A formal investigation of the redistribution of weak near-resonance radiation is presented for the case that the radiative transitions of the scattering atom occur between two well-separated groups of states. The lower states are assumed stable while the upper states are allowed to undergo arbitrary interactions with an environment. If the lower states are also degenerate, a Rayleigh component which is infinitesimally narrow in the atom's rest frame is shown to exist under extremely wide conditions and independent of the approximations made in previous work on redistribution. Like the absorption profile, the intensity of this component as a function of the detuning (Rayleigh response function) can be expressed in terms of the mean atomic time evolution operator projected on the upper-state manifold. As compared to the absorption profile, however, the Rayleigh response function is different in shape and may provide complementary information on the scattering medium.

Theoretical atomic parameters calculated with the q$Z$-expansion method and with the multicon-figuration Thomas-Fermi model set were recently reported and used in the analyses of dielectronic satellite spectra of hydrogenlike titanium observed from the Princeton Large Torus tokamak discharges. A comparison of our calculations, based on the Hartree-Fock-Slater atomic model, with the other two theoretical results show reasonable agreement with $n=2\mathrm{}$ satellites but systematic and sometimes significant differences are found for $n=3\mathrm{} \mathrm{and} 4$ satellites.

We examine phase separation of immiscible fluid mixtures in shear flow. Far from the critical point there are two regimes depending on the Reynolds number of the velocity field induced by surface tension. Near the criticality, domains are strongly anisotropic in the strong shear case.

A new approach for estimating small quantum tunneling rates by Monte Carlo calculation is proposed and demonstrated on a simple one-dimensional model. The application to many-body situations such as atomic exchange in solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is discussed.

We have investigated the origin of sidebranching in interfacial dynamics by considering the growth of a Saffman-Taylor finger with anisotropy. We find that in the absence of noise there are no sidebranches. White noise and periodic noise produce well-defined sidebranching.

We present a Hamiltonian system of two nonlinearly coupled oscillators which exhibits, as the coupling parameter is varied, a finite or infinite number of unstable and stable regions, depending on the initial condition. For two particular types of initial conditions, we present an analytic solution that describes the nature of the stable and unstable motions of this system, locates precisely the stability-instability transition points, and determines the behavior of the largest Lyapunov exponent near these transition points.

A new simple model for the evolution of the profile of a growing interface is presented. The model corresponds to diffusion-limited aggregation without branching; computer-simulation results indicate that it has nontrivial scaling features. A theoretical estimate of the exponent which can be systematically improved is presented. This treatment also yields an implicit proof of scaling.

A prototype model of nonlinear driven oscillators with a limit cycle is studied. In the fast-relaxation limit dynamics can be reduced to a one-dimensional mapping. The systematics of periodic orbits is investigated.

Magnetic susceptibility measurements are reported for the ternary system potassium laurate, 1-decanol, and ${\mathrm{D}}_2$O below the reentrant isotropic-nematic phase transition. The susceptibility was found to diverge with increasing temperature and exhibit a mean-field-like exponent. The results are analyzed and discussed in terms of micellar anisometry controlling the supercooling temperature and thus driving the reentrant transition.

The dynamics of bulk molecular reorientation in ferroelectric liquid crystals (FLC's) are modeled by a continuum of elastically coupled, overdamped, massless ferroelectric dipoles under the influence of an external electric field. Numerical solution of this system's equation of motion in one dimension shows that reorientation in response to an applied field step can proceed via the propagation of a solitary wave of universal shape and velocity. Application of the model to an initially helixed configuration shows that solitary waves reorient the bulk only if the applied field is strong enough that its relaxation length is shorter than $\frac{1}{30}$ of the helix pitch. Comparison of our calculations with previous experimental study of the optical response of an FLC indicates that the experimental results cannot be explained by these solitary waves.

Quantum-defect theory relies first and foremost on its characterization of long-range field solutions in terms of smoothly varying phase and amplitude parameters. We consider in detail some examples of long-range potentials for which this characterization is not known analytically, and we show that Milne’s phase-amplitude procedure determines these parameters simply and efficiently. Provided the boundary condition on the Milne amplitude function alpha(r) is chosen in an optimal fashion, all of the long-range field parameters vary smoothly with energy and radius.

Continuous (in time) measurements can be introduced in quantum mechanics by using operation-valued measures and quantum stochastic calculus. In this paper quantum stochastic calculus is used for showing the connections between measurement theory and open-system theory. In particular, it is shown how continuous measurements are strictly related to the concept of output channels, introduced in the framework of quantum stochastic differential equations by Gardiner and Collet.

