An improved version of our previously developed method [C.-Y. Hu, A. A. Kvitsinsky, and S. P. Merkuriev, Phys. Rev. A 45, 2723 (1992)] of solving the Faddeev equations in the total angular momentum representation is applied to calculate the dt${\mathrm{\mu }}^{\mathrm{-}}$ ground and excited S-state energies with an accuracy of ${10}^{\mathrm{-}6}$.

The distortions of the cloud of virtual photons surrounding a ground-state two-level atom, induced by an external field driving the atom, are investigated. It is first shown that if the driving field is coupled to the atom via diagonal dipole matrix elements, then a region of quasistability for the virtual cloud exists. Then the number of photons in this virtual cloud is evaluated by perturbation theory, as a function of the intensity of the external driving field. Finally, the analytical expression obtained is discussed using approximations appropriate to different ranges of the intensity of the driving field.

It is established here that a recently derived asymptotic solution for the Jaynes-Cummings model, for large quasiclassical fields, holds over a length of time which is proportional to n¯, the average number of photons in the field. When the initial state of the atoms is one of the semiclassical eigenstates, the purity of the atomic state is found to decay with time in a form approximately Gaussian, with a characteristic time proportional to n¯. When the initial state is not one of the semiclassical eigenstates, the collapses and revivals of the population inversion, for which the model is best known, become irregular also over the same time scale; an explanation for this fact using the asymptotic solution is presented here.

We analyze some aspects of the cumulant method for second-harmonic generation of light in the context of the numerical results of Schack and Schenzle [Phys. Rev. A 41, 3847 (1990)] and earlier papers. The cumulant method can be useful in studies of the modifications introduced by quantum mechanics into classical systems which manifest chaotic oscillations. This problem is frequently referred to as ‘‘quantum chaos.’’

We present a theory of modulating ionization by controlling the phases of incident laser fields. Specific calculations have been performed for the Na atom using the density-matrix equations. Significant modulation of the ion signal can be obtained by choosing the appropriate combinations of laser intensities and frequencies, in resonant as well as nonresonant processes.

Using linear analysis together with newly discovered exact solutions to a perturbation equation, it is shown analytically that one-transverse-dimensional spatial dark solitons in a Kerr-law self-defocusing homogeneous medium are stable.

We present a study of the high-order harmonic-generation (HG) spectra of atomic hydrogen at 248 nm based on the Fourier transform of the expectation values of the induced dipole moment and acceleration. The calculations were performed by extending a fast-Fourier-transformation split-operator technique (in spherical coordinates) to the solution of the time-dependent wave functions in intense laser fields. It is seen that the acceleration form provides a more satisfactory and accurate framework for the study of the photoemission HG spectrum at very intense fields, particularly when ionization becomes appreciable.

In a recent paper, Chou and Huang [Phys. Rev. A 45, 1403 (1992)] employ the multiconfiguration relativistic random-phase approximation (MCRRPA) in an attempt to remove discrepancies between experimental and theoretical oscillator strengths for the 6${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$→6s6p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$, ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ transitions in mercurylike ions. Their MCRRPA results are found to be still in poor agreement with beam-foil measurements, and the authors suggest that a significant part of this disagreement may arise from ‘‘an improper account of the cascade effects in beam-foil lifetime measurements.’’ However, Chou and Huang have overlooked several, more recent beam-foil measurements in which ‘‘proper’’ account has been taken of cascading by the application of an arbitrarily-normalized-decay-curve technique with which their MCRRPA results are still in poor agreement. We conclude that this disagreement is mainly due to the omission by Chou and Huang from their calculation of core-polarization effects. In fact, calculations in which such effects are included show quite satisfactory agreement with the beam-foil measurements in which an account of cascade effects has been taken.

Chaotic systems are known for their sensitivity to initial conditions. However, Pecora and Carroll [Phys. Rev. Lett. 64, 821 (1990); Phys. Rev. A 44, 2374 (1991); IEEE Trans. Circuits Syst. 38, 453 (1991)] have recently shown that a system, consisting of two Lorenz oscillators exhibiting chaos, could achieve synchronization if a portion of the second system is driven by the first. In this paper, a necessary and sufficient condition for synchronization is presented. This condition has been used to create a high-dimensional chaotic system with a nonlinear subsystem. This system shows synchronization both when it exhibits periodic limit cycles and when it turns chaotic.

