The Auger spectrum of LiF vapor has been measured in the energy region 600-680 eV by means of electron-beam excitation. The assignment of the peak structure is based on theoretical ab initio calculations with the use of the multiconfigurational complete-active-space self-consistent-field method and by comparison with the corresponding spectra of the neon atom and the hydrogen fluoride molecule.

We point out some problems with the usual quantum-mechanical theory of electrodynamics in nonlinear dielectric media which is used in nonlinear optics. In order to understand these problems, the Hamiltonian formulation of the theory is examined. It is found that many of the difficulties in the usual theory are a result of the fact that the canonical momentum for the interacting theory is not the same as that for the free electromagnetic field theory.

This paper reports an unusual photon-echo phenomenon where a train of echoes, generated by a repeating two-pulse sequence, exhibits growth rather than damping. The effect, which is observed in the impurity-ion crystal ${\mathrm{Pr}}^{3+}$: ${\mathrm{YAlO}}_3$, results from an electronic ground-state population grating that is created by the two-pulse sequence and is stored coherently as a modulation in the frequency domain. The depth of modulation increases with increasing $n$, where $n$ is the number of the two-pulse sequence—a result which is predicted in a three-level density-matrix theory. The effect is closely related to previous stimulated or three-pulse photon echoes but differs in that growth is observed directly for the first time in the simpler two-pulse sequence.

The stationary solution for optical bistability (OB) using a semiclassical exciton-biexciton model of CuCl is calculated exactly in the limit of large Fresnel number. The numerical solution of the second-order Maxwell equation is compared with corresponding results obtained with use of the slowly-varying envelope approximation (SVEA) as well as the mean-field approximation (MFA). It is found that results obtained using the SVEA are in close quantitative agreement with the numerical solution of the second-order Maxwell equation for each point in the parameter space considered, whereas the MFA correspondingly gives good qualitative results only. Furthermore, it is shown that the nonlinearity in the dielectric function for exciton-biexciton CuCl which causes OB is very nearly of the Kerr-medium type, and consequently, the two-photon biexciton resonance contributes only weakly to the OB characteristics.

The conditions are discussed for realizing an acoustic nonlinear resonator, showing bistable behavior analogous to the optical case. In the acoustic case the generation of the second harmonic takes place together with the nonlinear effects on the fundamental mode. The case in which the second harmonic can be neglected is first studied and it is shown that "dispersive" bistability can be obtained in an acoustic resonator on the fundamental mode. Bistability effects are also found on the second harmonic in cases in which its generation cannot be neglected. The most interesting crystals for experimental observation are piezosemiconductors, and some numerical estimates are given for InSb.

We study the semiclassical equations for a laser with a saturable absorber in the mean-field limit, assuming homogeneously broadened two-level atoms, for a set of parameters where the system displays optical bistability and time-periodic solutions. In the first part the bifurcation diagram for stationary and periodic solutions is obtained by numerical integration. Two different classes of stable periodic solutions arise: small-amplitude solutions and passive $Q$ switching. We observe hysteresis domains involving up to three solutions (stationary and/or periodic). We also discuss the validity of some standard approximations and show that even in the absence of detuning the phases play an important role. We also discuss the influence of the initial conditions whose symmetry properties induce important modifications of the bifurcation diagram. In the second part we introduce an alternative adiabatic elimination scheme which allows us to construct the small-amplitude periodic solutions over nearly their whole range of existence. We then study these solutions near the Hopf bifurcation from which they emerge and derive analytic conditions for their stability. When they are stable, $\stackrel{\mathrm{´}}{\mathrm{w}}$e also give the conditions under which a secondary Hopf bifurcation will occur, leading to quasiperiodic solutions.

In the preceding paper we have analyzed the bifurcation diagram of the steady and time-periodic solutions of the lasers with saturable absorbers (LSA) equations. However, a study of the experimental results presented in the literature indicates that, in general, the control parameter is a slowly varying function of time. In this second paper we analyze the influence of this time dependence on the bifurcation diagram of the LSA. We show that the stability changes of the slowly varying steady-state solutions do not correspond to their bifurcation or limit points in the case where all parameters are constant. In particular, we show that the zero-intensity state can be stabilized during a certain interval of time and that this stabilization can be controlled by the initial value of the time-dependent bifurcation parameter.

We develop a theory to take into account the effects in coherent propagation of a small overlapping of the pump and probe pulses in a three-level system. The Maxwell equations reduce to coupled equations for variables which are related to the time-integrated field envelopes. We make comparisons of the propagation results to the Burnham-Chiao theory for a two-level amplifier and can predict when this theory breaks down. An application to superfluorescence is presented where a lengthening of the delay time is found. We treat Doppler broadening and find simplified equations in two cases: (a) a very broad line and (b) a very narrow line where the initial and final states are degenerate. For the broad-line case, with an appropriate choice of initial parameters, we can make the probe pulse approach any desired area for certain configurations of the levels.

