The differential equation for the photon conditional probability distribution in a nonlinear amplifier is numerically solved, using the continuous approximation. Saturation effects on the development of fluctuations in the amplification of coherent light are studied. They are compared with the results obtained by solving the moment equations.

A fundamental theorem in nuclear magnetic resonance and quantum optics is derived for an atomic system subject to inhomogeneous broadening and coherent preparation by a pulsed electromagnetic field of arbitrary shape. We show that the coherent emission, free induction decay or echo, which follows is confined to an interval which precisely equals the duration of the applied pulse sequence. The theorem applies to two-level or multilevel transitions for which the inhomogeneous linewidth is infinitely broad and the sample is optically thin.

Double-quantum NMR is a useful way to obtain spectra of quadrupolar nuclei (${}_{}{}^2{}_{}{}^{}\mathrm{D}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$,...) in solids. This allows measurements of the chemical shifts for these nuclear spins. The theory of Hartmann-Hahn cross polarization between $I=\frac{1}{2}$ and such $S=1\mathrm{}$ spins is discussed. Particular attention is drawn to the cross polarization of the double-quantum transition. The thermodynamics and the dynamics of the process are evoked in detail using a fictitious spin-½ formalism. The spin $S=1\mathrm{}$ Hamiltonian can always be factored into two commuting parts (independent thermodynamic reservoirs), one of which behaves as a fictitious spin ½ which is cross polarized with the $I=\frac{1}{2}$ spins. Modified Hartmann-Hahn conditions emerge from the theory, and the dependence of cross-polarization times $T_{\mathrm{IS}}$ on rf intensity and frequency for spin locking and adiabatic demagnetization in the rotating-frame experiments are calculated. Measurements on the ${}_{}{}^1{}_{}{}^{}\mathrm{H}$-${}_{}{}^2{}_{}{}^{}\mathrm{D}$ double resonance in dilute solid benzene-$d_1$ are reported, verifying the predictions and indicating that cross polarization provides a sensitive means of detecting the ${}_{}{}^2{}_{}{}^{}\mathrm{D}$ double-quantum transition. Values are reported for the thermodynamic parameters and cross-polarization times as a consequence. Three possible versions of double-resonance detection of double-quantum spectra are possible—direct detection of the cross-polarized double-quantum decay, indirect detection of the frequency spectrum following Hartmann and Hahn, and indirect detection of the free-induction decay following Mansfield and Grannell.

We report on the semiclassical solution of the Bloch equations for cooperative resonance fluorescence with collective damping. These equations are shown to be equivalent to the relevant master equation, in the limit of large cooperation number and time scales faster than the one-atom lifetime (reciprocal Einstein $A$ coefficient). The resulting spectrum is derived for a coherent driving field of arbitrary intensity. Additional spectral peaks, as well as the central triplet, are predicted above threshold. A physical explanation of the extra peaks is proposed.

We consider the dynamical behavior of the (nonlinear) amplitude fluctuations in the transmitted radiation of the optical bistability in the transition region. A Fokker-Planck model with nonlinear diffusion coefficient (multiplicative Gaussian white noise) is used to describe the system in the "good-quality" cavity limit. Choosing a parameter set corresponding to a numerically small but tractable tunneling rate between the stable and metastable states we study, as functions of the external coherent field and system size, the spectrum and the response to a small additional injected coherent signal. The numerical calculations are facilitated by the construction of complex-valued continued-fraction representations for the spectrum of amplitude fluctuations and for the response function. This representation allows us to discuss the memory effects caused by deviations from a simple Gaussian-Markov behavior around the transition region. In addition, such a representation enables the construction of "a posteriori" error bounds on the power spectrum.

Microscopic scattering processes are discussed for two structures of light incident on thermal particles. One is composed of two collinear light beams originating from different oscillating modes of a laser, and another is composed of two counter propagating beams originating from the same oscillating mode. A comparison of the cumulant expansions for the above two cases has allowed discerning which terms in the scattering structures led to the same statistical properties of the scattered photons. It is shown that, for the scattering of multimode-laser light, the statistical properties of scattered photons are not affected by the noncorrelating random phases of the incident laser fields but are the same as those in the case of single-mode laser light under practical scattering experiments. The factorial moments $F_k[=〈n(n-1\mathrm{}\left)\mathrm{}\cdots \mathrm{}\right(n-k+1\mathrm{}\left)\mathrm{}〉\right]$ up to sixth order of the scattered photons were measured for various scattering situations including the above two cases, and they were found to support the theoretical results.

