The collective modes associated with oscillations of the order parameter in the $B$ phase are calculated. The phase is assumed to be the Balian-Werthamer state, and it is shown that there are three collective modes in which both the orbital and spin angular momenta of the Cooper pairs oscillate. The two modes with transverse polarization are found to have a velocity $\sqrt{2}$ times as large as the longitudinal mode. In the presence of the dipole interaction these modes are mixed, with one mode becoming the longitudinal resonance in zero field.

The distribution of ionization states in carbon, aluminum, copper, and tungsten plasmas is determined from the corona-model equilibrium. The variations of mean ionization level, internal energy, and radiation rates for continuum and lines with temperature are then determined by averaging over the ionization states. Results can be applied to studies of a variety of existing laboratory plasmas and to analyses of the effects of impurities in fusion plasmas.

The mobilities of ${\mathrm{Li}}^{+}$ ions in ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ gases have been measured at (26-38) °C gas temperature over a range of $\frac{E}{N}$, the ratio of electric drift field to the gas number density, from 8 to 280 Td (1 Td = ${10}^{-17\mathrm{}}$ V ${\mathrm{cm}}^2$). The zero-field reduced mobilities were measured to be 12.3 and 4.1 ${\mathrm{cm}}^2$/V sec in ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ gases, respectively. It was found that the mobility in ${\mathrm{N}}_2$ gas decreases monotonically down to a value 3.7 ${\mathrm{cm}}^2$/V sec below 90 Td with an increase in $\frac{E}{N}$, and thereafter increases. The mobilities of ${\mathrm{Li}}^{+}$ in mixtures of ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ gases have been measured at $\frac{E}{N}=15,31,93, \mathrm{and} 173$ Td. A slight deviation from Blanc's law is noticed at $\frac{E}{N}=173\mathrm{}$ Td. A simple numerical method to obtain the mobility in mixture gases is proposed.

The propagating fluctuations on the free surfaces of nematic, cholesteric, and smectic liquid crystals are evaluated in the absence of dissipation from the hydrodynamical equations. In the nematic there is full translational symmetry and this implies that the dispersion relation for propagating waves is the same as in an ordinary fluid. Surface fluctuations in a cholesteric distort the helical structure and the first-order elastic constant $k_{22}{q}_0^2$ associated with the twist gives rise to an additional restoring force besides the usual surface tension $\gamma$. When $\gamma q\gg k_{22}{q}_0^2$ ($q$ is the wave vector), the surface tension dominates and the dispersion relation $\omega \mathrm{}\left(q\right)\mathrm{}$ approaches that in an ordinary fluid: $\omega \propto q^{\frac{3}{2}}$. When $\gamma q\ll k_{22}{q}_0^2$, the twist elastic forces dominate and $\omega \propto q$. In both cases the waves penetrate less into the bulk than in an ordinary fluid. Similar results apply in the smectic-$A$ case provided that the elastic constant associated with layer displacement is small compared to the compressibility. This may be the case near the smectic-nematic phase transition.

An analytical expression for the threshold of absolute growth for a parametric-decay instability is given for the simplest three-frequency interaction in a homogeneous plasma. The validity of this expression as compared to the results of a four-frequency interaction (including the upshifted frequency) at densities near critical is investigated using saddle-point mapping criteria. The investigation is carried out using pump intensities sufficiently large so that the effects of the oscillating-two-stream interaction should be manifest in the dispersion mapping for the parametric decay interaction. It is found that the absolute decay instability is preserved through a regime of parameters corresponding to intensities of ${10}^{14}$ ${\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ and a critical parameter of $\frac{{\omega }_{\mathrm{pe}}}{{\omega }_0}=0.999\mathrm{}$. No parametric-decay instability is found for an overdense plasma. Finally, for a typical laser plasma, minimum threshold intensities are shown to exist for absolute instability of the parametric decay interaction at subcritical densities which are closer to the critical density than the previously known minimum thresholds for convective growth.

