The fully quantum-mechanical model of a single-mode laser is examined. A previously introduced method of solution where both the pump and loss reservoirs are treated simultaneously as a weak perturbation of the atom-light system is employed. This method is similar to perturbation theory for degenerate systems in that the reservoirs remove the nonuniqueness (degeneracy) of the steady state of the unperturbed atom-light system. In the limit of weak reservoir coupling, the exact steady-state solution of the master equation is derived. This solution still contains the atomic variables explicitly and therefore remains valid even in situations where the conventional adiabatic elimination of the atomic variables is no longer possible. A compact discrete representation of the master equation in terms of atomic occupation numbers and photon numbers is developed which allows one to perform all calculations in an elementary manner, requiring only appropriate summations over photon and occupation numbers. General exact relations are obtained for the steady-state probability distribution function $p(n,m)\mathrm{}$ to find $n$ photons in the light field and $m$ atoms in the excited state. Our solution constitutes the first steady-state laser distribution function that is valid for an arbitrary number of laser atoms and in the complete region from far below to far above threshold. It provides a quantitative criterion for the range of validity of approximate methods in laser theory.

The dynamical structure factor $S(q,\omega )$ for liquid rubidium obtained from recent neutron inelastic scattering experiments as well as from molecular dynamics calculations has been analyzed on the basis of Mori's memory-function approach. It has been found that the double Gaussian memory function with two distinct relaxation times gives an excellent representation of the experimental data on $S(q,\omega )$ in the range of momentum transfer 0.174-2.750 ${\mathrm{\AA }\mathrm{A}}^{-1\mathrm{}}$. For $q\ge 2.750$ ${\mathrm{\AA }}^{-1\mathrm{}}$, both one- and two-relaxation-time Gaussian models reproduce the experimental data very well.

A nonvariational equation, called the density equation, is proposed for the direct determination of the density matrix without using a wave function. It is connected with the Schrödinger equation by a necessary and sufficient theorem. The equation for the lowest order depends explicitly only on the fourth-order density matrix ${\Gamma }^{\mathrm{}\left(4\right)\mathrm{}}$ (or ${\Gamma }^{\mathrm{}\left(3\right)\mathrm{}}$ in a special case) and not on the higher-order density matrices. The equation always gives the density matrix and the associated energy which coincide with those obtained indirectly from the Schrödinger equation. This is true even if we solve the equation only with the known and tractable $N$-representability conditions, although in such a case some unphysical solution may also occur in the non-$N$-representable space. The equation is applicable to both fermion and boson systems, and to both ground and excited states. In contrast to the Schrödinger equation, the labor of solving the equation does not increase when the number of particles of the system is increased. When we have the Hartree-Fock solution, the equation is transformed such that the correlated density matrix and the correlation energy are the direct solution. The correlated density equation thus obtained is suitable for the study of electron correlations.

A theory is developed for spin-lattice relaxation in the nematic phase which includes both local and collective motion. It is found that the frequency dependence of the relaxation rate $T_1^{-1\mathrm{}}$ depends on the correlation time for the motion at the local molecular level, ${\tau }_c$. When $\omega {\tau }_c\ll 1$, where $\omega$ is the Larmor frequency, the theory gives the ${\omega }^{\frac{1}{2}}$ law characteristic of $p-\mathrm{azoxyanisole}$ (PAA). When $\omega {\tau }_c\lesssim 1$, the theory gives the more complex frequency dependence observed in the more viscous compound $4-n-\mathrm{methoxybenzylidene}-4^{\prime }n-\mathrm{butylanaline}$ (MBBA). A correlation is drawn between ${\tau }_c$ and the retarded relaxation time observed in electric dipole studies which corresponds to reorientation of the long molecular axis. The dependence of $T_1^{-1\mathrm{}}$ on the orientation of the director in the magnetic field is included in the calculation. A model is presented to include intermolecular effects on $T_1$.

Infinite-order perturbation theories of Vlasov turbulence are developed to obtain a renormalized formulation of the mode coupling and quasilinear equations for current-driven ion-acoustic turbulence. The renormalized theory eliminates divergence problems from nonlinear electron interactions and predicts an ion acceleration mechanism producing substantial ion tails at $t{\omega }_{\mathrm{pi}}\sim 50$ from initially cold-ion distributions. Time-dependent numerical solutions of the turbulence equations are presented, and comparisons are drawn from experiments and computer simulation.

