An atom in a near-resonant standing-wave laser field emits light spontaneously from its upper level which shows a dip at resonance. This calculation gives the intensity emitted as a function of laser tuning and of the saturation parameter. The case of oppositely directed waves of unequal amplitudes is also treated.

A perturbation scheme based on the slow adiabatic variation of the radiation-field characteristics is applied to the Maxwell-Bloch equations. The two leading orders in the perturbation expansion yield a set of partial differential equations for $\overrightarrow{\mathrm{k}}(\overrightarrow{\mathrm{r}},t)$, $\omega (\overrightarrow{\mathrm{r}},t)$, and $a(\overrightarrow{\mathrm{r}},t)$ (the local wave vector and frequency and the field amplitude). All the coefficients of these equations are derivable from a single dispersion function $H(\overrightarrow{\mathrm{k}},\omega ,a)$, this feature is used to further reduce the equations to a set of Hamilton-Jacobi-type ordinary differential equations (ray equations). Unlike the linear geometric optics case the properties of the "local lens" seen by a ray depend also on the amplitude of the field propagating along neighboring rays. A method to derive additional equations for the evolution of the local lens along a single ray and to decouple the equations for different rays is described, the resultant enlarged set of ray equations is derived. The limitations and advantages of this approximation scheme are discussed in comparison with other approaches.

The cross sections associated with absorption, scattering, extinction, and radiation pressure for homogenous isotropic spheres illuminated by plane waves are well known. We derive a new fundamental cross section, namely, the one which gives the time-averaged torque caused by circularly-polarized illumination. Consider a $z$-directed wave with pure circular polarization corresponding to a positive value for the $z$ projection of the photon spin. Formulation of the Maxwell stress dyad of the total (incident + scattered) field gives the following torque relative to the sphere's center, ${\Gamma }_z=\frac{I_L\pi {\alpha }^2{Q}_{\mathrm{abs}}}{\omega }$. Here $I_L$ and $\omega$ are the incident wave's irradiance and angular frequency and $\alpha$ and $Q_{\mathrm{abs}}$ are the sphere's radius and Mie-theoretic absorption efficiency. Consequently the effective cross section for torque is the same as that for energy absorption $\pi {\alpha }^2{Q}_{\mathrm{abs}}$ as might be expected since the scattered radiation is shown to have the same ratio of $z$ component of angular momentum to energy as the incident wave. This result is rigorous for stationary isotropic spheres in vacuo. It may be used to estimate the steady-state angular velocity ${\omega }_{\mathrm{sz}}$ of a sphere in a gas which is achieved when ${\Gamma }_z$ is balanced by the viscous-drag torque. A Rayleigh-scattering approximation for $Q_{\mathrm{abs}}$, which should be useful for small spheres, gives ${\omega }_{\mathrm{sz}}\simeq \frac{I_L{M}_g{M}^{\prime }{M}^{\prime \prime }}{\eta c(M^{\prime 2}+2)}$ where the sphere's refractive index is $M^{\prime }+{\mathrm{iM}}^{\prime \prime }$ relative to that of the gas $M_g$, $\eta$ is the viscosity of the gas, and $c$ is the speed of light. The radiation torque caused by elliptically-polarized illumination and the torque on stratified spheres are also discussed.

We consider the density matrix for weakly damped quantum oscillators. It is proved that the locally time-averaged density matrix derived from the full density matrix satisfies a closed set of equations, which reduce under specified conditions to population rate equations. Rate coefficients in these equations include contributions from collision-induced transitions and internal collisionless transitions explicitly arranged as sequential processes. We compare solutions of the new rate equations with the full density matrix for a four-level driven system. It is shown that despite some notable success in matching locally time-averaged quantities by extending the Wilcox-Lamb formalism to the weak-damping limit, the new equations are more naturally suited for this limit. In contrast with the Wilcox-Lamb formalism, we show that the new equations give a representation of the local time average whose accuracy is limited only by the degree of time-scale separation between collisions and internal dynamics.