The theory of line shapes in monomode weak-gain gas lasers which we have developed recently shows that asymmetries of Lamb dips are governed by opposite lens effects which arise from population and saturation inhomogeneities. The competition between these effects depends on the geometrical characteristics of the laser. It is our aim in this paper to illustrate experimentally this fact with the 3.39-μm line of a He-Ne laser. To get a strongly diverging beam we have chosen a quasihemispheric resonator whose length (57 cm) almost equals the radius of curvature of the concave mirror ($R=60\mathrm{}$ cm). The amplifying tube is about 20 cm long and is placed on the side of either the plane or the concave mirror, thus allowing us to vary the saturation inhomogeneity. In the first case the inhomogeneity is stronger and causes the maximum of intensity to be on the low-frequency side of the line, while in the second case population and saturation inhomogeneities are of the same order. We have repeated the experiment with two tubes having different internal diameters (8 and 4 mm) in order to vary the population effects. In the case of the narrower tube one observes a gradual passage from a low- to a high-frequency type of asymmetry when the discharge current is increased. This observation is explained by an increase of the lens effect due to saturation which overcomes the one due to population. Applying our previously developed theoretical methods, we find the results in qualitative agreement with these experiments.

The effects of nuclear forces (in contrast to pure Coulomb interaction) on the ion heating rate which results from small-angle scattering processes between charged particles in plasmas are investigated within the framework of Fokker-Planck theory. These effects are included through the addition of analytic Coulomb-nuclear interference and nuclear elastic cross sections in the scattering integrals of the dynamical friction coefficient and dispersion tensor. It is found that corrections to traditional Fokker-Planck predictions of the ion-ion energy exchange rate can be calculated and that these corrections are sensitive to the choice of the maximum scattering angle defining the cutoff between small- and large-angle scattering.

Diffusion in steady fluid flow through a porous medium with large fluctuations in the pore diameters is studied. For incompressible fluids, there are singular corrections to hydrodynamics in three dimensions and logarithmic divergences in $d=2\mathrm{}$. When the constraint of incompressibility is relaxed, we recover recent results for diffusion in a random environment.

de Gennes gave a three-parameter representation of strain energy in a cholesteric liquid crystal that is second order on the $Q$ tensor, and hence in order parameter. He discarded a term involving an elastic constant $K_{24}$ which is relevant at surfaces and disclinations. The splay and bend elastic constants $K_{11}$ and $K_{33}$ are alike in the second-order theory. The complete Oseen-Frank expression in terms of a director has five parameters, including $K_{24}$. If uniaxiality, which is implicit in the director theory, is imposed on the $Q$ tensor, five independent third-order tensor functions are found. These differentiate between $K_{11}$ and $K_{33}$ and show the third-order dependence of the Oseen-Frank elastic constants on order parameter. Numerical values of these second- and third-order elastic coefficients of 4-methoxybenzylidene-4′-$n$-butylaniline (MBBA), $p$-azoxyanisole (PAA), and E-7 (British Drug House designation of a cyano-biphenyl mixture) are obtained from published values of the dependence of Oseen-Frank elastic constants and various anisotropies on temperature, and from a relation of Nehring and Saupe.

Dissipative dynamical systems with two competing frequencies exhibit transitions to chaos. We have investigated the transition through a study of discrete maps of the circle onto itself. The transition is caused by interaction and overlap of mode-locked resonances and occurs at a critical line where the map loses invertibility. At this line the mode-locked intervals trace up a complete devil's staircase whose complementary set is a Cantor set with fractal dimension $D\sim 0.87$. Numerical results indicate that the dimension is universal for maps with cubic inflection points. Below criticality the staircase is incomplete, leaving room for quasiperiodic behavior. The Lebesgue measure of the quasiperiodic orbits seems to be given by an exponent $\beta \sim 0.35$ which can be related to $D$ through the scaling relation $D=1-\frac{\beta }{\nu }$. The exponent $\nu$ characterizes the cutoff of narrow plateaus near the transition. A variety of other exponents describing the transition to chaos is defined and estimated numerically.

We have studied the transition to chaos caused by interaction and overlap of resonances in some condensed-matter systems by constructing and analyzing appropriate return maps. In particular, the resistively shunted Josephson junction in microwave fields and charge-density waves in rf electric fields may be described by the differential equation of the damped driven pendulum in a periodic force. The two-dimensional return map for this equation is shown to collapse to a one-dimensional circle map in a parameter regime including the transition to chaos. Phase locking, noise, and hysteresis in these systems can thus be understood in a simple and coherent way by taking over theoretical results for the circle map, some of which were derived in the preceding paper. In order to understand the contraction to one dimensionality we have studied the two-dimensional Chirikov standard map with dissipation. A well-defined transition line along which the system exhibits circle-map critical behavior was found. At this line the system is always phase locked. We conclude that recent theoretical results on universal behavior can readily be checked experimentally by studying systems in condensed-matter physics. The relation between theory and experiment is simple and direct.

