The (e,2e) energy-separation spectrum of the 1${\mathrm{\pi }}_{\mathit{u}}$ orbital of acetylene has been measured in coplanar asymmetric kinematics for several values of the incident electron energy loss, ΔE. In the ΔE region dominated by resonant processes, a shift of the 1${\mathrm{\pi }}_{\mathit{u}}$ peak with respect to the value measured by photoelectron spectroscopy has been observed. This finding has been attributed to the change of the relative intensities of the vibrational components of the electronic transition induced by resonant processes. Moreover, a feature assigned as a molecular autoionizing transition is observed in an (e,2e) energy-separation spectrum.

We study the problem of barrier penetration in the presence of excitation degrees of freedom that at the incident energies considered are strictly closed. To this end we solve coupled-channel equations with boundary conditions that are asymptotically free only in the entrance channel. Particular aspects of the enhancements of the transmission coefficients which result from these conditions are discussed.

We have obtained a functional related to the differential Schrödinger equation that is the same as (ψ‖H-E‖ψ). By using this functional, we have shown that the variational calculation using polynomial functions is equivalent to the same calculations performed with the help of the associated Schrödinger differential equation with the same functions.

The additional vacuum-field Rabi splittings reported by Agarwal [Phys. Rev. A 43, 2595 (1991)] are explained using classical physics. The same splittings occur when a pair of classical coupled harmonic oscillators are driven by a stochastic field.

We have extended our previous studies of the trapping of alkali-atom resonance radiation to conditions where the unity optical depth points are in the quasistatic wings of the foreign-gas pressure-broadened line shape. Under these conditions, and based on the relatively simple Holstein theory, we expected to see a qualitatively different dependence of the effective radiative decay rate on pressure than is observed when the unity optical depth points are in the impact core. However, we found experimentally that the observed dependence is the same as was observed in the lower pressure limit, at least over the range of conditions we were able to access. On the other hand, these observations are found to be consistent with more accurate calculations based upon the Post theory using a recently available experimental line-shape function.

Quantum-statistical properties such as the photon-number probability distribution and sub-Poissonian distribution are studied by considering the resonant interaction of two radiation fields, one of which is in a squeezed state with a cascade-structure three-level atom. It is noteworthy to emphasize that the direction of squeezing, i.e., the angle θ, and the squeezing parameter r as well as the initial atomic state play important roles in the determination of the nonclassical behavior of the radiation field. At the same time we give a possible explanation for the effect of the ratio of the intensity of the two fields on the quantum-statistical properties.

The effect of intense laser fields on the resonant electronic-bridge process involving the isomeric E3 transition of ${}_{}{}^{235\mathit{m}}{}_{}{}^{}\mathrm{U}$, which has a photon energy of 73.5 eV, and an intermediate excitation of an electron from the P1(6${\mathit{s}}_{1/2}$) electronic shell of binding energy 71 eV is investigated for lasers of photon energies 1.16 and 2.32 eV within the intensity range ${10}^{10–}$${10}^{13}$ W/${\mathrm{cm}}^2$. It is found that in spite of the hindering effect of power broadening, the ratio η of the transition probability per unit time in the laser-assisted process to that of the laser-free γ decay can be enhanced by the intense laser field if the resonance condition is met.

We show that the Jaynes-Cummings model cannot be realized when using a strongly driven electric-dipole transition. The limitations are inherent in electric-dipole coupling and are much more severe than those recently discussed by Crisp [Phys. Rev. A 43, 2430 (1991)]. The level shifts associated with the violation of the rotating-wave approximation are roughly equal for circular and linear polarizations.

The convolution prescription given by Rhoades-Brown, Bottcher, and Strayer [Phys. Rev. A 40, 2831 (1989)] to calculate capture cross sections is critically examined. It is shown that their prescription introduces a spurious matrix element. This basically explains the discrepancy between the calculations by Rhoades-Brown, Bottcher, and Strayer and earlier results.

