A theory of nonlinear variations in the Faraday effect caused by a strong magnetic field is proposed. In atomic gases, the variation is defined by the nonlinear magneto-optical susceptibility tensor component ${\chi }_{x\mathrm{yzzz}}^{\mathrm{em}}$, which is expressed in terms of integrals of the radial Green's functions $G_E(r_1,r_2)$ of valence electrons of the atom. Applying for $G_E(r_1,r_2)$ and the wave functions analytical expressions in approximation of the model potential method, the authors carried out the first numerical calculations of ${\chi }_{\mathrm{xyzzz}}^{\mathrm{em}}$ for inert-gas, alkali, and hydrogen atoms. The calculations show that the variations in the Verdet constant induced by the square of the magnetic field are sufficiently large (even in frequency regions far from resonance) for detection by the currently available strong-magnetic-field pulse technique.

The intensity fluctuations in the output of a saturable optical amplifier are studied as the amplifier length is increased. Characteristics are determined by calculation of the diagonal elements of the density matrix of the optical field. Saturation affecting both upper-state and lower-state atomic populations is considered. Spontaneous emission distributed along the amplifier causes the "photon-number" distribution to approach a Bose-Einstein distribution during linear amplification if the input field is not Bose-Einstein. The onset of saturation reduces the relative fluctuations of the optical field both by introducing nonlinear gain and by reducing the spontaneous emission. Limiting solutions show that strong saturation leads to a major reduction in the fluctuations causing the photon-number distribution to approach a Poisson distribution.

The resolution of a quantum-beat experiment, which is basically limited by the atomic natural linewidth, has been improved by observing the fluorescence only from those atoms which have survived in excited states after some time delay. The resulting narrowing enables one to resolve previously overlapping lines in beam-foil quantum-beats experiments using $\mathrm{H}\alpha$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ii (4→3) deexcitation.

The force exerted by optical-frequency radiation on neutral atoms can be quite substantial, particularly in the neighborhood of an atomic resonance line. In this paper we derive from quantum theory the optical force, its first-order velocity dependence, and its fluctuations for arbitrary light intensity, and apply the results to the problem of creating a stable optical trap for sodium atoms. New results include the position dependence of the velocity-dependent force, a complete expression for the momentum diffusion constant including the substantial contribution from fluctuations of the dipole force, and an estimate of trapping times in excess of 1 sec even in the absence of effective damping. The paper concludes with a discussion of the prospects and difficulties in providing sufficient damping to stabilize such a trap.

Long-time behavior of transmitted and reflected field amplitude of optical bistability by a cavity including an absorptive resonant medium from an initial to a final steady state on switching the incident field is investigated by solving numerically the semiclassical dynamical equations without the mean-field approximation. The transmitted field amplitude as a function of time is monotonic as a whole, and an oscillatory character is seen on it in a shorter period. The dynamical character such as the oscillation amplitude and the duration of a whole process depend strongly on two parameters included in the equations.

Exact solutions of the master equations which describe single-mode $m$-photon absorption and $m$-photon emission processes in a two-level atomic system are obtained using a density-matrix approach. Some aspects of the photon statistics, e.g., antibunching, are discussed.

The interaction between a uniform, cylindrical electron beam and a counterstreaming, guided, electromagnetic wave is studied by means of a perturbation theory of the empty-waveguide modes. This model considers a relativistic velocity spread in the beam. In order to preserve the mirror feature of the beam, a condition is imposed upon the perpendicular temperature of the beam. This originates from the consideration of the relativistic dynamics of the electrons in the beam frame. Moreover, considering the current limitation for an uncompensated beam, the above condition leads to a limiting value of the Doppler conversion factor for a given perpendicular temperature.

The purpose of this work is to study the behavior of atomic fluctuations and the spectrum of transmitted light by a nonlinear medium with absorption and dispersion. The authors make use of the system-size expansion and apply it to the quantum-mechanical Langevin's equations for the atomic operators and obtain the characteristic curves for bistable behavior, macroscopic atomic expectation values, and the spectrum of the atomic fluctuations. The calculated spectrum of transmitted light exhibits line narrowing near bistable thresholds, discontinuous formation of bands along the high-transmission bistable branch, and hysteresis effects, etc., for detuning $\left|\delta \right|$ less than a critical value ${\delta }_c$. For $\left|\delta \right|>\mathrm{}{\delta }_c$, the discontinuous character of all the physical variables of the system vanishes; the system no longer exhibits bistable behavior. The system, however, still shows cooperative and single-atom behavior separated by a critical value of the intensity of the incident coherent pump at which a critical slowing down of the medium occurs, exhibiting a phase transition.

A numerical procedure to solve the differential equation for solitary waves via iteration for the continuum approximation of a generalized Frenkel-Kontorova model is presented. The generalization consists of adding a constant force and a phenomenological friction force proportional to particle velocity. The equation of motion is cast into integral form via a Green's function. Use is made of the sine-Gordon equation in choosing the form of an appropriate trial function. A good analytic approximation connecting applied force, friction, and the resulting solitary-wave velocity for a specific transport problem, as well as the exact numerical solution, is given. In addition, an exact functional relationship between applied force, friction, and velocity for a general transport problem is demonstrated.

The time-dependent pair-distribution function, which plays a central role in the description of nuclear magnetic relaxation and collision-induced absorption in classical fluids, is evaluated in a mean-field approximation proposed earlier. In this scheme the binary dynamics of the colliding pair is treated without approximation, and the interaction with the background fluid is taken into account via a renormalization of the pair potential. The result is expressed in terms of orbits having specified end points and specified elapsed times.