This is the second in a series of three papers on nonlinear resonance effects in multilevel quantum systems in which quantum-mechanical systems are considered that are under the influence of any number of classically described driving fields (well defined in amplitude and phase) and are in weak contact with a thermal reservoir, such that relaxation may be described by means of phenomenological decay constants. In the first paper, referred to as I, a projection-operator formalism was developed for separating the equation of motion for the density operator into a part which may be treated by conventional time-dependent perturbation techniques and another part which, because it would give rise to secular terms using a time-dependent perturbation theory, must be treated by more exact means. In this paper three applications of the formalism developed in I are considered. The first application is to a system in which a multiple-quantum transition is taking place between two levels of the system which contains many levels between the two levels under consideration. In particular, the transition probability is calculated for these two levels, which are not directly connected by matrix elements of the interaction but are connected indirectly through intermediate states. The next application considered is the Raman effect in a four-level system. As a final application of the formalism developed in I an expression is derived for the magnetization $M_{+}\mathrm{}\left(t\right)=M_x\mathrm{}\left(t\right)+i{M}_y\mathrm{}\left(t\right)\mathrm{}$ of a system of $N$ noninteracting spins under the influence of a static field in the $z$ direction and an arbitrary number of rf fields in the $x$ direction. As in I, a phenomenological form is assumed for the relaxation in all of these applications. It is shown in this problem that fields which are not involved in directly causing transitions in this system give rise to frequency shifts in the resonance conditions, which are accounted for in this treatment in a very natural and straightforward manner. For these fields, the rotating as well as the counter-rotating fields give shifts in the resonance condition.

The plasma virial theorem is derived from the equation of mass motion and evaluated for rotationally field-symmetric configurations so as to yield a general dynamic Bennett relation. The acceleration term is formulated in different ways. Magnitudes of expansional and compressional terms are discussed. The relation extends the recent Baker-Phillips result that magnetic field diffusion has a deconfining action in the late stage of $z$ pinching.

The two- and three-particle distribution functions of the weakly interacting Bose gas in its ground state are studied via the calculation of their Fourier transforms. The form obtained for the three-particle distribution function shows that the familiar convolution approximation is not correct even in the lowest nontrivial order of perturbation theory. For the special case of the charged Bose gas at high density, the two-particle distribution function is obtained to second order in the expansion parameter $r_s^{\frac{3}{4}}$, a result which disagrees with a recent calculation. The discrepancy is traced to a use of the convolution approximation for the three-particle distribution function. Finally, Landau's theory of quantum hydrodynamics is employed to relate the long-range part of the three-particle distribution function to the Grüneisen constant. These results emphasize the need to treat properly the dynamic three-particle correlations in any quantitative theory of liquid helium.

The role spin fluctuations play in determining the stable superfluid phases of ${\mathrm{He}}^3$ is investigated. It is shown that the feedback effects of the gap on the spin fluctuations can stabilize the anisotropic Anderson-Morel (AM) state if they are sufficiently strong. The effect is calculated both near $T_c$ and at zero temperature. It is found that the Balian-Werthamer (BW) state is more stable at low temperatures and that the slope of the calculated transition from the AM to BW states qualitatively agrees with the experimental slope of the $A \mathrm{to} B$ transition as a function of pressure.

The exact differential equations with periodic coefficients characterizing the transition in a two-level quantum system are solved by the stroboscopic method which is a nonperturbative approach. This method is based on an averaging over the fluctuations in the system. The solution is unitary and is valid for large times also, as opposed to the short-time validity of the perturbative solution. It should also be noted that this method gives Rabi's well-known solution to the two-level system at resonance by the so-called transformation to the rotating coordinate frame.

The solution of the isotropic $n$-component spin models by expanding in powers of $\frac{1}{n}$ has been very helpful in studying static critical phenomena. The limit $n\to \infty$ is the spherical model. There are many possible generalizations of these models for studying dynamic (time dependent) critical phenomena. In this paper we study the propagation of sound waves and heat diffusion near the critical point in a $\frac{n}{2}$- component complex-spin (each complex component has two real components) model in the limit of large $n$. This model is a particular dynamic generalization of the spherical model and is equivalent to a system of bosons obeying quantum mechanics.

