We consider a single quantum state coupled equally to each of a set of evenly spaced quasicontinuum (QC) states. We obtain a delay differential equation for the initial-state probability amplitude, and this equation is solved analytically. When the QC-level spacing goes to zero, the initial-state probability decays exactly exponentially. For finite QC-level spacings, however, there are recurrences of initial-state probability. We discuss Tolman's "quantum-mechanical spreading" of probability and also a classical analog of our model.

It is shown that the field emitted by a free-electron laser oscillating on a single mode in the no-gain regime can exhibit antibunching. The quantum-statistical properties of field are also discussed.

A two-photon laser is modeled as $N$ two-level atoms interacting via a two-photon transition with a single resonant-cavity field mode. The quadratic form of this interaction makes such a system a candidate to exhibit reduced quantum fluctuations (squeezing) in one quadrature of the output field. A Fokker-Planck equation containing all leading quantum noise terms is derived following the method of Haken. A linearized fluctuation analysis reveals that there is no squeezing in a two-photon laser with injected signal. A small amount of squeezing may be present in two-photon optical bistability. Our calculations confirm the results of Lugiato and Strini, who adopted a factorization of moment equations.

The proton-proton pair potential for protons in a finite-temperature electron gas is calculated without making the usual approximations of second-order pseudopotential theory, linear response, etc., which are known to be untenable for protons. This is achieved by the inversion of the proton-proton pair distribution of an electron-proton plasma obtained by a full nonlinear finite-temperature density-functional calculation for the two-component system. As the latter is a spherically symmetric calculation, the method affords a means of obtaining ion-ion pair potentials in plasmas and liquid metals which go beyond second-order pseudopotential-type formulations without solving a two-center Schrödinger problem.

The nematic-hexagonal discotic phase transition is treated in the framework of the Landau theory of phase transitions. We assume the existence of an intermediate phase, separating the nematic and the hexagonal, characterized by translational invariance and sixfold rotational order around the nematic director. As order parameter for the condensation of the hexagonal phase from this intermediate phase, we use a set of complex parameters describing the onset of a triple mass-density wave in the plane orthogonal to the nematic director. The Landau free energy contains a coupling term between the director and the order parameter, arising from local invariance under simultaneous rotations of the director and of the axis of the liquid tubes. The fluctuations of the order parameter slightly above the weakly first-order phase transition give a critical contribution to the Frank elastic constants. Following the response-function method of Jahnig and Brochard, we find that splay and twist elastic constants behave as ${(T-T^{*})}^{-\frac{1}{2}}$ for $T>\mathrm{}{T}^{*}$ in the mean-field approximation and hydrodynamic regime, while bend is noncritical.

Anomalies in the degree of dissociation near a critical point of a ternary mixture are analyzed for a reaction of the type $A\rightleftarrows B+C$. The concentration-temperature curve has, at the critical point, an infinite slope ${(T-T_c)}^{-\frac{(\delta -1)}{\delta }}$, where $\delta$ is the critical index. An isobutyric acid and water mixture, which consists of four components, has the same singularity in the charge density near a critical point. In any of the anomalies in the electrical conductivity in this mixture, or in similar systems, the singularity in the charge density must be considered.

This paper provides a critical comparison of several approximate microfield distributions. Included are versions of the nearest-neighbor and next-nearest-neighbor approximations together with two approximations based on independent-perturber models. Where appropriate, results from a more complete theory will be used as reference. Monte Carlo results will be used in circumstances where the validity of the reference results are uncertain.

A molecular-dynamics study of the temperature dependence of the dynamic structure factor for liquid rubidium was made in order to clarify the role of density fluctuations in determining the stability limit of the supercooled liquid. Neutron scattering measurements on supercooled liquid gallium and on supercooled mixtures of lead and tin have led to conflicting interpretations of the temperature variation of the dynamic structure factor. The molecular-dynamics results for supercooled liquid rubidium indicate that the temperature variation of the dynamic structure factor correlates with the self-diffusion coefficient. By reexamining the data for liquid gallium we show that the experimental and the molecular-dynamics results can be given a common interpretation and that the density fluctuations are not an indicator of the limit of stability of a supercooled liquid.

The structure of the phase-locked zones in the sine map is examined. Attention is drawn to general features of the map's phase diagram and two, dynamically distinct kinds of bistability are distinguished: One type arises locally through a cusp catastrophe and the other, nonlocally, through crossing (in the parameter plane) of remote stable manifolds. Numerical work indicates that a Cantor set of cusp bistabilities and other related features forms an infinite binary tree in every Arnol'd tongue. (An infinite set of such structures lies arbitrarily close to the parameter line for the quasiperiodic transition to chaos, and also appears in other phase-locked zones.) The binary tree of features obeys the vector scaling found in the quartic map and seems to be generic for multiple-extrema, one-dimensional maps.

A model of an open system of oscillators which transmit energy from a source to a bath predicts nonthermal excitation of a single mode at sufficiently high energy flux. A nonlinear interaction between the oscillators and the bath produces this far-from-equilibrium steady state by channeling through a single mode energy which may be introduced diffusely into the system. The steady state is stable against fluctuations, and relaxation to the steady state is dominated by a single rate characteristic of the collective nature of the excitation. As predicted by Fröhlich, the model is in qualitative agreement with phenomena observed in metabolizing cells.