A new method of picosecond and femtosecond transient spectroscopy yielding information about ultrafast relaxation processes without requiring ultrashort light pulses is presented. It is based on the present theoretical analysis of the resonant degenerate four-wave-mixing process excited by two temporally incoherent light beams with wave vectors ${\overrightarrow{\mathrm{k}}}_1$ and ${\overrightarrow{\mathrm{k}}}_2$ which are originated from a single beam at frequency $\omega$ but have mutual time delay $\tau$. Under the assumption that the incoherent light field has Gaussian random complex amplitude and that the resonant material consists of the usual two-level atoms, the statistically averaged intensity of the output light field with ${\overrightarrow{\mathrm{k}}}_3=2\mathrm{}{\overrightarrow{\mathrm{k}}}_2-{\overrightarrow{\mathrm{k}}}_1$ at $\omega$ is calculated as a function of $\tau$. Even with the light having a much longer duration than both $T_1$ (the longitudinal relaxation time) and $T_2$ (the transverse relaxation time), the correlation trace, i.e., output intensity versus $\tau$, represents a decay profile determined mainly by $T_2$ for both homogeneously and inhomogeneously broadened transitions, as long as the light correlation time ${\tau }_c$ is much shorter than the relaxation times. The correlation trace does not always represent a single-exponential decay but is sometimes slightly deformed by the $T_1$ effect. However, it does not cause a significant error in the determination of $T_2$. Moreover, as $\frac{T_2}{T_1}\to 0$, the trace becomes a single-exponential decay curve determined only by $T_2$. The feature of the results obtained by the present method is similar to that obtained by the conventional coherent transient spectroscopy with short pulses, such as the photon echo. The time resolution in the present method, however, is limited only by ${\tau }_c$ much shorter than the light duration. By regarding the incoherent light as a series of random ultrashort pulses, the present four-wave-mixing process is also interpreted as the ensemble of numerous transient four-wave-mixing processes caused by various combinations of these pulses.

We derive a new systematic expansion of the electric field distribution at a test charge immersed in an infinite two- or three-dimensional one-component plasma. The lowest-order truncation of this expansion leads to a mean-field theory very similar to the adjustable-parameter exponential approximation (APEX). The next-order corrections to this mean-field theory are explicitly computed in terms of the distribution functions of the plasma particles. All these approximations are compared to the Monte Carlo results for a two-dimensional system at $\Gamma =2\mathrm{}$ and various test charges. The systematic approximations appear to be useful. Even the zeroth-order approximation is quite accurate for large test charges or strongly coupled systems and the next order improves on it. Still, APEX is found to be most reliable (as it is also in three dimensions) and remains accurate in the practical interesting limit where the test charge vanishes, i.e., at a neutral atom.

An amplitude equation is derived for thermal convection in a binary fluid mixture in a porous medium and in bulk, in the vicinity of the intersection point of the lines of stationary and oscillatory instabilities. Slow spatial modulations are included in the amplitude equation near this codimension-2 bifurcation. The experimental realizability in binary fluid mixtures is discussed with use of data for specific systems such as alcohol-water mixtures and normal-fluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures. Analogies are drawn to other physical systems which are easily accessible to experiment, such as the convective instability in nematic liquid crystals in an external magnetic field.

A lattice model for binary mixtures of prolate and oblate molecules is studied, by a mapping onto a 13-state Potts-Ising model, followed by an approximate renormalization-group analysis. Four different types of phase diagram are obtained, exhibiting prolate uniaxial, biaxial, and oblate uniaxial phases. Local disorder has the nonordering property of an effective vacancy and is thus included into our mapping. Such effective vacancies can cause first-order phase transitions. Thus the biaxial phase can disorder either directly through a ridge of first-order transitions, or via an intermediate uniaxial phase which vanishes at a multicritical point. In the biaxial region, the system is shown to be related to the six-state clock model, so that the latter point may be replaced by a segment of algebraic (Kosterlitz-Thouless) order in films. Similar considerations are applied to one-component systems of biaxially shaped molecules.

Comprehensive studies of the hydrodynamics and energy transport in laser-produced plasmas are presented. Thin low-$Z$ foil targets (${10}^{-5\mathrm{}}$—${10}^{-3\mathrm{}}$ g/${\mathrm{cm}}^2$) were irradiated with 300-ps pulses from the Asterix-III iodine laser ($\lambda =1.3\mathrm{}$ μm). Different diagnostics such as high-speed photography, plasma calorimetry, Ulbricht sphere for laser-light absorption measurements, and x-ray and ion techniques were used. Results on the velocity and energy of the accelerated foil, pressure, ablation rate, and lateral energy spread were obtained for a wide intensity range ${10}^{11}$—${10}^{16}$ W/${\mathrm{cm}}^2$. Pressures exceeding 10 Mbar and foil velocities of up to ${10}^8$ cm/se observed. The experimental data are compared with one-dimensional hydrodynamic calculations using different values of electron heat-flux limitation. An indication of intensity-dependent flux inhibition was found: $f\ge 0.1$ at intensities below ${10}^{13}$ W/${\mathrm{cm}}^2$, but $f=0.015-0.03\mathrm{}$ at intensities above ${10}^{14}$ W/${\mathrm{cm}}^2$.