The Galitskii-Feynman $T$ matrix, which sums the ladder diagrams for both particle-particle and hole-hole scattering in a many-fermion system, is shown to have a singularity at negative values of the c.m. energy of the interacting pair. The singularity appears as a first-order pole in the $T$ matrix, the position of which is a function of both the density of the system and the total c.m. momentum of the pair, and corresponds to the formation of bound pairs in the medium. The singularity structure exists in two distinct Fermi systems (liquid ${\mathrm{He}}^3$ and nuclear matter), and detailed numerical results are presented using a potential appropriate to liquid ${\mathrm{He}}^3$. The singularity in this case is shown to be present at all densities above a certain critical density which is lower than the physical density.

Theoretical ${\mathrm{H}}_{\beta }$ profiles by Vidal, Cooper, and Smith (VCS) and by Kepple and Griem (KG), convolved with the appropriate Doppler and instrument widths, have been compared to experimental ${\mathrm{H}}_{\beta }$ profiles obtained over the electron density range $4\times {10}^{14}\le n_e\le 2\times {10}^{15}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The data were taken in a laminar argon plasmajet seeded with up to 1% ${\mathrm{H}}_2$. Electron and atom temperatures were ∼ 8 × ${10}^3$ and ∼ 6 × ${10}^3$ K, respectively. Independent determinations of $n_e$ were based on Stark-shift measurements of the 7273-Å Ar I line using a Fabry-Perot interferometer. Experimental ${\mathrm{H}}_{\beta }$ profiles were compared to theory by fitting the logarithms of the intensity by least squares while maintaining profile area normalization to obtain "best-fit" values for $n_e$. A log fit effectively deweights the points near the line center, where the theoretical accuracy is poor, and thus, compared to a linear fit, yields $n_e$'s in better agreement with the independently determined $n_e$'s. For a given theory, no statistically significant difference was observed between values of $n_e$ obtained using log-profile fitting and half-widths over the $n_e$ rang examined—for both methods, $\frac{n_e\left({\mathrm{H}}_{\beta }\right)}{n_e}$ (7273-Å Ar I) = 0.89 ± 0.20 and 0.80 ± 0.20 for VCS and KG theories, respectively. However, $n_e$'s obtained using the two methods do not necessarily agree on a point-by-point basis. Finally, recent theoretical profiles including ion dynamic effects calculated by Cooper, Smith, and Vidal have been compared to our experimental profiles. Although improved agreement is noted in the vicinity of the line center (shallower theoretical dip-depth), the best-fit $n_e$'s are ∼ 10% lower than from VCS theory neglecting ion dynamics.

The Coulomb-gas activity expansion of Rogers and DeWitt is extended to include more terms. This is an expansion in the activities of electrons and nuclei, and it converges slowly in regions where composite-particles are present. It is shown that by treating certain products of terms as composite-particle activities, the convergence of the expansion is greatly increased. The important element of the present work is the recognition that terms in the original expansion correspond to the Taylor-series expansions of a similar expansion involving an augmented set of activity variables, i.e., the composite particles enter the expansion similar to fundamental particles (electrons and nuclei). This reorganization of the activity expansion makes it possible to calculate the equation of state for electron-nucleus gases of any charge. All stages of ionization and dissociation are treated to the same order of approximation in the new expansion. To illustrate these features some calculations for helium are given. To demonstrate the improved convergence properties, some calculations for hydrogen are compared with those obtained by Rogers and DeWitt.

We have studied the self-focusing of ruby laser light in the isotropic phase of the nematic liquid crystals $p$-azoxyanisole (PAA), $p$ - ($p$-ethoxybenzylidene) amino-benzonitrile (EBAB), and $p$-methoxybenzylidene $p-n$-butylaniline (MBBA) as a function of temperature. The observed threshold power for self-focusing follows a $T-T^{*}$ relationship with the critical exponent unity for PAA and EBAB, in agreement with de Gennes's theory. We could also explain our results for MBBA, observed with three laser pulse widths, taking into account the transient response of the order parameter. Calculated values of the nonlinear index from the observed thresholds for self-focusing are found to be large for the three materials compared to that for C${\mathrm{S}}_2$.