A recent study has demonstrated that several scales of neocortical interactions can be consistently analyzed with the use of methods of modern nonlinear nonequilibrium statistical mechanics. The formation, stability, and interaction of spatial-temporal patterns of columnar firings are explicitly calculated, to test hypothesized mechanisms relating to information processing. In this context, most probable patterns of columnar firings are associated with chemical and electrical synaptic modifications. It is stressed that synaptic modifications and shifts in most-probable firing patterns are highly nonlinear and interactive sets of phenomena. A detailed scenario of information processing is calculated of columnar coding of external stimuli, short-term storage via hysteresis, and long-term storage via synaptic modification.

A general technique is developed to calculate the poles of the Schwinger $T$ matrix. All quantities are calculated numerically including the negative-energy Green's function. A short-range potential is defined and used to calculate quantum defects for states of very high $n$ and $l$. Full exchange is included and no coupled equations are solved. This method is applied to the Rydberg states of lithium in the static-exchange approximation.

The effects of the fractal nature of intermittent fully developed turbulence on the fluctuations of passive scalars are assessed. Significant intermittency corrections to the "$\frac{2}{3}$ (-power) law" for the length-scale dependence of the structure function and other laws concerning fluctuation spectra are found. The implications of these findings on phenomena found in the context of wave propagation through turbulent media are investigated. Intermittency effect on scintillation of light sources, scattering of sound or electromagnetic waves, and fluctuations in phases and amplitudes of these waves are studied theoretically and compared to experiments.

Using the definition due to Landau, we present a closed-form expression for the optical-activity tensor for a cholesteric liquid crystal. The rotatory power is calculated in the pretransitional regime (above the isotropic-cholesteric transition), as well as in the ordered blue phase. The expression obtained for the first case reduces, in the low-chirality limit, to that of Dolganov et al. The result for the blue phase is new, and indicates the possibility of distinguishing between some of the ordered cubic structures that were recently proposed by various workers.

Sensitive volumetric measurements show a classical second-order $A-C$ transition in mixtures of $\overline{8}S5$ with $\overline{7}S5$ in agreement with findings of Schantz and Johnson for pure $\overline{8}S5$, and apparently a first-order $A-N$ transition (although an extremely weak one) for 30 and 37 mole% of $\overline{7}S5$; thus an earlier suggestion of a (critical) end point where a second-order $A-C$ line meets the border of a first-order region, $N-A$ and then $N-C$, is corroborated.

We have determined experimentally the amplitudes of the correlation length and susceptibility along the three principal trajectories: critical isochore, coexistence curve, and, for the first time in a critical mixture, critical isotherm. We have also determined the amplitude of the coexistence curve and that of the specific heat along the critical isochore. These amplitudes allowed us to compute several universal amplitude combinations, which are all in agreement with current theoretical predictions, except $\frac{C^{+}}{C^{-}}$ which agrees better with the renormalization-group value than with the high-temperature-series one. Moreover, linewidth measurements allowed us to determine the dynamic constant $R$, found to be close to unity.

A special nondegenerate perturbation theory is developed for solving the "nonlinear Schrödinger equation" of the type $[\hat{H}+\hat{V}(\Psi \left)\right]\Psi =E\Psi$, which arises, e.g., from the study of the environmental effects on molecules. The interaction operator is taken as $\hat{V}\left(\Psi \right)=\hat{A}〈\Psi \left|\hat{B}\right|\Psi 〉$. The in vacuo problem $\hat{H}\Phi =\epsilon \Phi$ is considered the zeroth-order description. For the perturbed energies and wave functions recursive formulas are derived at any order of the perturbation. The formulas obtained are compared to the usual Rayleigh-Schrödinger perturbation theory where $\hat{V}$ is supposed to be independent of $\Psi$. The formal results are applied to the case of the Onsager cavity model.

Auger rates for a mesic atom consisting of a lithium nucleus and two electrons are presented. It is shown that the results are sensitive to the screening of the initial and final state of the ejected electron by the spectator electron. These results are compared to transition rates one would obtain by following the procedure used by Burbridge and de Borde, which neglect screening of one electron by the others. Our results show a 40% reduction in transition rates.

A second-order differential equation is derived for the electric potential of an electron system with slowly varying density. It includes consistently the first-gradient corrections to both the kinetic energy and the exchange energy. In the regime of high density, the equation reduces to the one derived by Schwinger [Phys. Rev. A 24 2353 (1981)]

It has been established here that the direct transformation from electron density to electron momentum density [Phys. Rev. A 24, 2906 (1981)] is exactly identical to the locally averaged method of Lam and Platzman [Phys. Rev. B 9, 5128 (1974)] for a spherically symmetric, monotonic-decreasing atomic-electron density. However, the former approach brings out more clearly the physical features associated with the momentum density extracted from the electron density and also has the potential to effect reverse transformations.