The Rayleigh-Brillouin spectrum of He, Ne, and Ar is reported for 90° scattering at a number of densities spanning the kinetic and hydrodynamic regime. A purely experimental test of scaling is made and it is found that deviations from scaling at high density can be attributed to mean-field effects. At low densities there is evidence that deviations from scaling, which arise from the detailed dependence of the spectrum on the intermolecular potential, are detectable at the few percent level. Some insight into scaling is obtained by comparing the results at low densities with curves predicted from a $3E$ kinetic model and from hydrodynamic theory.

The Rayleigh-Brillouin spectra of He, Ne, and Ar are reported for the hydrodynamic region. The experiments show that light scattering may be used to determine thermodynamic and transport properties of gases as a function of density and thus provide another method of probing intermolecular potentials. In addition, the transition from the hydrodynamic to the kinetic regime is examined in terms of generalized hydrodynamics.

The Debye absorption of electromagnetic waves by a dielectric fluid near the critical point of the liquid-vapor phase transition is treated regardless of the polar or nonpolar behavior of the fluid. The critical behavior of the Debye absorption is related to long-scale fluctuations in the density and entropy, and it is rather insensitive to any microscopic property of the fluid. The critical dynamics of fluctuations is treated in the framework of mode-mode coupling theory. The local fluctuation of the polarization vector, whose correlation function is related to the absorption coefficient, is expressed as a superposition of modes. The main contribution to the critical behavior comes from the coupling between electromagnetic waves and stationary sound waves, because the fluid is highly compressible near the critical point. Energy of the stationary sound wave coupled with the electromagnetic wave is mainly dissipated by thermal conduction processes; therefore, the critical Debye absorption is mainly related to the thermal conductivity. The Debye spectrum shows a cutoff frequency above which the critical Debye absorption vanishes. The height of the Debye line grows as ${(T-T_c)}^{-\nu }$, while the cutoff frequency vanishes as ${(T-T_c)}^{2\nu }$.

Fluctuating hydrodynamics is extended to the nonequilibrium regime. Two modifications to the equilibrium theory are made: (i) The dynamics of the fluctuations are linearized about a nonequilibrium steady state (NESS). (ii) The stochastic behavior of the random forces (noise) is equilibriumlike, satisfying a local fluctuation-dissipation theorem. Thus, the noise correlations depend on position through their dependence on the NESS temperature, chemical potential, and velocity. It is shown that this is sufficient to give the results of our earlier microscopic analysis and sheds new light on their interpretation. A microscopic justification of the fluctuating hydrodynamic procedure is offered.

The observed behavior of the emissivitives of boronlike Fe xxii, lithiumlike Fe xxiv and Ti xx, and the heliumlike Fe xxv ions in the Princeton large torus tokamak during high-power neutral (${\mathrm{H}}^0$ or ${\mathrm{D}}^0$) beam heating is described. A substantial lowering of the dominant ionization state in the center of the discharge, while the electron temperature is rising, is attributed primarily to increased recombination rate of the ions through charge exchange with neutral hydrogen. This interpretation is supported by the different space and time behavior or the lithiumlike and boronlike ions of comparable ionization potentials, and by comparisons of neutral beam heating of the plasma with ion cyclotron resonance heating, which does not appreciably change the neutral hydrogen concentration. The observations are compared with approximate zero-dimensional model calculations, using experimental plasma conditions and estimated charge-exchange rates.

Phenomenological models for the nonlinear hydrodynamic behavior of 2D solids and hexatic liquid crystals are proposed and analyzed by perturbation expansions and renormalization-group techniques. It is shown that conventional hydrodynamics breaks down in two dimensions due to infrared divergences. Nonlinear effects give rise to long-time tails and anomalous dispersions.

Molecular-dynamics calculations were done for hard parallel squares (HPS) at areas relative to close packing of 4.5, 2.0, 1.345, and 1.31. A Maxwellian velocity distribution (which was maintained in time) was used. A phase transition was found at 1.345 which, from these previous results, appears most likely to be a first-order transition. The normalized velocity autocorrelation function for the densities of 4.5 and 2.0 displayed a "long-time" tail whose decay approximates a minus-one power of the time. These results agreed with other molecular-dynamics simulations using a different initial velocity distribution but disagreed with Monte Carlo calculations. Speculation is presented on the ability of certain nonergodic systems such as the HPS to mimic the behavior of an ergodic system with regards to a number of properties.

