In this paper, the order-α contributions of the self-energy and outer-vertex graphs to the decay rate of orthopositronium in the Fried-Yennie gauge are obtained in analytic form.

Simple and accurate upper bounds to the exact atomic kinetic energy in terms of density functionals, in particular, the Thomas-Fermi kinetic-energy functional ${\mathit{T}}_0$ and the expectation value 〈${\mathit{r}}^{\mathrm{-}2}$〉=4π${\mathcal{F}}_0^{\mathrm{\infty }}$ρ(r)dr are derived.

An extension of work by Drake [Phys. Rev. A 18, 820 (1978)] to the treatment of radial and angular integrals occurring in N-electron systems is presented. It is shown that the essential results pertaining to two-electron systems adapted to Hylleraas coordinates also apply to many electrons when pairs of electrons are chosen to interact with each other in a spin-adapted basis set. These results are derived using graphical-analysis techniques in the context of the unitary-group approach.

Angular distributions of free electron-positron pairs produced in relativistic ion-atom collisions are calculated within a first-order Born approximation. The electron and positron continuum states in the field of the high-Z target nucleus are described by relativistic Sommerfeld-Maue wave functions. The cross-section dependence on the polar angles and on the lepton energies is calculated for several experimentally relevant cases. The azimuthal anisotropy for given polar angles is also presented.

We present a method for calculating the spectrum emitted by an atom in an intense laser field. This method is based on the direct use of the acceleration of the atomic electron rather than the dipole moment of the atom. We show, using a numerical calculation in one dimension, that this method produces a more exact numerical evaluation of the spectrum. This technique is particularly important in determining the background to the high harmonics emitted by the atom.

Computer simulations of nonlinear quantum-dynamical systems have presented several unexpected difficulties, such as divergences. Using s-order positive-quasiprobability representations for the problem of a nonlinearly damped interferometer, it is found that the divergences disappear for s=2/3.

The possible forms the intensity dependence of the nonlinear refractive index would have to take for bistable light bullets to exist are examined. Bistable light bullets are propagating spheroidal optical solitons characterized by different sizes and intensity profiles but with the same energy.

The q-deformed quantum oscillator for q=${\mathit{e}}^{\mathit{i}2\mathrm{\pi }/(\mathit{s}+1)}$ has reducible representations that admit unitary phase operators. In the classical limit s→∞, of zero deformation, they provide the phase angles of the ordinary quantum oscillator. The formalism is applied to the master equation of a q-deformed laser mode that is introduced and solved in the steady state and then used to evaluate the statistical moments of the cosine and sine operators.

We examine the issue of determining an acceptable minimum embedding dimension by looking at the behavior of near neighbors under changes in the embedding dimension from d→d+1. When the number of nearest neighbors arising through projection is zero in dimension ${\mathit{d}}_{\mathit{E}}$, the attractor has been unfolded in this dimension. The precise determination of ${\mathit{d}}_{\mathit{E}}$ is clouded by ‘‘noise,’’ and we examine the manner in which noise changes the determination of ${\mathit{d}}_{\mathit{E}}$. Our criterion also indicates the error one makes by choosing an embedding dimension smaller than ${\mathit{d}}_{\mathit{E}}$. This knowledge may be useful in the practical analysis of observed time series.

A resonancelike phenomenon in a class of bistable oscillators driven by a periodic dichotomous noise process is described. The phenomenon manifests itself as fractal trajectory patterns in the phase plane of the Poincaré map of the flow. The nature of these discrete stochastic trajectories depends on damping and the bias and sharpness of the periodic noise process. In the underdamped regime the map shows self-similar spirals and other intrinsically two-dimensional patterns, whereas in the overdamped regime a one-dimensional description is possible. This one-dimensional map dynamics depends on the contraction factors ${\lambda }_{0,1}$ for the two map branches. For strong damping ${\lambda }_0$+${\lambda }_1$<1, and the dynamics produces an invariant measure, on a Cantor set, whose scaling properties depend on the bias. For weaker damping ${\lambda }_0$+${\lambda }_1$>1, and the map allows periodic orbits that induce multifractal-invariant measures. Infinite lattice families of such periodic orbits exist in the ${\lambda }_{0\mathrm{-}}$${\lambda }_1$ plane, and we examine the properties of one such lattice family. In experimental realizations, fluctuations in the periodicity of the dichotomous noise process produce parametric noise in the Poincaré map, and the dynamics of such a noisy map is studied with respect to scaling properties and self-similarity in the invariant measure.