The differences between Baur’s approximate formalism [as presented, e.g., in C. A. Bertulani and G. Baur, Phys. Rep. 163, 299 (1988)] and the Feynman–Monte Carlo integration for electron capture in heavy-ion colliders [Rhoades-Brown, Bottcher, and Strayer, Phys. Rev. A 40, 2831 (1989)] is discussed. In particular, the use by Baur of approximate wave functions for the bound electron and continuum positron are highlighted.

The influence of colored noise on the Hopf bifurcation in a first-order delay-differential equation (DDE), a model paradigm for nonlinear delayed feedback systems, is considered. First, it is shown, using a stability analysis, how the properties of the DDE depend on the ratio R of system delay to response time. When this ratio is small, the DDE behaves more like a low-dimensional system of ordinary differential equations (ODE’s); when R is large, one obtains a singular perturbation limit in which the behavior of the DDE approaches that of a discrete time map. The relative magnitude of the additive and multiplicative noise-induced postponements of the Hopf bifurcation are numerically shown to depend on the ratio R. Although both types of postponements are minute in the large-R limit, they are almost equal due to an equivalence of additive and parametric noise for discrete time maps. When R is small, the multiplicative shift is larger than the additive one at large correlation times, but the shifts are equal for small correlation times. In fact, at constant noise power, the postponement is only slightly affected by the correlation time of the noise, except when the noise becomes white, in which case the postponement drastically decreases. This is a numerical study of the stochastic Hopf bifurcation, in ODE’s or DDE’s, that looks at the effect of noise correlation time at constant power. Further, it is found that the slope at the fixed point averaged over the stochastic-parameter motion acts, under certain conditions, as a quantitative indicator of oscillation onset in the presence of noise. The problem of how properties of the DDE carry over to ODE’s and to maps is discussed, along with the proper theoretical framework in which to study nonequilibrium phase transitions in this class of functional differential equations.

An analysis of exact enumeration data is used to estimate the location of the surface-adsorption transition for lattice trees attached to a surface. The existence of a sharp transition can be established by rigorous arguments.

Although fluctuations have been known to change the long-time behavior of homogeneous diffusion-reaction phenomena dramatically in dimensions d≤4, simulations of reaction fronts in two-dimensional A+B→C inhomogeneous systems have only shown marginal departure from mean-field behavior. We perform cellular-automata simulations of the one-dimensional case and find that the width W(t) of the reaction front behaves as ${\mathit{t}}^{0.293\pm 0.005}$, in contrast to mean-field behavior ${\mathit{t}}^{1/6}$. We develop a scaling theory to obtain inequalities for the exponents in the more general mechanism nA+mB→C. Heuristic arguments about the range of fluctuations imply that the mean-field behavior should be correct in dimensions larger than an upper critical dimension ${\mathit{d}}_{\mathrm{u}\mathrm{p}=2\mathrm{}}$, irrespective of the values of n and m. This leads us to reinterpret the two-dimensional data obtained previously in terms of a logarithmic correction to mean-field behavior.

We present an example of a single-component, one-dimensional interacting particle system with a discontinuous transition into an absorbing state. The basic processes in the model are spontaneous annihilation (X→0), autocatalytic creation by trimers (3X→4X), and hopping. The transition is continuous, and in the directed percolation class, for low diffusion rates, and first order for sufficiently high diffusion rates. The transition in a similar model with creation by pairs (2X→3X) remains continuous even at high diffusion rates.

Analytic and numerical results are obtained concerning the entrainment and migration of dynamic systems, which are governed by ordinary differential equations ẋ=E(x) (x∈${\mathit{openR}}^{\mathit{n}}$=1,2,3), when they have attracting sets. Using the control ẋ=E(x)+ġ-E(g) (t≥0), the goal dynamics g(t), to which x(t) is entrained, ${\lim }_{\mathit{t}\to \mathrm{\infty }}$‖x(t)-g(t)‖, is confined to convergent regions of phase space g(t)∈${\mathit{C}}_{\mathit{k}}$={x‖ ∥λ(x)${\mathrm{\delta }}_{\mathit{i}\mathit{j}}$-∂${\mathit{E}}_{\mathit{i}}$/∂${\mathit{x}}_{\mathit{j}}$∥=0, Reλ<0 ?λ; i,j=1,...,n}. These regions can be determined analytically, using the Routh-Hurwitz theorem, without explicitly determining the roots λ(x) of the characteristic determinant. The control is only initiated when the system is in the basin of entrainment x(0)∈BE{(g)}, which ensures entrainment. BE(${\mathit{g}}_0$) is proved to exist for any fixed-point goal ${\mathit{g}}_0$∈${\mathit{C}}_{\mathit{k}}$. It is conjectured that BE({g(t)}) exists for all g(t)∈${\mathit{C}}_{\mathit{k}}$ which are ‘‘dynamically limited’’: ‖ġ‖<D(min[Reλ(x)],max g), where the function D is system specific.

