In this paper the equations of motion for open systems, derived recently by one of the present authors, are applied to the case of spontaneous emission from a system of $N$ identical two-level atoms. Three different observation levels of the atomic system are considered. First, exact closed integrodifferential equations for the expectation values of each observation level are obtained. Second, making the standard approximations—Born, Markov, and long-time approximations, we find that these equations reduce to closed differential equations for the expectation values. The quality of the Born approximation for different observation levels is also discussed. Moreover, in the obtained equations no kind of rotating-wave approximation was made.

In this work a promising new electron cyclotron maser oscillator is proposed and analyzed. The configuration utilizes an open resonator cavity containing a gyrating electron beam which translates along an external magnetic field. The magnetic field is directed perpendicular to the axis of symmetry of the open resonator. Because the wave-particle interaction volume is extremely large, the total input electron beam power can be high and the power density low. This configuration has a number of potentially very attractive features. Among them are (i) high operating radiaion power levels (>MWs); (ii) high efficiency operation (>45%); (iii) naturally suited to short wavelength operation ($\lambda <2\mathrm{}$ mm); (iv) operates efficiently at low electron beam voltage (10-100 keV); (v) natural transverse mode selectivity; (vi) moderate insensitivity to beam temperature effects. The nonlinear interaction between the electrons and resonator field have been analyzed and an expression for the steady-state efficiency obtained. The expression for efficiency has a rather simple analytic form when the amplitude of the resonator fields are small, i.e., small-signal regime. In this case, the efficiency is an essentially odd, nonoscillating function of the frequency mismatch (difference between resonator frequency and relativistic cyclotron frequency). For a uniform external magnetic field, total efficiencies in excess of 30% can be realized. We have considered enhancing the efficiencies by spatially contouring the magnetic field. Appropriately contouring the magnetic field across the resonator by ∼5% increases the efficiency from ∼35 to ∼45%.

Processes leading to second-harmonic generation when a single polarized beam is focused into neutral or partially ionized atomic vapor are considered, including electric-field-induced third-order mixing, and quadrupole and magnetic dipole processes. Estimates of the relative strengths of these processes are given. In addition, the polarization properties given by the tensor susceptibilities are discussed in detail.

Triple-quantum NMR on spins with $S=\frac{3}{2}$ in solids can be of much help by the determination of the chemical shielding parameters. Excitation and detection of the triple-quantum coherences of $S$ spins with small quadrupolar frequencies (${\omega }_Q\lesssim 300$ ${\sec }^{-1\mathrm{}}$), was accomplished by weak rf pulses. On spins with large quadrupolar frequencies modulated rf-pulse techniques have been explored in order to obtain their narrow-line triple-quantum spectra. In this publication cross-polarization-enhancement techniques on the single-, double-, and triple-quantum transitions of $S=\frac{3}{2}$ spins, in systems with abundant $I=\frac{1}{2}$ spins and rare $S=\frac{3}{2}$ spins, are developed. The theory of these experiments is an extension of the theory of double-quantum cross polarization. The $S=\frac{3}{2}$ spin Hamiltonian can always be divided in three commuting parts, of which two are fictitious spin-1/2 Hamiltonians. Cross polarization can occur between one of these transitions and the $I$ spins in the system. Hartmann-Hahn conditions for these processes are derived. Nonmodulated and partially modulated rf irradiation fields are used for the enhancement of single- and triple-quantum coherences. Efficiency factors of the different cross-polarization experiments are calculated. ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$-${}_{}{}^1{}_{}{}^{}\mathrm{H}$ spin-lock cross-polarization measurements are performed on an oriented single crystal of sodium ammonium tartarate tetrahydrate in order to verify the different Hartmann-Hahn conditions. A full modulation cross-polarization experiment is designed to obtain large enhancements of the signal intensities of center-frequency lines of $S=\frac{3}{2}$ spectra from single crystals.

It is shown how the analytic properties of classical equilibrium time-autocorrelation functions (TACF's) and the corresponding memory functions (MF's), associated with the generalized Langevin equation in the Schmidt-orthogonalized representation, are intimately connected. In particular, the Maclaurin expansions of the TACF and Schmidt MF's and the continued-fraction representations of the corresponding Laplace transforms exist and converge in well-defined domains and under conditions consistent with the existence of finite positive transport coefficients.