I determine the critical behavior of a nonequilibrium three-dimensional lattice model exhibiting a phase transition to an absorbing state. Time-dependent Monte Carlo simulations in the vicinity of the critical point yield very accurate estimates for the location of the critical point and several critical exponents. Time-dependent simulations in the supercritical and subcritical regimes yield estimates for further critical exponents from the asymptotic behavior of the survival probability and the average number of particles. The results in the super- and subcritical regimes are also analyzed by utilizing the scaling laws describing the behavior of the model. The results for the critical exponents are the best obtained so far for a three-dimensional model with directed-percolation critical behavior.

We analyze the spectral properties of the Perron-Frobenius operator U, associated with some simple highly chaotic maps. We obtain a spectral decomposition of U in terms of generalized eigenfunctions of U and its adjoint. The corresponding eigenvalues are related to the decay rates of correlation functions and have magnitude less than one, so that physically measurable quantities manifestly approach equilibrium. To obtain decaying eigenstates of unitary and isometric operators it is necessary to extend the Hilbert-space formulation of dynamical systems. We describe and illustrate a method to obtain the decomposition explicitly.

We compare the transition from ordered to chaotic motion in a potential with that in a billiard, whose borders are defined by the maximal equipotential line of the potential system in the case of hydrogen in a uniform magnetic field. For the billiard we calculate the Poincaré maps, the fraction of regular motion on the surface of section, and the stability properties of the shortest periodic orbits. In contrast to the H atom, the billiard shows a generic transition to chaos. While the shape of the orbits is determined by the boundary and is thus very similar, their properties of stability are different: The potential tends to stabilize the motion. The onset of instability in the billiard can be understood in terms of the curvature of the boundary; for the potential system the Gaussian curvature of the potential-energy surface is shown to be the relevant parameter.

A projection superoperator is introduced that is able to extract (from the full nonequilibrium exciton-phonon density matrix) the bare- as well as the dressed-exciton (exciton-polaron) single-particle density matrices. Applying it to a standard model of the exciton interacting, via a linear local coupling, with harmonic phonons in a linear chain, a general theory of exciton propagation is constructed. This theory well interpolates between the standard generalized stochastic Liouville equation (GSLE) approach and the Grover-Silbey (GS) theory [M. Grover and R. Silbey, J. Chem. Phys. 54, 4843 (1971)] depending on an interpolation parameter determining details of the basis used. As this parameter (not connected with the model but depending just on our choice of the mathematical language used) can have no impact on the regime as well as the time dependence of the exciton propagation (measured by site occupation probabilities), all famous contradictions between GSLE (or stochastic Liouville equation) and GS approaches are interpreted as only formal and, in fact, seeming. This regards mainly the lack of the local ${\gamma }_0$ parameters and dependence of the ${\gamma }_1$ parameter on the exciton resonance integrals in the Grover-Silbey theory.

We present an alternative continuation method for tracking unstable periodic orbits by slowly varying an available system parameter. This is a predictor-corrector method for which we assume that initially the orbit is on a chaotic attractor. As we vary the parameter, the method can be used to track the orbit through regimes not necessarily chaotic. The method is designed for experimental situations in which we have no analytical knowledge of the system dynamics and only an experimental time series of the variables involved is available. We present numerical results of the method using the Hénon map.

We consider the one-dimensional dynamical Burridge-Knopoff stick-slip model for an earthquake fault with spatially inhomogeneous friction. The model is self-organizing under the externally imposed constraint of a spatial irregularity of strength which is designed to simulate residual damage to the system due to earlier earthquakes. The dissipation due to seismic wave radiation is adjusted so that the system is asymptotic to elasticity at all wavelengths. The model yields a self-organizing, spatially localized sequence of seismic events constrained by the spatial fluctuations. Repetitive, localized patterns of seismicity are erratically interrupted due to dynamical breaching of friction barriers. The model simulates an earthquake phenomenology that includes (1) the usual Gutenberg-Richter power-law energy-rate distribution at low energies with a rolloff at large energies, (2) spatial localization of large events on parts of a fault system and small events in the other parts of the system, (3) an ability to radiate seismic energy to distances far from the fault, and (4) a set of fractures whose lengths are never equal to the dimensions of the lattice or that intersect a free edge.

