Magnetic-field-induced resonant third-harmonic generation in ${\mathrm{I}}_2$ with circularly polarized light is studied. With a magnetic field perpendicular to the propagating direction of the light, the axial symmetry is broken and the angular momentum is no longer conserved in such a system, and the third harmonic may be generated under such conditions. Quantum beats in photon-echo-like third-harmonic generation with nonsynchronous laser pulses are also studied. The intensity of the harmonic generated may be interpreted in terms of the interference between a molecule and itself as well as the interference between different molecules. The gyromagnetic ratio of the resonant states is measured.

The question is raised whether nonlinear coherence can be created in coupled systems whose subsystems interact with distinct radiation fields. The simplest coupled system consisting of two two-level subsystems is treated in interaction with two electromagnetic fields, each close to resonance of one of the subsystems. The problem is treated within the SU(4) symmetries. The generators of SU(4) are defined and their properties under transformations deduced. The Hamiltonian and the density operator of the coupled system are expressed in terms of the generators of SU(4) and the Liouville equation is then used to find the time evolution of the density operator. When the frequencies of the radiation fields are equal to the resonant frequencies of the uncoupled subsystems, one obtains two two-photon nutation processes, provided that the interactions of the subsystems with the radiation fields are weaker than the mutual interaction of the two subsystems. The nutation frequency is proportional to the product of the field strengths and inversely proportional to the coupling parameter which in this case represents the resonance offset of the intermediate levels. Alternatively, the frequencies of the radiation fields can be arranged so that only one two-photon transition is on resonance. The amplitude of the nutation then depends on the strengths of the radiation fields, and acquires maximum value for ${\omega }_1={\omega }_2$. The nutation frequency increases when one approaches the resonance with the intermediate level. With a two-photon $\pi$ pulse one transfers the population difference from the levels of one subsystem to those of the other. This procedure can be used to polarize rare spins in the case of strong spin-spin coupling with the abundant spins when the method of thermodynamic contact is inapplicable. Both magnetic and optical coupled systems can be described with the same equations.

A microscopic correlation-function theory for coherent, parametric, four-photon processes (four-wave mixing) and for single-absorber two-photon processes (two-photon absorption, Raman, and fluorescence spectra) is developed. Both types of experimental observables are expressed in terms of four-point correlation functions of the dipole operator. The latter are then evaluated semiclassically or within the factorization approximation in which they are expressed in terms of ordinary single-photon line-shape functions. The common results of the Bloch equations are shown to be the outcome of two successive approximations: the factorization approximation and the impact limit whereby the single-photon line-shape functions are taken to be Lorentzian. Effects of fluctuations in the radiation fields are easily incorporated within the present approach.

A new method is proposed which involves a canonical transformation leading to the nonsecular part of time-independent perturbation calculus. The method is used to derive expressions for effective Shen-Walls Hamiltonians which, taken in the two-level approximation and on the inclusion of non-Hamiltonian terms into the dynamics of the system, lead to generalized Maxwell-Bloch equations. The rotating-wave approximation is written anew within the framework of our formalism.

The coexistence curve for Xe measured in the range $3.4\times {10}^{-6\mathrm{}}\le -t\le 3.2\times {10}^{-2\mathrm{}}$ [where $t\equiv \frac{(T-T_c)}{T_c}$] by focal-plane interference methods has been analyzed in terms of the correction-to-scaling prediction $\frac{({\rho }_l-{\rho }_v)}{{2\rho }_c}=A_1^M{\mathrm{}\left|t\right|\mathrm{}}^{\beta }(1+A_2^M{\mathrm{}\left|t\right|\mathrm{}}^{\Delta }+A_3^M{\mathrm{}\left|t\right|\mathrm{}}^{2\Delta }+A_4^M{\mathrm{}\left|t\right|\mathrm{}}^{3\Delta })$ to yield the correction-to-scaling amplitudes. By combining the value of $A_2^M$ with the corresponding amplitude $A_2^{{\chi }^{-}}$ obtained from recent compressibility measurements on Xe, we arrive at the ratio $\frac{A_2^M}{A_2^{{\chi }^{-}}}\simeq 1.5$, which is somewhat above the universal ratio 0.85 predicted by renormalized perturbation theory.

A general lattice-model partition function for condensed phases with partial or total positional ordering (in one to three dimensions) as well as orientational ordering of the molecules in the system is presented. Each molecule is composed of a rigid core and one or two semiflexible tails and has site-site hard repulsive intermolecular interactions. This general model can be applied to a number of special cases, one of which is presented in the following paper.

