}{T_c})}^{\mu }$, with ${\sigma }_o=55.13\mathrm{}\pm 2.6$ dyn/cm and $\mu =1.285\mathrm{}\pm 0.016$. No critical anomaly in shear viscosity $\overline{\eta }$ is found, and $\overline{\eta }=[425+14.5(T_c-T)\pm 15]\times {10}^{-6\mathrm{}}$ poise. The theory of Fisk and Widom for both the magnitudes and critical scaling of the exponents has been tested and the Kawasaki form of the thermal diffusivity ${\Lambda }_h=\frac{k_{B}T}{6\pi \eta \xi }$ has been computed from our measurements of $\overline{\eta }$ with the interfacial thickness $L^{\prime }$ and the associated correlation length $\xi$ and compared with the published measurements of the spectral linewidth of Rayleigh scattering.

Scaling laws of strong plasma turbulence are obtained with the aid of similarity transformation of physical parameters in the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy equations. Possible existence of a universal spectrum proportional to $k^{-3\mathrm{}}$ is discussed. The scaling arguments are extended to the analysis of the rate of turbulent heating and the anomalous resistivity. It is also shown that the scaling laws are useful in resolving an apparent paradox in the interpretation of the Crab pulsar spectrum.

The transient order induced in the isotropic phase of the $N-(p-\mathrm{M}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{x}\mathrm{y}\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{z}\mathrm{y}\mathrm{l}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{e})-p-\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{y}\mathrm{l}\mathrm{a}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{e}$ by the plane-polarized electric field of a $Q$ -switched laser beam, is experimentally measured and analyzed. Good agreement is found with considerations deduced from the theory of de Gennes. It allows direct measurements of the optical Kerr constant and of the orientational relaxation time in these materials.

The ground state of an electron gas in an intense magnetic field is studied using a wave function of the product form ${\Psi }_0^B\Phi$. The correlation factor ${\Psi }_0^B$ is taken to be the ground-state solution of a charged Bose gas and $\Phi$ a determinant of single-particle Landau states. In the quantum strong-field limit so that only the lowest Landau state is populated, the correlation energy is computed using the cluster-expansion technique and a variational determination of the boson energy. Numerical results obtained are lower than those derived under the random-phase approximation.

The thermodynamic fluctuations of hot bodies emitting thermal radiation generate corresponding fluctuations in the emitted intensity. A simple derivation using standard fluctuation-dissipation arguments shows that such fluctuations manifest themselves in the time correlations of the emitted radiation intensity. An experiment is proposed to detect the intensity correlations. A modified form of the main result satisfying the stationarity condition of the intensity correlations is also obtained.

A systematic formulation of the theory of a ring laser is given, based on first principles and using a well-known model for laser operation. The discussion begins with a simple physical derivation of the electromagnetic field equations to first order in $\Omega$ for a noninertial reference frame in uniform rotation, and a qualitative analysis of the traveling-wave Fox-Li modes for a polygonal cavity. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory. The formalism can also be applied to another problem of current interest: the absorption line shape for a weak wave in the presence of a strong one traveling in the opposite direction. In the last few sections, the small-signal ring-laser theory is recovered as a special case, and a systematic calculation of the various equations of this theory is included. The limitations of laser gyroscopes arise mainly because of effects of backscattering of radiation and nonreciprocities of the optical path, leading, for example, to frequency-locking phenomena. Non-reciprocal losses have been used to shift the locking threshold, but for rotation rates above this threshold the observed beat note departs from the desired rotation rate in a typical manner shown in previous articles. However, the theory indicates that if more-detailed measurements are made, they should provide sufficient information for determining the rotation rate (apart from noise fluctuations).