A modified mode-coupling theory is presented to explain discrepancies between measured values and theoretical predictions for the long-time tail of the velocity-autocorrelation function of diffusing particles. The measurements of Paul and Pusey and of Ohbayashi et al. are analyzed and shown to be in much better agreement with theory than previously supposed, provided that the new, modified theory is used. The new theory regularizes spatial singularities in order to remove temporal singularities. In doing so, it provides a natural explanation of both the diffusion constant and the amplitude of the long-time tail of a multiplicative stochastic process.

It is shown by dimensional analysis that Pauli's ground-state-energy theorem, which expresses the ground-state energy in the form of a coupling-constant integration of the potential energy, and the virial theorem are equivalent for a many-particle system interacting with a homogeneous interparticle potential ($\propto r^l$) in arbitrary ($d$) dimensions. The finite-temperature case is also discussed.

We have measured detailed profiles of plasma-broadened neutral-carbon lines, utilizing a wall-stabilized arc source and a specially designed data acquisition and processing system. We analyzed the lines in terms of symmetric Lorentzian profiles in order to isolate the deviations due to asymmetries and found regular patterns of an antisymmetric nature around the line centers. The asymmetry patterns have a common shape with a minimum, maximum, and zero crossing at the same points on a reduced wavelength scale, but they vary widely in their amplitudes. These findings are in excellent qualitative agreement with the quasistatic theory of ion broadening due to the quadratic Stark effect. A comparison and match of experimental and theoretical amplitudes has thus been used to determine the ion broadening parameters of these lines, which are in satisfactory agreement with directly calculated values.

A type of metastable state is found and analyzed for a nonlinear model of self-replicating biomolecules under constraint. This state, described by the deterministic theory as one of the stable steady states, is studied stochastically by using various approximation schemes. The time-dependent behavior is derived so that the lifetime can be estimated numerically. The possible transitions induced by the fluctuation perturbations are also discussed.

We consider the manifestations of Bose and Fermi statistics on the original quantum distribution function. Initially, we consider some general symmetry properties of the density matrix. Next, we convert these results into distribution-function language for the case of a system of spin-0 particles. Finally, we consider a system of spin-½ particles, for which we treat the combined effects of both spin and statistics.

We have calculated the exchange and correlation corrections to the free energy ($F_{\mathrm{xc}}$) and the chemical potential (${\mu }_{\mathrm{xc}}$) of an electron system at arbitrary degeneracies and temperatures. These are needed for density-functional, average-atom-type calculations of properties of plasmas and liquid metals. The problem of inverting the parametric relation between ${\mu }_{\mathrm{xc}}$ and the density correction $n_{\mathrm{xc}}$ is considered. We present easy-to-use analytic fits to $F_{\mathrm{xc}}$ and ${\mu }_{\mathrm{xc}}$ as functions of the temperature and density. We also consider the effect of a lineraly responding ion background on the electron chemical potential as well as the ion chemical potential, as these are needed in calculations of ionelectron systems at arbitrary degeneracies and densities.

The classical treatment of thermal heat transport in the presence of magnetic fields has been modified to include effects associated with steep temperature gradients by extending the one-dimensional model of Shvarts et al. [Phys. Rev. Lett. 47, 247 (1981)] to three dimensions. The effects of magnetic field inhibition are described in terms of the parameter ${\beta }_0={\omega }_c{\tau }_{\mathrm{ei}}$, where ${\omega }_c$ is the electron gyrofrequency and ${\tau }_{\mathrm{ei}}$ the (thermal) electron-ion collision time. The model has been applied to plasmas whose zeroth-order distribution functions ($f_0$) are Maxwellian, and solutions have been obtained for the components of the heat flux across the magnetic field, parallel and perpendicular to the temperature gradient. It is found that it is only for small ${\beta }_0 (\lesssim 0.2)$ that the anisotropic portion of the distribution function (${\overrightarrow{\mathrm{f}}}_1$) is limited, according to the prescription of Shvarts et al., to $\delta f_0$ where $\delta$ is an ad hoc cutoff parameter of value approximately unity; for higher values of ${\beta }_0$, a strong reduction of both components of the heat flux occurs due to the inhibition of the more energetic heat-carrying electrons in the distribution, and the classical Braginskii results are valid (in the sense that $f_1\lesssim f_0$ for heat-carrying electrons). The sensitivity of the results to the parameter $\delta$ is examined. For parameters typical of glass-laser-generated plasmas, strong inhibition may occur for magnetic fields as small as 100 kG.