The general kinetic equation for the density-density correlation function $S(\overrightarrow{\mathrm{k}},\omega )$, derived from projection-operator methods, provides a convenient framework for the modeling of collision processes in plasmas. We present results of the calculation of $S(\overrightarrow{\mathrm{k}},\omega )$ for the dense one-component plasma utilizing four-collision models. In each case exact static-correlation data available from particle simulations are used as input to the calculation. Numerical results are presented and compared with "exact" results from computer experiments.

It is shown that the flat interface separating two coexisting phases of a binary liquid is unstable under nonequilibrium conditions corresponding to quenching the system deeper into the two-phase region. For given quench depth the instability persists out to a finite wave number $k_0$; for larger wave numbers surface tension renders the interface stable. As a by-product of the calculation, the effect of diffusive relaxation on the ordinary capillarywave dispersion relation and power spectrum is evaluated. Results indicate that previous experiments were conducted in a regime in which diffusive effects do not affect the extraction of the surface tension from the power spectrum.

The time evolution of a system of particles which initially occupy points on a lattice and subsequently undergo pairwise annihilation, is investigated with the help of the Master equation. An exact analysis is given for a onedimensional lattice of finite as well as infinite extent. Hierarchy equations are derived with the help of a generating function technique, and are solved to give expressions for the number of particles, pairs, and $n$-tuples for arbitrary time. Computer calculations for the number of singletons left behind are given for lattices of various sizes and shown to be in complete agreement with the analytical results. The motivation of this study comes primarily from pycnonuclear reactions in the interiors of dense stars and secondarily from recombination of free radicals on surfaces and annihilation of Frenkel excitons in molecular crystals.

High-resolution x-ray measurements (error ∼200-400 ppm) of smectic layer spacing $d$ of six homologs (TB3A-TB8A) of terephthal-bis-($4n$)-butylaniline (TBBA) have been made as a function of temperature. In the smectic-$C$ phase, the exponent of the tilt angle for TB3A and TBBA has a value close to $\frac{1}{3}$, implying critical behavior. For higher homologs the smectic-$A$ to -$C$ transition becomes weakly first order. Two new effects, asymmetry of the Bragg reflections in the smectic-$C$ phase due to layer undulations in the bulk sample, and existence of domains with different values of $d$ in smectic-$H$ and lower-temperature phases, were observed. The jump in $d$ at the smectic-$C$ to -$\frac{F}{H}$ transition and its variation in the $H$ phase with temperature are strongly dependent on the size of the molecule. In the smectic-$H$ phase the molecular tilt (also measured by conoscopy) for TB8A decreases with decreasing temperature in contrast to other homologs. However, the (110) spacing (measured with error less than 50 ppm) of the smectic-$H$ phase increases with temperature for both TB5A and TB8A. The smectic-$F$ phase of TB8A was, for the first time, detected by miscibility with TB7A.

High-resolution ac calorimetry measurements on the nematic-smectic-$A$ transition in liquid-crystal compounds, whose values of $\frac{T_{\mathrm{NA}}}{T_{\mathrm{NI}}}$ range from 0.94 to 0.99, indicate a crossover point at a value of $\frac{T_{\mathrm{NA}}}{T_{\mathrm{NI}}}$ equal to 0.96 between critical behavior where ${\alpha }^{+}={\alpha }^{-}$ is less than or equal to zero to behavior characterized by ${\alpha }^{+}={\alpha }^{-}=0.25\mathrm{}$.

Turbulence in binary fluid mixtures is studied. Because concentration gradients can react back on the advecting velocity field, such systems support (overdamped) transverse waves. The primary effect of this coupling in miscible high-Prandtl-number fluids is to shorten the viscous-convective cascade of concentration fluctuations. When concentration fluctuations are injected at short wavelengths, we find at time-dependent inverse cascade with spectrum $C\left(k\right)\mathrm{}\sim k^{-\frac{7}{3}}$. This cascade may be related to the dynamics of phase-separating binary mixtures at intermediate times.

We show that in the absence of magnetic shear the convective-cell modes in a magnetized plasma are strongly coupled. A three-wave decay instability can occur among two magnetostatic and one electrostatic zero-frequency modes. It is found that here cascading of energy is only in the direction of small wave numbers in the magnetostatic spectrum. Our results are compared with other cascading processes. The role of magnetic shear is also discussed.