On the basis of the known experimental properties of $\frac{1}{f}$ noise, some previous models are analyzed. The presence of $\frac{1}{f}$ noise in the simplest systems such as beams of charged particles in vacuum, the existence of $\frac{1}{f}$ noise in currents limited by the surface recombination rate, bulk recombination rate, or by the finite mobility determined by interaction with the phonons in solids, suggests a fundamental fluctuation of the corresponding elementary cross sections. This leads to fluctuations of the kinetic transport coefficients such as mobility $\mu$ or recombination speed, observable both in equilibrium and nonequilibrium. In the first case the available Johnson noise power $\mathrm{kT}$, determined by the Nyquist theorem, is free of this type of $\frac{1}{f}$ fluctuation. An elementary calculation is presented which shows that any cross section, or process rate, involving charged particles, exhibits $\frac{1}{f}$ noise as an infrared phenomenon. For single-particle processes, the experimental value of Hooge's constant is obtained as an upper limit, corresponding to very large velocity changes of the current carriers, close to the speed of light. The obtained ${sin}^2\left(\frac{\theta }{2}\right)$ dependence on the mean scattering angle predicts much lower $\frac{1}{f}$ noise for (low-angle) impurity scattering, showing a strong ($\sim \frac{{\mu }^2}{{\mu }_{\mathrm{latt}}^2}$) noise increase with temperature at the transition to lattice scattering. This is in qualitative agreement with measurements on thin films and on heavily doped semiconductors, or on manganin. The theory is based on the infrared quasidivergence present in all cross sections (and in some autocorrelation functions) due to interaction of the current carriers with massless infraquanta: photons, electron-hole pair excitations at metallic Fermi surfaces, generalized spin waves, transverse phonons, hydrodynamic excitations of other quanta, very low-energy excitations of quasidegenerate states observed, e.g., in disordered materials, at surfaces, or at lattice imperfections, etc. The observed $\frac{1}{f}$ noise is the sum of these contributions, and can be used to detect and study new infraquanta.

The Kirkwood-Buff molecular theory of surface tension is used to determine the location of the surface of tension for a planar liquid-vapor interface of liquid argon near the triple point. A nonzero interfacial thickness is considered in this phenomenological study for the cases of a linear and a cubic density profile. It is found that the product of the surface tension and the location of the surface of tension is independent of the width of the liquid-vapor transition zone. Both linear and cubic density profiles lead to the same invariance relation. The realistic Barker-Fisher-Watts (BFW) potential and the Parson, Siska, and Lee (MSV-III) potential are used for numerical calculation. The experimental radial-distribution function of Yarnell et al. is used for the bulk liquid and as an approximation for the transition zone. Results are compared to those previously reported. Curvature dependence of the surface tension for large-size droplet or cluster is also discussed.

A simple exact solution of a one-dimensional Schrödinger equation which describes the motion of a particle in a continuous potential $V\left(x\right)\mathrm{}$ and scattering from a finite set of $\delta$-function potentials of arbitrary positions and strengths is found.

We performed molecular-dynamics simulations of liquid rubidium and the Lennard-Jones fluid at several densities and temperatures, and of a system whose pair potential is the repulsive core of the rubidium potential. In all cases, propagating density fluctuations occurred in the rubidiumlike systems at much shorter wavelengths than in the Lennard-Jones system. This indicates that the repulsive part of the pair potential is the dominant factor in determining the relaxation of short-wavelength density fluctuations.

For all gauges of the Göppert-Mayer type, the two-body Schrödinger equation for charged particles in a plane-wave electromagnetic field fails to separate into center-of-mass and relative-coordinate equations when the field is sufficiently intense.

In the realsitic approximation that the expansion coefficient of a fluid vanishes, the hydrodynamic fluctuations around a steady state characterized by a small temperature gradient are determined entirely by the variations of the strength of the random forces from point to point. The assumption of local hydrodynamic equilibrium for the random forces leads to a long-range static density momentum correlation, as well as to a significant odd-in-frequency correction to the Brillouin light scattering, whose integrated intensity agrees with other work of Ronis et al. and Kirkpatrik et al. Consequences of the long-range correlations for $\frac{1}{f}$ noise ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and local equilibrium postulates are discussed.

Using well-stabilized microwave sources in the extended frequency range 50-315 GHz, we have observed very narrow millimeter resonances between Rydberg levels of sodium with principal quantum number $n$ ranging from 23 to 41. Measurement of the resonance frequencies yields improved values for quantum defects and $P$-level fine-structure intervals.