In this contribution, the generalized thermodynamic formalism is applied to a nonhyperbolic dynamical system. The system is used to discuss the occurrence of combinations of phase transitions among different entropylike scaling functions. For the discussion, the associated generalized entropy function is calculated from an approximation of finite level and for the asymptotic case. From this unified description of the system, the information contained in the particular spectra as well as the relation among the different spectra can be elucidated in an elegant way. The phase-transition-like behavior leads to the manifestation of a critical line in the surface described by the generalized entropy function which, in turn, determines the occurrence of phase transitions for the particular spectra. Furthermore, apparent phase transitions are encountered in approximations of a finite level. They do not persist in the asymptotic limit.

Measurements of osmotic compressibility (near the lower consolute point, ${\mathrm{T}}_{\mathrm{L}}$) in two reentrant liquid mixtures [3-methylpyridine (MP)+water (W)+heavy water (HW) and MP+W+NaCl] are presented. The closest approach to the double critical point (DCP) was marked by a sample of loop size (ΔT)=250 mK. Analyzing the data by means of the conventional field variable t[=|(${\mathrm{T}}_{\mathrm{c}}$-T)/${\mathrm{T}}_{\mathrm{c}}$|] yielded an exact doubling of the critical exponent (CE) γ for a ΔT=250 mK. The approach to double criticality (for intermediate ΔT) is described by a crossover of the CE from the doubled to its single limit as t→0. Recourse to a more appropriate field variable, ${\mathrm{t}}_{\mathrm{UL}}$[=|(${\mathrm{T}}_{\mathrm{U}}$-T)(${\mathrm{T}}_{\mathrm{L}}$-T)/${\mathrm{T}}_{\mathrm{U}}$${\mathrm{T}}_{\mathrm{L}}$|], restores the Ising value of γ(=1.24) for any ΔT. The salt-doped mixtures permitted us to observe a doubling of the extended scaling exponent (Δ) and also to scrutinize the ionic critical phenomena. The range of simple scaling in MP+W+HW was found to be extremely large. Switching to a modified variable ${\mathrm{t}}_{\mathrm{UL}}^{\prime }$[=|(${\mathrm{T}}_{\mathrm{U}}$-T)(${\mathrm{T}}_{\mathrm{L}}$-T)/${\mathrm{T}}^2$|] led to a remarkable enhancement in the weight of the extended scaling term in both the mixtures—in apparent disagreement with the earlier findings that reported a widening of the asymptotic region. Non-phase-separating samples of MP+W+HW showed the expected saturating divergence preceded by a region of doubled γ as ${\mathrm{T}}_{\mathrm{D}}$ (DCP temperature) was neared. Most of the facets of our investigations can be comprehended in terms of the geometrical picture of phase transitions as well as the Landau-Ginzburg theory as applied to the reentrant phase transitions.

The conformation and scaling properties of self-avoiding fluid vesicles with zero extrinsic bending rigidity subject to an internal pressure increment Δp>0 are studied using Monte Carlo methods and scaling arguments. With increasing pressure, there is a first-order transition from a collapsed branched polymer phase to an extended inflated phase. The scaling behavior of the radius of gyration, the asphericities, and several other quantities characterizing the average shape of a vesicle are studied in detail. In the inflated phase, continuously variable fractal shapes are found to be controlled by the scaling variable x=Δ${\mathit{pN}}^{3\nu /2\mathrm{}}$ (or, equivalently, y=〈V〉/${\mathit{N}}^{3\nu /2\mathrm{}}$), where N is the number of monomers in the vesicle and V the enclosed volume. The scaling behavior in the inflated phase is described by a new exponent ν=0.787±0.02.