It is argued that van Kampen's objections to linear-response theory do not apply to transport processes driven by quasi-forces (gradients in thermodynamic quantities like density, temperature, or average local velocity), but are applicable to calculations of response to real forces (externally imposed, like electric fields). A nonperturbative derivation of generalized Green-Kubo formulas is displayed. They clearly show a qualitative difference in behavior for small forces between the real and quasi-cases. A computer experiment on a simple classical model for diffusion and electric conductivity by independent electrons in a two-dimensional solid is described. The results are consistent with the predictions of linear-response theory in this case, with certain qualifications. The role of dissipation is crucial. Without it there can be no steady conduction. With a small amount of dissipation and small electric fields, the conductivity is related to the diffusivity in accord with linear-response theory, and the diffusion coefficient smoothly approaches a limit when the dissipation is reduced to zero. The key to the reconciliation of these results with van Kampen's objections is that the electric field exactly factors out of the expression for the response current, independent of any assumption of smallness or analyticity. It is shown that this is the case in both classical and quantum theory. It is noted in an appendix that the conductivity in the wind-tree model is pathological, violating linear-response theory.

A theoretical discussion of the temperature and magnetic-field dependence of the contribution to the thermal boundary conductance (Kapitza conductance) from the interaction between liquid-${\mathrm{He}}^3$ nuclear spins and electron spins in a magnetic solid is presented for the case where $T$ lies below the ordering temperature $T_0$ of the solid. Our calculations apply to the temperature range $3\le T\le 100$ mK, where the ${\mathrm{He}}^3$ may be regarded as a normal Fermi fluid. We consider three cases: (i) a dilute alloy with magnetic impurities which experience random internal fields, (ii) an array of ferromagnetically aligned spins arranged on a crystal lattice, and (iii) a ferromagnetically aligned, but spatially disordered, array of spins. We also examine the presently available data on the magnetic contribution to $R_K$ in the light of the theoretical results.

The spatial decay of temperature nonuniformities in the weakly interacting Bose gas is studied bv utilizing Ma's low-temperature solutions of the Boltzmann equation. These results, which give exponential decay lengths varying as $T^{-9\mathrm{}}$, may be relevant to He II for $T\lesssim 0.1$ K. The longest two decay lengths, ${\delta }_1$ and ${\delta }_2$, are found to be in nearly a ten-to-one ratio, with ${\delta }_1\approx 3.41\times {10}^3$ cm for He II at 0.1 K. At higher temperatures the decay lengths are expected to decrease less rapidly than $T^{-9\mathrm{}}$ because of phase-space considerations, but an extrapolation to 0.3 K does indicate ${\delta }_1$ to be on the order of 1 cm. Two types of experiments are suggested for determining these lengths. It is pointed out that information about phonon dispersion can be obtained from such measurements.

We study the Zawadowski-Ruvalds-Solana (ZRS) model of quasiparticle interactions in liquid helium both quantitatively and theoretically. We find that the model cannot account quantitatively for the multiphonon peak in the neutron-scattering spectrum even if we vary the quasiparticle spectrum phenomenologically. We find that the model can account for the experimental light-scattering spectrum if the effective roton-roton coupling $g_4(\overrightarrow{\mathrm{k}},{\overrightarrow{\mathrm{k}}}^{\prime })$ is sharply peaked at the roton minimum ($k\cong k^{\prime }\cong k_0$). We suggest that the neutron-scattering results would be improved without changing the light-scattering prediction if the density operator contained nonlinear terms in the quasiparticle operator. We criticize the implicit assumption in the ZRS model that the zero-order ground state is nondegenerate. The relationship of this model to one devised by Jackson is discussed.

Two types of nonlinear transmission of light pulses associated with phase modulation are observed in experiments connected with self-induced transparency (SIT) in ruby. Anomalous pulse-power transmission is observed to be an order of magnitude greater than linear transmission during the condition of zero-area pulse propagation, where the inhomogeneous line spectral width is greater than the applied pulse spectral width. For application of a pulse off-resonance by the order of a linewidth, nonlinear transmission occurs in which a type of "precursor" phase-modulated signal appears ahead of a developing SIT pulse. The precursor pulse velocity is greater than the SIT pulse velocity, but less than the background velocity of light in the medium.