This dynamic limitation is illustrated for the Duffing oscillator. Basins of entrainment are explicitly determined in one-dimensional flows and for the van der Pol limit cycle (n=2) in the Liénard phase space. This example is used to show that convergent regions are not topologically invariant. The convergent regions are obtained for both the Lorenz and Rössler systems (n=3). The global character of the basin of entrainment for a class of goals is analytically proved for the Lorenz system. The transfer of systems between different attractors in multiple attractor systems (MAS) is demonstrated both in one-dimensional flows and in the Lorenz system, where the transfers between stable fixed points and from a strange attractor to a stable fixed point are illustrated.

We study the effect of correlated noise on a model of molecular-beam epitaxy (MBE), in which desorption and formation of defects can be neglected. The MBE growth model is described by a random deposition process in which the deposited particles can relax to kink sites maximizing the number of saturated bonds. With only Gaussian white noise, the growth exponent β, defining the interface width W∼tβ at intermediate time t, is known to be β=38. We have solved exactly a continuum model and have determined the surface growth exponents α and β, in the presence of spatially and temporally correlated noise of the form 〈η(x,t)η(x′,t)〉∼|x-x′|2ρ-d′|t-t′|2θ-1, where d′ is the interface dimension and ρ and θ are the noise correlation parameters. Direct simulation of this noise spectrum in a (1+1)-dimensional model confirms our theoretical predictions. Agreement between theory and simulation in this more general case of correlated noise lends further support to the correspondence between the continuum model on which the theory is based and the discrete lattice models that are closer to experimental situations.

We show how a chaotic system is able to generate a desired aperiodic orbit by making only small temporal perturbations to an available set of system parameters. The appropriate controls are obtained by applying the method developed by Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)] to an artificially constructed dynamical system such that when this dynamical system is at its steady state the output of the chaotic system should be the desired aperiodic orbit. We illustrate our method with some numerical examples in which the motion of a chaotic system is converted to two different aperiodic orbits.

We consider mean-first-passage times and transition rates in bistable systems driven by dichotomous colored noise. We carry out an asymptotic expansion for short correlation times ${\mathrm{\tau }}_{\mathit{c}}$ of the colored noise and find results that differ from those reported earlier. In particular, to retain corrections to O(${\mathrm{\tau }}_{\mathit{c}}$) we find that it is necessary to retain up to four derivatives of the potential function. We compare our asymptotic results to existing ones and also to exact ones obtained from numerical integration.

The equations of motion for a chain of six particles with fixed ends (a 4+2 chain), interacting via nearest-neighbor linear and cubic forces, have been numerically integrated for the case of odd-mode excitations. Positive Lyapunov exponents are seen for sufficiently large anharmonic forces. However, no corresponding stochastic Poincaré surface of section intersections or broadband power spectra are observed. These latter chaotic phenomena may in this case be at a level below the resolution of the numerical data.

We present analytical and numerical results showing 1/${\mathit{f}}^{\mathrm{\omega }}$ characteristics in the time series of growth velocity in a class of surface-growth models. The exponent ω is found to be related to the scaling exponents by ω=(2α-z+d-1)/z. The time series of surface width in the steady state are also shown to have power-law scalings in the frequency domain. We establish a mapping between the single-step model for ballistic growth and a random cellular automaton. We conclude that the steady state of the surface-growth models, in particular the ballistic deposition model, is a self-organized critical state.