An analysis of the intensity of the spectrum of light scattered from the director fluctuations of butoxybenzilidene octylaniline around the nematic to smectic-$A$ transition shows the critical properties of this single-layer material to be wholly analogous to the well-studied bilayer smectics, i.e., the He analogy holds only for the nematic phase while it breaks down for $T<\mathrm{}{T}_c$. The unusually large temperature dependence of the splay elastic constant $K_1$ can be partly understood on the basis of an enhancement of the nematic order parameter $S$ by the smectic ordering.

The decay of unstable equilibrium states is accompanied by large-scale fluctuations. The statistical properties of such processes can be characterized by using the time at which a representative observable first passes through a fixed threshold value. We present an asymptotic probability distribution for that passage time which is valid when the threshold is set sufficiently far from the initial state. For the simplest example of linear isotropic amplification of an $n$-component vector we calculate both the exact first-passage time distribution and our asymptotic distribution. We verify that the asymptotic distribution coincides with the exact one in the appropriate limit. We then evaluate our asymptotic distribution for a number of more complicated systems including one in which an $n$-component vector field in $d$ spatial dimensions departs from an unstable equilibrium state. The resulting expression has a considerable degree of universality. Its form is independent of $d$ and of details of the field dynamics. It is insensitive, in particular, to whether the underlying field considered is conserved or not. Our procedure is applicable to a wide variety of problems in which an order parameter departs spontaneously from an unstable initial value.

An induced bremsstrahlung process is found to originate from electrons resonating with the ion-wave turbulence. The growth rate due to this process gives the same order of magnitude as those of decay and nonlinear scattering.

A perturbation analysis of the Landau-de Gennes model for the nematic-isotropic phase transition is made. Particular attention is given to the calculation of the difference between the transition temperature $T_c$ and the temperature $T^{*}$. The temperature $T^{*}$ is the extrapolated divergence point for isotropic phase fluctuations. For space dimension greater than four, the calculation yields smaller values for this difference than does the mean-field approximation. Since smaller values are in the direction of better agreement with experiment the calculation supports the point of view that the Landau-de Gennes model is a correct phenomenological description of the nematic state.

The $S$-matrix formulation of quantum statistics, due to Dashen, Ma, and Bernstein, is extended to a multicomponent system and is then applied to a two-component nonrelativistic system of charged particles. A summation of terms corresponding to ring diagrams leads, in the high-temperature low-density limit, to the Debye-Hückel equation of state. Finally, the second virial coefficients for a system of reacting charged particles are derived, the reactions being described by multichannel scattering theory. The application of these results to deuterium plasma undergoing fusion is discussed.

We examine numerically the properties of solutions to the spherically symmetric sine-Gordon equation given an initial profile which coincides with the one-dimensional breather solution and refer to such solutions as ring waves. Expanding ring waves either exhibit a return effect or expand towards infinity. This can be explained by means of a perturbation approach. For a moderate initial radius of the shrinking ring wave we find an evolution of pulson modes. The ring waves are shown to survive the interaction between other ring waves.

A detailed study of the complex dynamics generated by a quadratic one-dimensional map near period three is presented. A resonance model for the tangent bifurcation process is constructed, which leads to an expression for the probability density as a sum of three Lorentzian contributions whose widths are expressed in terms of the fixed points of the third iterates of the map in the complex plane. It is also shown that the coarse-grained dynamics near period three can be analyzed in terms of an intermittency picture where deterministic motion, localized at the density maxima, is interspersed with chaotic bursts. An analysis of this motion explains the square-root dependence of the computed Liapunov number on the deviation of the map parameter from its bifurcation value. The origin of the fine structure, which decorates the spikes in the probability density, is described. The applicability of this model to the chaotic flows of ordinary differential equations is also discussed with respect to the dynamics on the Rössler strange attractor.

Angle-resolved photoelectron spectra were taken of the fourth band in C${\mathrm{O}}_2$ ($C{}_{}{}^2{}_{}{}^{}{\Sigma }_g_{}^{+}{}_{}{}^{}$) as a function of photon energy using synchrotron radiation. It was found that the value of $\beta$ dropped strongly in the vicinity of the photon energy of 42 eV. This result is shown to be in convincing agreement with theoretical predictions of a shape resonance, particularly when consideration is made of variations in internuclear distance.