The general partition function of the preceding paper is applied to the special cases of smectic-$A$ and nematic liquid crystals and isotropic liquids in bulk phases. The relative stabilities of the isotropic, nematic, smectic-$A$, and reentrant-nematic phases are studied as a fucntion of temperature, pressure, tail flexibility, and tail length. The following thermodynamic and molecular ordering properties are studied in these phases and at the phase transitions: smectic-$A$ order parameter, core and tail intermolecular orientational order parameters, tail intramolecular orientational order parameter, density, and entropy. The role of the semiflexible tails in stabilizing the smectic-$A$ and reentrant-nematic phases is explicitly elucidated.

Deviations from the ideal geometry and less-than-perfect alignment of the field coils in an ELMO bumpy torus generate perturbations to the ideal magnetic field configuration, resulting generally in failure of the field lines to close on themselves and thereby causing degradation in plasma confinement. The sensitivity of the field-line displacement to certain types of errors in coil parameters is studied by means of a perturbation formalism developed for an action integral representing the longitudinal adiabatic invariant. Reflection-symmetry properties satisfied by the magnetic field and the vector potential are employed, and it is demonstrated both analytically and numerically that the leading term of the field-line displacement per period of $2\pi$ around the major axis is second order in the perturbation parameter if the field coils are planar loops and the coil planes remain invariant under the perturbation. Numerical analyses for the field-line displacement also reveal some more useful properties for the first- and second-order terms in the perturbation series.

The Fermi-Pasta-Ulam model has been studied following the time evolution of the space Fourier spectrum through the numerical integration of the equations of motion for a system of 128 non-linearly coupled oscillators. One-mode and multimode excitations have been considered as initial conditions; in the former case, an approximate analytic technique has been applied to describe the "short-time" behavior of the system, which fits well the experiment. The main result in both cases is the presence of different stationary states towards which the system is evolving: a $\frac{1}{k^2}$ spectrum (corresponding to the equipartition of energy) or an exponential spectrum can be reached, depending on the value of some parameter, which takes into account the relative weight of the nonlinear to the linear term of the equations of motion.

The cholesteric blue phases (BP I and BP II) can be modeled as cubic lattices of disclinations in a cholesteric matrix. In an earlier paper we presented results of free-energy calculations for three models with $O^2\left(P{4}_{2}32\right),O^5\mathrm{}\left(I432\mathrm{}\right)\mathrm{}$, and $O^8\left(I{4}_{1}32\right)$ space-group symmetry. In the present paper calculations for a fourth model, also of $O^8$ symmetry, are presented (we differentiate these models as $O^{8(+)\mathrm{}}$ and $O^{8(-)\mathrm{}}$, respectively). For a number of cholesterol derivatives we assign the $O^{8(-)\mathrm{}}$ structure to the BP I, and the $O^2$ structure to BP II, on the following evidence: For the case of equal elastic constants the calculations show a crossover of the free energy, the $O^2$ structure being lowest at the higher temperatures, and $O^{8(-)\mathrm{}}$ at lower temperatures. (However, the crossover may disappear for other values of the elastic constants.) The assignment is consistent with the observed BP I and BP II lattice constants in terms of cholesteric pitch. There is excellent agreement between calculated and observed intensities of the Bragg reflections. Some details of the observed Bragg-diffraction spectra are also discussed.

We obtain the energy of an interacting electron gas in the deformable jellium model using screened potentials and periodic solutions to the Hartree-Fock equations. We compare our results with the plane-wave energies at different values of the screening parameter and with those in the literature when the screening is turned off. In the Coulombic case and low-density regime ($r_s\simeq 100$) the periodic solutions become more stable than the plane-wave state. But quantitatively our results differ substantially from those previously reported.

Convection-diffusion equations and equations for concentration profiles are derived using a simple network-theory technique which shows the bifurcation of the solutions when $J_v=0\mathrm{}$.