We investigate the connection between two recent investigations on flux-periodic effects in one-dimensional normal-metal rings with inelastic diffusion length larger than the size of the ring. Büttiker, Imry, and Landauer have pointed out that closed rings, driven by an external flux, act like superconducting rings with a Josephson junction, except that $2e$ is replaced by $e$. Gefen, Imry, and Azbel considered such a ring connected to current leads and found a flux-periodic electric resistance. We establish a connection between these Aharonov-Bohm-like effects by demonstrating that the transmission probability of the ring, which determines the electric resistance, exhibits resonances near the energies of the electronic states of the closed ring. It is the flux dependence of the resonances which gives rise to the strong oscillatory behavior of the electric resistance.

The results of optical rotatory dispersion (ORD) measurements in the third cholesteric blue phase (BP III) are reported for both pure compounds and mixtures. The spectra possess weak, broad, anomalous regions at short wavelength, the sign and wavelength dependence of which follows the sense and pitch of the cholesteric helix. A temperature-pitch phase diagram for the alkyl esters of cholesterol is presented which, together with the calorimetric measurements of others, indicates that the BP III—isotropic transition is in fact the liquid crystal to isotropic liquid transition. In addition, the ORD measurements reported here provide evidence for a BP III structure which lacks longrange periodic order.

The relationship between Weinhold's metric geometry and the Riemannian geometry of thermodynamics is presented.

The elastic-distortion free-energy density of biaxial nematics is derived with use of the formalism of tensor analysis. The macroscopic description of biaxial nematics involves 12 bulk elastic constants. The appearance of chirality introduces an additional number of 5 twist terms.

We evaluate the electric microfield distribution in a multicomponent plasma (MCP). The method employed is an adaption of the very simple adjustable-parameter exponential approximation previously developed for one-component plasmas (OCP). We also discuss a still simpler approximation in which the MCP is replaced by an effective OCP. The results are generally close to each other and the former is in very good agreement with computer simulations.

Using the renormalization-group method, numerical results, and analytical arguments, we obtain the universal metric properties of one-dimensional iterated maps which exhibit period doublings. Such maps can be classified according to their behaviors around the extremum. For maps with the extremum (at $x=0\mathrm{}$) of the symmetric form $f\left(x\right)\mathrm{}\sim {\left|x\right|}^{z}b\left(x\right)\mathrm{}$, with $z>\mathrm{}1\mathrm{}$, where the function $b\left(x\right)\mathrm{}$ modifies ${\left|x\right|}^z$ by less than any power of $\left|x\right|$, the quantitative universal properties of the perioddoubling approach to chaos is described for asymptotically large $n$, by ${\delta }_n=\frac{({\lambda }_n-{\lambda }_{n-1\mathrm{}})}{({\lambda }_{n+1\mathrm{}}-{\lambda }_n)}=\delta [1+\epsilon \mathrm{}(n\left)\mathrm{}\tau \ln \alpha \right]$ and ${\alpha }_n=\frac{-d_n}{d_{n+1\mathrm{}}}=\alpha [1+\epsilon \mathrm{}(n\left)\mathrm{}\kappa 1\mathrm{n}\alpha \right]$, where ${\lambda }_n$ is the value of the parameter at the $n$th period-doubling bifurcation, $d_n$ is the typical distance from the extremum at the $n$th bifurcation point, and $\epsilon \mathrm{}\left(n\right)={\left[\frac{\partial \ln b\left(x\right)\mathrm{}}{\partial \ln \left|x\right|}\right]}_{\mathrm{}\left|x\right|\mathrm{}\sim {\alpha }^{-n}}$, where terms of order $n^{-2\mathrm{}}$ are neglected. Here $\delta$, $\alpha$, $\kappa$, and $\tau$ are all functions of $z$ only; they obey the relations $\frac{d\ln \alpha }{\mathrm{dz}}=\kappa \ln \alpha$ and $\frac{d\ln \delta }{\mathrm{dz}}=\tau \ln \alpha$, where $\alpha$ and $\delta$ are the Feigenbaum constants. In particular, for $f\left(x\right)\mathrm{}\approx {\left|x\right|}^z{\left|\ln \right(x^2\left)\right|}^p {\left|\ln \right|\ln \left(x^2\right)\left| \right|}^q\cdots$, where $z>\mathrm{}1\mathrm{}$, then $d_n\approx {\alpha }^{-n}{n}^{\kappa p}{\left(\ln n\right)}^{\kappa q}\cdots$ and ${\lambda }_{\infty }-{\lambda }_n\approx {\delta }^{-n}{n}^{\tau p}{\left(\ln n\right)}^{\tau q}\cdots$, where ${\lambda }_{\infty }$ is the critical value of the parameter beyond which is chaos. For $z=2\mathrm{}$, $\alpha =2.502\mathrm{}91$, $\delta =4.669\mathrm{}20$, $\kappa =-0.444\mathrm{}53$, and $\tau =0.369\mathrm{}54$. For the sake of completeness, an analysis of maps with asymmetric extrema is also presented. In this case, $\alpha$ and $\delta$ are functions of $z$ as well as the size of the asymmetry.