The purpose of this paper is to obtain a Lie algebra with the property that suitable linear combinations of its basis operators are ladder operators for the quantum number l in the eigenkets ‖nlm〉 of the nonrelativistic Coulomb problem. By analogy with the way in which the Pauli-Lenz operator A is constructed from the classical Laplace-Runge-Lenz vector ${\mathrm{A}}_c$, we deduce a new Hermitian vector operator B as a quantum-mechanical analog of a conserved classical vector ${\mathrm{B}}_c$ which is orthogonal to ${\mathrm{A}}_c$ and the orbital angular momentum L, and has the property $B_c$=$A_c$. Apart from a standard modification, B→${\mathrm{B}}_c$ as ħ→0. We show that the combination A+iB provides abstract ladder operators for the quantum numbers l, and l and m, and we calculate the coefficients for these transformations. The operators L and B are a basis for a Lie algebra which is the same as that of L and A, namely, O(4). The Hermitian operators H, $B_z$, and $L_z$ are a set of commuting operators and we determine the corresponding eigenvalues and eigenkets. Finally we show that the ten operators A, B (both suitably modified), L, and (${ħ}^{\mathrm{-}2}$${\mathrm{L}}^2$${+(1/4))}^{1/2}$ can be combined to form a Hermitian basis for a Lie algebra, the de Sitter algebra O(3,2).

Energies of the singlet states of the doubly charged chlorine cation have been determined experimentally by the technique of double charge transfer, and are compared with the results of multireference single- and double-excitation configuration-interaction calculations. The good agreement obtained permits an assignment of all the peaks in the experimental spectrum, and confirms the accuracy of these calculations, which also predict energies of the unobserved triplet states. The experimental spectrum due to single charge transfer is explained in terms of the photoelectron spectrum.

Multiconfiguration Hartree-Fock calculations with Breit-Pauli relativistic corrections are reported for the metastable core-excited quartet states 2$p^5$3s3p, 2$p^5$3s3d, and 2$p^5$3s4s in Na i and Mg ii, and also for 2$p^5$3$p^2$ in the latter. Both correlation and relativistic effects play an important role, as expected, but in addition it was found that term dependence of the radial functions was important. In Na i the latter tended to reduce the mixing of the different terms. Lifetime determination of the odd quartets included decay to 2$p^5$3s3p, 2$p^6$3s, and 2$p^6$3d levels as well as autoionization. The resulting lifetimes of several levels in Na i are in somewhat better agreement with experiment than those reported from other theories.

Galilean time in nonrelativistic quantum theory and historical time in parametrized relativistic quantum theories such as the four-space formulation are examined. Clear physical distinctions are drawn between Galilean time, Minkowski time, and historical time. Minkowski time is the temporal coordinate of a space-time four-vector. Galilean time and historical time are evolution (ordering) parameters in their respective theoretical frameworks. Using N-body formulations, a physically unambiguous procedure for measuring evolution parameters in terms of familiar observables is presented. The procedure is illustrated by the design of a simple evolution-parameter clock.

A complex-coordinate rotation has been applied to the standard Hartree-Fock equations, in order to form a complex-rotated Hartree-Fock procedure. The resulting complex differential equations were solved by direct numerical integration. This method was then used to study the position and width of the ${}_{}{}^2{}_{}{}^{}\mathrm{P}$ shape resonance in ${\mathrm{Be}}^{\mathrm{-}}$. The results were found to be quite independent of the value of the rotation angle theta for theta greater than the value at which the complex pole was uncovered.

Transition matrix elements and oscillator strengths are calculated for various transitions between discrete levels of the neutral Li atom in the Dirac-Fock approximation, in the ‘‘length’’ and ‘‘velocity’’ forms, using nonlocal effective currents determined from quantum field theory. The matrix elements and oscillator strengths are shown to be numerically equal in the two forms, for this specific example, thereby verifying a previously given general proof of this equality.

The mutual consistency and structural interconnection between the Wentzel-Kramers-Brillouin (WKB) and Wigner-Kirkwood (WK) semiclassical approximations is investigated for nonrelativistic N-particle systems, with mutual scalar interactions and coupling to an external time-varying electromagnetic field. The generalized WK expansion of the propagator 〈x‖U(t,s)‖y〉 is obtained from a large-mass expansion of the higher-order WKB approximation. Two techniques are described for computing the WK coefficient functions. One relies on a large-mass expansion of classical paths and the transport representation of the WKB approximation; the other is recursive in nature. For time-independent Hamiltonians H the standard WK expansion of the heat kernel 〈x‖$e^{\mathrm{-}\beta H}$‖y〉 is recovered.

The role played by clock synchronization procedures for coordinate transformations which account for time dilation and length contraction is discussed. Special relativity is here compared with the ether theory based on the Tangherlini transformations. These transformations are shown to be theoretically distinguishable from the Lorentz ones by means of an internal synchronization procedure which makes use of rods kept in contact with a rotating disk. This procedure makes it possible, in principle, to measure the one-way velocity of light and to test the theories. First-order experiments confirm special relativity and rule out the ether theory.