Secondary-electron thermalization ranges $b_{\mathrm{GP}}$ and free-ion yields $G_{\mathrm{fi}}^E$ have been measured in the coexistence vapor and liquid of spherelike (methane) and nonspherelike (ethane) molecules at densities $0.14\lesssim \frac{d}{d_c}\lesssim 2.8$, where $d_c$ is the density of the critical fluid. The density-normalized range $b_{\mathrm{GP}}d$ at low $d$ is 5.5×${10}^{-6\mathrm{}}$ kg/${\mathrm{m}}^2$ in both compounds. In the dense gas at $\frac{d}{d_c}\gtrsim 0.3$, $b_{\mathrm{GP}}d$ increases slightly; the effective cross section for epithermal electron scattering is lessened. The large density fluctuations at these conditions, which cause quasilocalization of thermal electrons, appear to affect epithermal electrons in an opposite fashion. At $\frac{d}{d_c}>1.0\mathrm{}$, conduction-band formation lifts $b_{\mathrm{GP}}d$ in liquid methane to ∼4 times the value in liquid ethane. The density effect is in the same direction as, but less marked than, that for thermal electrons. At $\frac{d}{d_c}=2.5\mathrm{}$, $b_{\mathrm{GP}}$ in methane is 1.2 times larger than at $\frac{d}{d_c}=1\mathrm{}$, but the mobility $\mu$ of thermal electrons is 15 times larger than at $\frac{d}{d_c}=1\mathrm{}$. In ethane at $\frac{d}{d_c}=2.5\mathrm{}$, $b_{\mathrm{GP}}$ is 3.4 times and $\mu$ is 33 times smaller than at $\frac{d}{d_c}=1\mathrm{}$. The degree of sphericity of the molecules greatly affects electron energy loss and localization interactions.

We study the properties of Suzuki's systematic approximations to the exponential operator $\exp (-\beta H)$ by calculating the thermodynamic functions of three simple quantum models. We demonstrate that the path-integral representation of the partition function obtained from these approximations can be simplified and made more accurate by constructing Hermitian versions of Suzuki's expressions.

Structural properties of macromolecular solutions have been investigated with a wide variety of techniques, among which light scattering is one of the most powerful. In the present paper we report the results of both elastic and quasielastic light scattering in a DNA solution at small angles. It is shown that in solution the macromolecules arrange themselves in an ordered structure that extends over semimacroscopic distances. The comparison between the static and dynamic response allows a better understanding of the physical meaning to be attributed to the structure, in terms of a $\overrightarrow{\mathrm{k}}$-dependent characteristic time for the regression of fluctuations.

We introduce a generalized model of polymerization on a lattice in which the activities of single-site monomers [single-site walks (SSW's)], of the two end points of a self-avoiding linear polymer chain [self-avoiding random walk (SAW's)] and of a bond are given by independent variables ${\zeta }^2$, ${\eta }^2$, and $\kappa$, respectively. This model covers various physical models of polymers as special limits. The model is then mapped onto the $n\to 0$ limit of an $n$-component spin system on a lattice by introducing an auxiliary variable not characterizing the spin system. The mapping enables us to make a distinction between single-site monomers (SSW's) and monomers belonging to SAW's of nonzero lengths, and to treat them independently. We also show that the critical behavior of our model does not depend upon the density of SSW's and is described by the $n\to 0$ limit of the spin system, as expected.

The interaction of an electron with two electromagnetic waves propagating in an isotropic plasma is studied with the use of a super-Hamiltonian formalism. Large-scale stochasticity thresholds are analytically estimated. The results may be relevant to laser-plasma interaction.

In this paper several methods are compared which connect the effective pair potential to the pair-correlation function. These methods are a self-consistent method using molecular dynamics, the so-called modified STLS (Singwi-Tosi-Land-Sjölander) theory, the Weeks-Chandler-Andersen approach, the Percus-Yevick theory, the hypernetted-chain approximation, and the Born-Green equation. Since the pair potential is, in general, very sensitive to small variations in the paircorrelation functions, structure data were used with sufficient accuracy in the determination of the pair potentials from the pair-correlation function. Narten performed measurements on liquid gallium with high precision, and, therefore, all calculations given in this paper have been performed on the basis of Narten's structure data. It turned out that the self-consistent method and the Weeks-Chandler-Andersen approach led to reasonable results. The results for the pair potential obtained from the other methods are unsatisfactory and cannot be used in the determination of liquidgallium properties.

We describe a method for the solution of initial-value problems for random processes arising through adiabatic approximations from Markov processes of higher dimension. In applications to overdamped Brownian motion and to the single-mode laser we calculate correlation functions and discuss initial slips.

Experiments using monochromated synchrotron radiation revealed that for densities of the order of ${10}^{19}$ atoms/${\mathrm{cm}}^3$ and more, xenon exhibits a continuous photoresponse excitation spectrum below the atomic ionization potential (12.12 eV). The lower limit of the continuum is at about 11.10 eV, the energy difference between the ground state of the molecular ion $\mathrm{Xe}_2^{}{}_{}{}^{+}$ and that of the free atom. This is attributed to excimer formation at the wings of the atomic absorption lines followed by ionization and creation of xenon dimer ions. Dips appearing in the continuum very near to positions of atomic lines are discussed invoking the quasistatic theory.