The branching ratio between the one-electron–one-photon and two-electron–one-photon transitions in doubly ionized K shells has been evaluated using an equivalent two-particle model with wave functions including angular correlations and relaxation in the length and velocity gauges. The accuracy of the results (choice of screening parameters and gauge dependence) will be discussed.

The atomic superradiant emission is treated in the single-particle mean-field approximation. A single-particle Hamiltonian, which represents a dressed two-level atom in a radiation field, can be obtained and it is verified that it describes the transient regime of the emission process. While the line-shape emission for a bare atom follows the ${\mathrm{sech}}^2$ law, for the dressed atom the line shape deviates appreciably from this law and it is verified that the deviation depends crucially on the ratio of the dynamic frequency shift to the transition frequency. This kind of deviation is observed in experimental results.

We report the results of a theoretical study of resonant vibrational excitation of formaldehyde by low-energy electrons. The cross sections were calculated by using a one-dimensional complex-potential model. The electronic resonance energies and decay widths needed in this treatment were extracted from fully ab initio scattering calculations carried out using the complex Kohn variational method at a number of different values of the C-O bond distance. The substructure observed in the calculated cross sections is in reasonably good agreement with the available experimental data.

Photoconductivity in Xe due to a ${\mathrm{CH}}_3$I impurity is presented as a function of incident photon energy at Xe number densities with range (3–15)×${10}^{19}$ ${\mathrm{cm}}^{\mathrm{-}3}$, with constant ${\mathrm{CH}}_3$I concentrations. The Xe absorption spectrum between 9.5 and 10.6 eV, including both the strongly perturbed allowed transitions and molecular bands associated with forbidden lines, appears as dips in the photocurrent. At photon energies below 9.5 eV the photocurrent increases exponentially with photon energy, and members of the nd and ns Rydberg series of ${\mathrm{CH}}_3$I appear as steps. From the shift of the step positions with density the electron scattering length in xenon was determined as a=-0.324 nm. The photocurrent versus photon energy curves shift more strongly with density than the superimposed Rydberg lines as a consequence of adiabatic polarization effects. The results provide clear evidence that photoconduction below the vertical ionization potential takes place by ionization of Rydberg states.

We report the results of a computer simulation of neutral atoms trapped in a magnetic quadrupole trap formed by two coils carrying opposite currents. Effects of hyperfine structure have been neglected. We conclude from this study that approximately a quarter of the particles are initially trapped in stable orbits and the successive later loss of particles due to the nonadiabatic region is insignificant.

We calculate the effect of a weak gravitational field on a resonator of length L bounded by two phase-conjugating mirrors. The phase-conjugating mirrors are pumped by separate laser sources having identical proper frequencies. When the resonator is injected with a continuous optical wave, the output pulsates at a repetition rate given by twice the gravitational redshift frequency for the distance L.

The coherent transient signal emitted when a sample of two-level atoms is irradiated by a sequence of two fluctuating pulses is discussed. The pulses have bandwidth ${\mathrm{\tau }}_{\mathit{c}}^{\mathrm{-}1}$. They are correlated with one another, and have a relative delay time ${\mathit{t}}_{12}$. It is shown that for strong excitation pulses the transient signal, as a function of ${\mathit{t}}_{12}$, can exhibit a peak of width of order ${\mathrm{\tau }}_{\mathit{c}}$. This peak is found to disappear when the Doppler width of the atomic ensemble becomes sufficiently large, in qualitative agreement with existing experimental data.

Solitons are generated in stimulated Raman scattering using a π phase shift of a weak Stokes input field; diffraction effects are retained in the calculation. For strong diffractive coupling, we observe an on-axis increase in both the laser and the Stokes intensities and a corresponding narrow transverse profile for both fields; these results are elucidated and explained.

We present a general technique for the numerical calculation of the behavior of an electron in an intense laser field, by the direct integration of the time-dependent Schrödinger equation in the Kramers-Henneberger frame. We give results for a model potential; these include above-threshold ionization spectra for the transition regime to over-the-barrier escape. We also show how satellite spectra can develop in long pulses.

In this paper a periodically driven, bistable system with additive noise is considered in the overdamped limit. Here we have adopted the probability density of residence times as the tool for dynamical studies on the system. We contrast this to the body of previous work, in the area now known as ‘‘stochastic resonance,’’ wherein the power spectral density was the preferred physical quantity. It is shown, both by analytic theory and by analog simulations, that the density of residence times has a detailed structure reflective of the inherent symmetries of the system. Closed-form expressions are developed for the distribution function as well as for several averaged quantities of interest. It is emphasized that all our analytic results predict observable physical quantities, which are then demonstrated with measurements on the analog simulator.

The π/3-rhombus billiard is an example of the simplest pseudointegrable system having an invariant integral surface of genus g=2. We examine the fluctuation properties of eigenvalue sequences belonging to the ‘‘pure rhombus’’ modes (the eigenfunctions take nonzero values on the shorter diagonal). The nearest-neighbor spacing statistics follow the Berry-Robnik distribution with a chaotic fraction ν¯ (corresponding to the Liouville measure of the chaotic subspace) equal to 0.8. The spectral rigidity closely agrees with such a partitioning of phase space. The nodal patterns and the path correlation function exhibit irregularity for most of the corresponding eigenfunctions. Though the amplitude distributions for these closely approximate a Gaussian distribution, the spatial correlations do not agree well with the well-known Bessel oscillations. A few eigenfunctions, however, show regularity. These are localized in those regions of configuration space where the bouncing-ball modes form rectangular bands. The Born-Oppenheimer approximation offers a suitable explanation in terms of a confining potential, and the agreement between the exact and adiabatic eigenvalues improve at higher energies. On the basis of these observations, it turns out that the quantities ν and ν¯ are, in fact, the fractions of regular and irregular states in the eigenvalue sequence under consideration. Thus irregular eigenfunctions do occur for systems with zero Kolmogorov entropy, and the eigenvalue sequence corresponding to these yield Gaussian orthogonal ensemble statistics.