Percus-Yevick and hypernetted-chain models connecting the structure factor $S\left(k\right)\mathrm{}$ with effective pair potential $\phi \mathrm{}\left(r\right)\mathrm{}$ have been studied in detail. Recent neutron-scattering data of Yarnell et al., for liquid argon at 85°K, have been employed to generate these potentials. Using 0.01 uncertainty in the experimental data, the uncertainty in the pair potentials has been computed. Having developed a general method of error propagation analysis, the effect of experimental errors in $S\left(k\right)\mathrm{}$ on Percus-Yevick and hypernetted-chain potentials is investigated and the resulting potentials are compared with Lennard-Jones and Barker, Fisher, and Watts potentials.

Measurements of the electron drift velocity in liquid argon, krypton, and xenon were performed in an electric field up to 100 kV ${\mathrm{cm}}^{-1\mathrm{}}$. At higher field strengths saturation velocities were observed in agreement with other authors. The addition of a small concentration of molecular solutes leads to an increase of the electron drift velocity above the saturation value of the pure liquid. The drift velocity either reaches a higher constant value or passes through a maximum at field strengths greater than ${10}^4$ V ${\mathrm{cm}}^{-1\mathrm{}}$. This effect was investigated as a function of solute concentration for ${\mathrm{N}}_2$, ${\mathrm{H}}_2$, methane, ethane, propane, and butane. Inelastic energy losses in collisions of electrons and solute molecules are assumed and by means of the Cohen-Lekner theory the energy dependence of the loss processes is derived.

As a first step toward constructing a general molecular model for cholesteric liquid crystals, we propose here a planar model in which the intermolecular potential is required to contain chiral contributions as a result of symmetry considerations. By means of a mean-field analysis, we identify the microscopic basis for the existence of the cholesteric phase. The latter is shown to be a consequence of chirality. The temperature dependence of the cholesteric pitch is discussed, and several numerical examples are given. Our theoretical deductions are consistent with experimental observations. We indicate, however, that under exceptional circumstances two unobserved phenomena may be found to exist. First, particular systems made up of chiral molecules may exist in the nematic phase. Next, as temperature is varied, a particular pure cholesteric substance may undergo untwisting and reverse its helicity after passing through a divergence in pitch.

Three-wave interaction is analyzed in a coherent-wave description with assumption of different linear damping (or growth) of the individual waves. It is demonstrated that when two of the coefficients of dissipation are equal, the set of equations can be reduced to a single equivalent equation, which in the nonlinearly unstable case where one wave is undamped, asymptotically takes the form of an equation defining the third Painlevé transcendent. It is then possible to find an asymptotic expansion near the time of explosion. This solution is of principal interest since it indicates that the solution of the general three-wave system, where the waves experience mutually different dissipations, belongs to a higher class of functions, which reduces to Jacobian elliptic functions only in the case where all waves experience the same damping.

The parametric decay of a transverse electromagnetic (em) wave with a frequency close to, but larger than, the electron plasma frequency is investigated for an infinite, homogeneous, weakly magnetoactive plasma. A two-component fluid description is employed, and the damping of the linear plasma waves is introduced phenomenologically to include both Landau and collisional damping. The transverse em wave will decay into a longitudinal electron plasma wave and an em ion-acoustic wave. Only the latter wave is assumed to be affected by the weak, constant magnetic field. The threshold expression for growth of electron plasma waves is equal to that of the isotropic plasma when the em ion-acoustic wave's direction of propagation lies inside a wide double cone whose axis is along the constant magnetic field. When the em ion-acoustic wave propagates outside this double cone, an additional factor, which depends directly upon the magnetic field, appears in the threshold expression. This factor can, under certain conditions, reduce the threshold for growth of electron plasma waves below that of the isotropic plasma.

New accurate diamagnetic measurements of the order parameter, just below the nematic-isotropic transition temperature $T_c$, are given for two nematic liquid crystals. The variations with temperature of the order parameter are described well by theory based on the Landau expansion of the free energy. The subsequent determinations of $T_c-T^{*}$ and the latent heat are in good agreement with values obtained by an independent way.

We consider the simultaneous interaction of a transparent finite plasma slab with two laser beams coming from opposite directions. We show that induced Compton scattering may produce induced reflections of the beams on each other. As a consequence, the energy flux through the slab has an upper limit, however large the intensity of the beams.