For periodically driven damped oscillators with the ability to escape from a potential well, the erosion of the nonescaping basin of attraction begins at the homoclinic tangency of the stable and unstable manifolds of the hilltop saddle cycle. The consequent rate of erosion, however, is intrinsically dependent upon the manifold organization, which to a large extent is determined by the heteroclinic events following the homoclinic tangency. In this paper we outline how, under small parameter changes, there can exist a rapid erosion of the nonescaping basin.

An analysis is presented of the kinetics of irreversible adsorption of k-mers on a line in which attempts are made to place a ${\mathit{k}}_1$- and a ${\mathit{k}}_2$-mer with probability α and 1-α. The rate equation for this process is solved in the case ${\mathit{k}}_1$=${\mathit{k}}_2$+1, and an expression is obtained for the coverage as a function of α and ${\mathit{k}}_1$.

The structure and dynamics of powders subjected to vibration are investigated by a nonsequential and cooperative computer-simulation approach in three dimensions. Starting from a microscopic model of the physics, we are able to probe independent and collective effects in the dynamics of vibrated powders, as well as in the resulting structures. In particular, we analyze the role of cooperative structures such as bridges, which are always present in reality and which cannot be formed by purely sequential processes. We look in depth at the behavior of the volume fraction and coordination number as a function of the intensity of vibration, as well as at correlation functions describing contacts between neighboring grains, also as a function of intensity. Satisfying agreement with the qualitative predictions of earlier analytic work is obtained, and a framework is laid for future investigations.

We present two alternative methods for evaluating the probability densities of structures defined by d degrees of freedom in random fields. For Gaussian random fields, both differentiable and nondifferentiable, the application of these methods is considered in detail. The relationship between structures, maxima, and connected regions above a certain level is investigated. The connected correlation functions of these objects are expressed in terms of the autocorrelation of the field.

The dynamics of a chain of N oscillators with one end fixed–a model originally invoked to describe charge-density waves–is dominated by the coexistence of a large number of attractors. One of these attractors, the minimally stable state, plays a central role. We report analytic and numerical results for the case of N=2. The model exhibits polarization phenomena and bimodal distributions of depinning times like those seen in experiments on so-called switching samples. However, the model is at odds with experiments away from threshold.

The features of various bifurcations in forced Duffing oscillators are extensively investigated by means of numerical simulation. Some common features in four types of potential well are found. With reference to the transition boundaries in parameter space, the influences of local symmetry properties of the potential well on the bifurcation routes are indicated and definite functional forms of the border line in ω-k space separating the region with simple stable period-1 solutions from the region with complicated solutions are determined. A method combining Floquet theory with harmonic balance is presented to describe the mechanism of the transitions.

Concepts from the theory of transient chaos are applied to study the classical ionization process of a one-dimensional model of kicked hydrogen Rydberg atoms. It is proved analytically that for a range of field parameters the associated classical phase space is devoid of regular islands. In this case, the fraction of atoms ${\mathit{P}}_{\mathit{B}}$(t) not ionized after time t decays asymptotically according to ${\mathit{P}}_{\mathit{B}}$(t)∼${\mathit{t}}^{\mathrm{-}\mathrm{\alpha }}$ with α≊1.65. The origin of the algebraic decay can be traced back to the fractal structure of the invariant set of never-ionizing phase-space points, and is explained by the symbolic dynamics of this system, which consists of a countably infinite number of symbols. The algebraic decay is reproduced by an analytically solvable diffusion model that predicts α=3/2. Replacing zero-width δ kicks with smooth finite-width pulses, a subset of phase space is regular. For this case we observe that ${\mathit{P}}_{\mathit{B}}$(t) shows a transition between two power-law regimes with α≊1.65 for short times and α≊2.1 for long times, where the effect of Cantori and regular islands is felt.

Dependence of the level-density fluctuations on the interaction strengths for the ${}_{}{}^{106}{}_{}{}^{}\mathrm{Ag}$ energy spectrum calculated in the interacting-boson-fermion-fermion model is investigated. Breaking of symmetry is accompanied by a rapid transition from a nearly Poissonian distribution to the intermediate pattern between Poisson and Gaussian-orthogonal-ensemble distributions. Fluctuation measures show sensitivity to details of nuclear dynamics. Possible connection with the degree of chaos is discussed.