A method is presented for studying hard-disk systems by Monte Carlo computer-simulation techniques within the NpT ensemble. The method is based on the Voronoi tesselation, which is dynamically maintained during the simulation. By an analysis of the Voronoi statistics, a quantity is identified that is extremely sensitive to structural changes in the system. This quantity, which is derived from the edge-length distribution function of the Voronoi polygons, displays a dramatic change at the solid-liquid transition. This is found to be more useful for locating the transition than either the defect density or the pressure-area isotherm.

The Helmholtz free energy is computed for an ensemble of initial conditions for a one-dimensional particle falling down a staircase potential, while in contact with a thermal reservoir. Initial conditions are chosen from the equilibrium canonical ensemble, with the gravitational field applied either as a step function (steady field) or a δ function (pulsed perturbation). The first case leads to a fractal steady-state distribution, while the second case leads to relaxation of a perturbed distribution back toward equilibrium. Coarse-graining is applied to the computation of the non- equilibrium entropy, with finer resolution in phase space accompanied by an increase in the number of trajectories. The limiting fine-grained (continuum) prediction of the Liouville equation is shown to be consistent with the numerical simulations for the steady state, but with incredibly slow (logarithmic) divergence appropriate to a lower-dimensional fractal distribution. On the other hand, simulations of the relaxation process show little or no sign of converging to the prediction obtained from the Liouville equation. Irreversible phase-space mixing of trajectories appears to be a necessary modification to the Liouville equation, if one wants to make predictions of numerical simulations in nonequilibrium statistical mechanics.

We report a study of the relaxation process of Bak-Tang-Wiesenfeld’s sand pile under uniform initial conditions. For most geometries and initial conditions the final states consist of intricate geometric patterns, some of which are self-similar. Even without randomness, the flow of sand during relaxation often displays 1/f behavior, and this arises from interactions between the diffusive flow and the development of the final pattern.

We prove that the quasienergy spectrum of the kicked quantum rotator model with separable potential that has been recently introduced by Combescure [J. Stat. Phys. 59, 679 (1990)] is singularly continuous under certain conditions. The time evolution of this system is numerically investigated in detail.

We propose a non-Markovian extension of the Lévy walk model of Shlesinger and Klafter [Phys. Rev. Lett. 54, 2551 (1985)], termed self-avoiding Lévy walk, to study a polymer configuration having a broad persistance length distribution. We use the Flory-type argument in a manner analogous to the self-avoiding walk and the self-avoiding Lévy flight schemes to include the excluded-volume effect and find that the Flory exponent ${\nu }_{\mathit{F}}$ varies continuously from the flexible limit [${\nu }_{\mathit{F}}$=3/(d+2)] to the stiff limit (${\nu }_{\mathit{F}}$=1), when the spatial dimension d and the Lévy index μ are varied. We also discuss the fractal dimensions and the morphology of Lévy walks in comparison with the Lévy flights.

We study the self-organizing behavior exhibited in a Bonhoffer–van der Pol–type equation in the following form for the activator u(x,t) and the inhibitor v(x,t): ετ${\mathrm{\partial }}_{\mathit{t}}$u=${\mathrm{\epsilon }}^2$${\mathrm{\partial }}_{\mathit{x}}^2$u+f(u)-v and ${\mathrm{\partial }}_{\mathit{t}}$v=${\mathrm{\partial }}_{\mathit{x}}^2$v+u-γv, where ε, τ, and γ are positive constants and f(u) has a cubiclike nonlinearity. The above set of equations admits a spatially periodic solution where the excited and the rest domains are arrayed alternatively. For small values of τ, these domains are found to undergo sustained oscillation. We employ a singular-perturbation method in the limit ε≪1 to derive the equation of motion for the domain boundaries (interfaces). Two interfaces separated from each other can interact through the diffusion current of v. The bifurcation from the nonoscillatory to the oscillatory state is investigated based on this interface equation of motion. We show that, when the nonoscillatory state loses its stability, an in-phase motion of domains emerges first in a wide range of the parameters.

We propose a new statistical-mechanical formalism to extract the multifractal structure from intermittent phenomena. A simple stochastic model reproducing universal properties of intermittency is solved rigorously, and phase transitions associated with the spectrum of the generalized entropies are studied. We also apply the formalism to the logistic map near the critical point for a period-three cycle. The results are in good agreement with numerical results.

The effective-potential expansion method, namely, a variational approach to the many-body problem at zero temperature, is extended to nonzero temperatures by the introduction of a new trial density matrix in the Gibbs variational principle for the grand potential Ω. The trial density matrix contains an effective potential as a variational parameter. We have given an expansion form for Ω in terms of the effective potential. Special care is taken to evaluate the entropy term correctly.

A one-dimensional many-electron system with a repulsive δ-function interaction is studied by the application of the variational method developed in the preceding paper [Takada and Kita, Phys. Rev. A 42, 3242 (1990)] in order to illustrate its actual implementation. Our results on the grand potential, the entropy, and the specific heat are compared in detail with the exact ones that are calculated by the numerical solution of the coupled integral equations obtained by the Bethe ansatz.