Expressions for the wave-energy density and wave-momentum density of each species of a collisionless plasma are derived. The sum of the wave-energy (momentum) densities of all the species and the electromagnetic-energy (momentum) density gives the previously known result for the total wave-energy (momentum) density of a dispersive medium.

The radiation emission from dense, high-temperature aluminum plasmas has been studied to appraise the influence of photoexcitation on several spectral diagnostics currently used to determine average plasma parameters. The plasma state is described by a set of collisional-radiative rate equations characterizing the competing atomic processes occurring in a homogeneous plasma volume of constant density and temperature. Radiation is transported through the plasma by the method of frequency diffusion, a technique which employs collision times of the photons as they diffuse through the wings of a broadened line profile. Line spectra and line-intensity ratios for several pairs of emission lines of the $K$ shell are calculated in optically dense plasmas and compared with those obtained from the model within the optically thin approximation. The radiation-trapping effects are shown significantly to modify the behavior of the optically thin constant-density or constant-temperature line ratio curves, which become double valued in some cases. Comparisons of state populations obtained from this model and the local-thermodynamic-equilibrium model are also shown.

The density-functional method is applied to excess electrons and positronium atoms in helium fluids. The self-trapping is investigated in a fully self-consistent fashion, and formulas are given for the particle energy and Ps pick-off annihilation rate in quasifree as well as localized states. The numerical results compare well with experimental data. However, the need for a more sophisticated treatment of threshold effects near the onset of bubble formation is indicated.

A lattice model for three liquid crystalline phases is presented and solved in the mean-field approximation. Numerical results are obtained for the bulk phases. We find isotropic, nematic, and smectic-$A$ phases, with the possibility of nematic-isotropic, smectic-$A$—isotropic, and nematic-smectic-$A$ (NS) transitions. The NS transition can be first or second order, depending upon the choice of molecular potential. Examples modeling the materials octyl-oxycyanobiphenyl (8OCB) and cholersteryl myristate are considered.

Employing the fluid model for the nonlinear response of electrons, we have studied the phenomenon of second-harmonic generation of upper-hybrid electromagnetic radiation in an inhomogeneous plasma. In the case of laser-pallet fusion, the maximum contribution for harmonic generation comes from the vicinity of the upper-hybrid layer, and the harmonic conversion efficiency turns out to be ∼0.1% at the power densities ∼${10}^{14}$ W/${\mathrm{cm}}^2$ (C${\mathrm{O}}_2$ laser), the same order as observed experimentally. In the case of electron cyclotron heating experiments of tokamak, a strong second harmonic must be generated at the cyclotron resonance layer. The wave-number-matching condition could be satisfied in a tokamak, which adds to the conversion efficiency.

We derive new inequalities to be fulfilled by the nonequilibrium critical exponents by considering the contributions of fluctuations to the transport near the critical point. The main result is that the critical exponent associated with the bulk viscosity must be larger than 0.54, and we conjecture a new equality between equilibrium and nonequilibrium critical exponents.

This paper presents an investigation of the generation of an ion-acoustic pulse by two electromagnetic (EM) pulses in a collisionless hot unmagnetized plasma at the difference frequency of the two EM pulses. On account of the interaction of the two EM pulses, a ponderomotive force at the difference frequency becomes finite and leads to the generation of an ion-acoustic pulse. When the two EM pulses have a Gaussian intensity distribution in time and uniform intensity distribution in space, the generated ion-acoustic pulse is also Gaussian in time with a pulse width $={\left[\frac{t_{10}^2{t}_{20}^2}{(t_{10}^2+t_{20}^2)}\right]}^{\frac{1}{2}}$, where $t_{10}$ and $t_{20}$ are the initial pulse widths of the incident EM pulses. Moreover, if the incident EM pulses have a Gaussian intensity distribution in space and time, the nonuniform intensity distribution of the EM pulses in a plane transverse to the direction of propagation leads to the redistribution of electrons and ions, and transient (time-dependent) cross focusing of the pulses may occur for appropriate initial powers of the EM pulses. The ion-acoustic-pulse generation is seen to be drastically modified by cross focusing of the two EM pulses.

The purpose of this paper is to calculate the mobility of excess electrons in compressed argon (20-100 atm) both in single-scattering and multiple-scattering approximations. Calculations in the single-scattering approximation are carried out with the aid of the Cohen-Lekner theory. A new formula for the mobility of excess electrons in the multiple-scattering approximation is derived from the Kubo-Greenwood relation for electric conductivity. Numerical results inferred from this formula and from the Cohen-Lekner theory are compared with the experimental data reported in the literature. The results obtained in this paper indicate that the Cohen-Lekner theory is applicable only at very low densities of gaseous argon and that inclusion of the long-range part of the electron-atom potential gives a significant improvement in the theoretical results. The multiple-scattering corrections have been estimated to be about (10-25)% of the value of mobility calculated in the single-scattering approximation.

A renormalization procedure is proposed for the coupled Maxwell-Klimontovich equations including the full, nonlinear electrical current. The renormalized equation for the two-point field correlation function is used to derive a renormalized quasiparticle representation of the theory.

Broadened and oscillatory Kerr profiles in time were observed in neat liquids by means of intense picosecond optical excitation. This new observation can be used to measure the molecular relaxation time and a nonlinear index of refraction.