A consistent approach to the inference of a probability distribution given a limited number of expectation values of relevant variables is discussed. There are two key assumptions: that the experiment can be independently repeated a finite number (not necessarily large) of times and that the theoretical expectation values of the relevant observables are to be estimated from their measured sample averages. Three independent but complementary routes for deriving the form of the distribution from these two assumptions are reviewed. All three lead to a unique distribution which is identical with the one obtained by the maximum-entropy formalism. The present derivation thus provides an alternative approach to the inference problem which does not invoke Shannon's notion of missing information or entropy. The approach is more limited in scope than the one proposed by Jaynes, but has the advantage that it is objective and that the operational origin of the "given" expectation values is specified.

The influence of an isolated critical point (Landau point) on the first-order lyotropic isotropicnematic transition lines is studied with regard to magnetic birefringence $\Delta n$ in the disordered (isotropic) phase. Near the Landau point $\Delta n\sim {\chi }_{Q}h[1+fh+O(h^2\left)\right]$, where ${\chi }_Q$ is the zero field ($h=0\mathrm{}$) order-parameter susceptibility and $f=\frac{1}{2}\left[\frac{\partial \left(\ln {\chi }_Q\right)}{\partial h}\right]$ is the $h=0\mathrm{}$ "curvature" correction. Critical exponents and universal scaling functions for ${\chi }_Q$ and $f$ are obtained through renormalization-group $\epsilon$-expansion methods ($d=4-\epsilon$). It is suggested that magnetic birefringence experiments in the pretransitional region be analyzed in terms of the effective exponents for the susceptibility ${\gamma }_{\mathrm{eff}}$ and curvature ${\left({\phi }_f\right)}_{\mathrm{eff}}$. To $O\left(\epsilon \right)$, the results are ${\gamma }_{\mathrm{eff}}=1+\left[\frac{7\epsilon }{26(1+Y)\mathrm{}}\right]$ and ${\left({\phi }_f\right)}_{\mathrm{eff}}=2+\left[\frac{4\epsilon }{13(1+Y)\mathrm{}}\right]$ where $Y=g_4{g}_r^{\left|{\phi }_4\right|}$; $g_r$ is the thermal scaling field, ${\phi }_4=\frac{-\epsilon }{2}+O\left({\epsilon }^2\right)$ is the universal correction to scaling exponent, and $g_4$ is a nonuniversal amplitude ("slow transient" scaling field).

It is shown that the existence of a critical point, with $\gamma \le 2\nu$, of the Yvon-Bron-Green equation depends sensitively on the very-short-distance part of the net correlation function $h\left(r\right)\mathrm{}$. However, if $\gamma >2\mathrm{}\nu$, then the asymptotic ($r\to \infty$) behavior of $h\left(r\right)\mathrm{}$ suffices. Also, the approximate nonlinear differential equation describing the long-distance part of the full integral equation allows for a critical point with positive net correlations for $d=3\mathrm{}$, provided that the scaling or long-ranged part of $h\left(r\right)\mathrm{}$, $h_c\mathrm{}\left(r\right)\mathrm{}$, vanishes at the critical point.

A field theory for random walks on a lattice with random traps is introduced and related to the field theory for the Green's functions of an electron on a lattice with randomly placed repulsive potentials. The moments [${\phi }_N^k$] and [${\phi }_N^k\mathrm{}\left(0\right)\mathrm{}$] of the survival and return functions ${\phi }_N$ and ${\phi }_N\mathrm{}\left(0\right)\mathrm{}$ measuring, respectively, the probability that a random walk will survive or will return to the origin in $N$ steps for a given configuration of traps is calculated from instantons of the field theory. Both $\ln \left[{\phi }_N^k\right]$ and $\ln \left[{\phi }_N^k\mathrm{}\right(0\left)\right]$ are proportional to ${\mathrm{}\left(\mathrm{kN}\right)\mathrm{}}^{\frac{d}{\mathrm{}(d+2\mathrm{})\mathrm{}}}$ in $d$ dimensions with correction terms of order ${\mathrm{}\left(\mathrm{kN}\right)\mathrm{}}^{\frac{\mathrm{}(d-1\mathrm{})\mathrm{}}{\mathrm{}(d+2\mathrm{})\mathrm{}}}$. Thus [${\phi }_N^k$] is always much larger than ${\left[\phi N\right]}^k$ for large $N$ and similarly for [${\phi }_N\mathrm{}\left(0\right)\mathrm{}$].