A modified Thomas-Fermi equation of state has been developed for description of materials at temperatures and pressures of interest in laser-fusion research. For high-density plasmas with $1<\mathrm{}\Gamma <100\mathrm{}$, nuclear motions give rise to ion-pair correlations intermediate between those of gas and solid. This pair correlation is approximately described by allowing the Thomas-Fermi ion-sphere volume to vary according to the isobaric distribution law. The resulting equation of state automatically includes corrections for nuclear motion. Numerical results are presented for 10 and 100 times solid density.

A stochastic theory of line shape is considered for describing molecular reorientational processes in liquids. The theory takes into account both secular and nonsecular terms in the interaction Hamiltonian. A general solution for the line shape is given in a matrix form by assuming a Markovian modulation for the random process. The usefulness of the theory is demonstrated by doing perturbation theory calculations in the motionally narrowed limit. A resolvent-operator technique is employed for collecting higher-order terms in perturbation theory. Two models for molecular motion, (i) rotational diffusion and (ii) strong-collision approximation, are treated and their predictions compared. In the case of the rotational-diffusion model, the results are illustrated by considering a $g$-tensor interaction in liquids. Expressions for line width and shift are given up to fourth order in perturbation theory, and a detailed comparison is made with the existing theories.

We give a physical explanation for the existence of multiple phase transitions in certain Ising-like models. They are due to the presence of competing interactions propagating along paths of different lengths. The idea is illustrated by constructing Ising models with an arbitrary number of phase transitions. The physical insight thus gained is used to develop a mean-field approximation which reproduces correctly the phase diagram of the two-dimensional fcc Ising problem. The mean-field approach can be generalized to three dimensions.

The eikonal approximation has been used to calculate differential and total cross sections for $1s\to 2s$ excitation of atomic hydrogen by 50-, 100-, and 200-eV incident positrons. As in the case of elastic scattering, the positron scattering cross sections are found to differ from the corresponding electron scattering cross sections. Comparison is made with the eikonal Monte Carlo results of Byron.

It is shown that in the superfluorescent decay of $N\gg 1$ atoms, off-diagonal atom-field correlations are very simply related to diagonal ones. This link allows one to eliminate immediately off-diagonal atom-field correlations from the hierarchy which describes the time evolution of the atomic system and of the photon statistics in oscillatory superfluorescence.

Simultaneous vibration ($v$) and rotation ($j$) excitation of ${\mathrm{N}}_2$ by electron impact is calculated in the hybrid theory from the relevant formulas (involving $a$-matrix elements previously calculated). All cross sections (labeled $v,j\to v^{\prime },j^{\prime }$) involving states with $v=0,1$; $0\le j\le 1$; $0\le v^{\prime }\le 2$; $0\le j^{\prime }\le 5$ have been evaluated. A representative sample of graphical results is presented. In particular, we find large discrepancies in magnitude from the partially phenomenological theory of J. C. Y. Chen.

The negative signs of the fine-structure constant and dipolar and contact hyperfine constants for the $4{}_{}{}^2{}_{}{}^{}D$ state of the rubidium atom are all explained by the common mechanism of exchange polarization of core states by the valence $4d$ state. The results of the present one-electron theory for the fine-structure, dipolar, and contact hyperfine structure constants are -3.7 (6.1 - 9.7) ${\mathrm{cm}}^{-1\mathrm{}}$, -0.37 (0.29 - 0.65) × ${10}^{24}$ ${\mathrm{cm}}^{-3\mathrm{}}$, and -2.1 (0.0 - 2.1) × ${10}^{24}$ ${\mathrm{cm}}^{-3\mathrm{}}$, respectively, where the values given in parentheses are, first, the (restricted) Hartree-Fock and, second, the exchange core-polarization contributions. By including the exchange core-polarization contribution, the resulting estimates are in reasonable accord with the corresponding observed values of these coupling constants: -0.176 ${\mathrm{cm}}^{-1\mathrm{}}$, -0.318 × ${10}^{24}$ ${\mathrm{cm}}^{-3\mathrm{}}$, and -4.22 × ${10}^{24}$ ${\mathrm{cm}}^{-3\mathrm{}}$, respectively. The possible importance of many-body and relativistic effects is discussed.

The method of polarized pseudostates has been used to obtain the $R$ matrix for low-energy electron scattering by atomic oxygen. This $R$ matrix has been subsequently used to obtain the angular distribution of the scattered electrons. Reasonable agreement is obtained with recent experimental results of Dehmel, Fineman, and Miller at 5 and 15 eV, although the small-angle dip reported in the experiment is not explained by the calculation.