Rydberg atomic wave packets have demonstrated striking classical properties. In particular, the wave packets display regions in which they evolve like classical atoms. However, between these regions the wave packet is dispersed and its evolution departs from the classical model. In these nonclassical regions, the wave packet can either be dispersed or coalesced into a number of equally spaced sub-wave-packets. The regions in which the sub-wave-packets appear have come to be known as fractional revivals. This paper reports the observation of these fractional revivals and discusses their implications.

Previously reported calculations of the photoionization rate for atomic hydrogen interacting with a linearly polarized laser beam have been repeated using an improved computer algorithm. Good agreement now exists between our calculated rates and those predicted by three other groups [M. Pindzola (private communication); K. Kulander (private communication); S. Chu and J. Cooper, Phys. Rev. A 32, 2769 (1985)]. Our results are, however, in apparent disagreement with reported measurements of these rates [T. Nichols and G. Kyrala, Bull. Am. Phys. Soc. 35, 1156 (1990)]. Calculations are also reported of the photoionization rates for atomic hydrogen interacting with a circularly polarized laser beam. Results for linear and circular polarizations are compared with each other, as well as with the predictions of several analytic formulas [L. Keldysh, Sov. Phys–JETP 20, 1307 (1965); H. Reiss, J. Opt. Soc. Am. B 4, 726 (1987)].

The dependence of the phenomenon of squeezing for the field quadratures on the phases of the field and atomic coherent states when the atom is assumed to start in an atomic coherent state is investigated. It is found that increasing the relative phase difference results in larger amounts of squeezing for fixed θ. An explanation for the occurrence of squeezing is given on the idea of the interference between the slowly varying and fast oscillating terms.

The quantum Zeno effect is not a general characteristic of continuous measurements. In a recently reported experiment [Itano et al., Phys. Rev. A 41, 2295 (1990)], the inhibition of atomic excitation and deexcitation is not due to any ‘‘collapse of the wave function,’’ but instead is caused by a very strong perturbation due to the optical pulses and the coupling to the radiation field. The experiment should not be cited as providing empirical evidence in favor of the notion of ‘‘wave-function collapse.’’

Various interpretations of quantum mechanics are valid insofar as they predict the same experimental results. Some invoke ‘‘wave-function collapse’’ and some do not. An interpretation based on the collapse postulate provides a simple explanation for a recent experimental demonstration of the quantum Zeno effect [Itano et al., Phys. Rev. A 41, 2295 (1990)], but other interpretations are also valid.

We prove that lasing without inversion is impossible in the three-level system with two active upper levels that are mixed by applied low-frequency electromagnetic radiation. Such lasing was recently proposed by Blok and Krochik [Phys. Rev. A 41, 1517 (1990)].

Zhu, Cresser, and Fearn [preceding Comment, Phys. Rev. A 43, 5170 (1991)] give an erroneous formal proof that lasing without inversion in the system with two upper optically identical levels is impossible. Their approach has little to do with the case of two close but different, well-separated split levels, considered in our previous paper [Blok and Krochik, Phys. Rev. A 41, 1517 (1990)]. It is evident even without laborious calculation that lasing without inversion is impossible in the system of indistinguishable levels, considered by Zhu, Cresser, and Fearn, because one cannot provide the interference among identical transitions. Their formal proof is, in addition, incorrect because they apply a steady-state approximation to the conditions where it is not valid; the transient response of the medium must be calculated instead. We also used the steady-state approximation in our previous paper, but very cautiously, in a domain where it is valid to obtain some analytical formulas, which proved to be qualitatively correct under the transient response approach [Blok and Krochik (unpublished)].

Molecular-orientation parameters for K-shell photoionization of the N(1s) and C(1s) orbitals of ${\mathrm{N}}_2$ and CO, calculated using Hartree-Fock continuum states, are reported. These studies were motivated by recent measurements of the N(1s) orientation parameter, where substantial shape-resonance enhancement is observed, and by earlier indirect studies of molecular orientation for both N(1s) and C(1s) photoionization via the angular distributions of Auger-electron emission. Through the shape-resonance region nearly isotropic Auger-electron angular factors were obtained by fitting the calculated (continuum multiple-scattering method) molecular-orientation parameters to these latter measurements. However, based on the present results one can extract larger Auger angular factors than previously reported. This supports the earlier prediction of uniquely molecular effects in K-shell Auger processes, i.e., anisotropic emission. In addition, the present results show that to obtain accurate shape-resonance-enhanced molecular-orientation parameters, the Hartree-Fock approximation including relaxation effects must be invoked.

Coincidences between two sulfur K x rays were detected from collisions of hydrogenlike S ions with ${\mathrm{H}}_2$ gas in the projectile energy range between 150 and 225 MeV. These K x rays are emitted in the decay of doubly excited states formed in the collisions via transfer and excitation. The excitation function for two coincident Kβ transitions peaks at about 175 MeV, slightly above the expected KMM resonance energy for resonant transfer and excitation (RTE). This demonstrates the occurrence of ΔN≥2 transitions (i.e., KMM and higher resonances) in the RTE process. The cross sections for the population of the very highly excited states are higher than those predicted by theoretical calculations that use dielectronic recombination rates folded with the Compton profile for the bound electrons.

Results of calculations of double excitation of helium to n=2 states for fast projectiles of charge Z are presented. Nonzero ${\mathit{Z}}^3$ contributions for single and double excitation occur only when time-ordering contributions from the second-order amplitude are nonzero. For double excitation, electron correlation must also be nonzero to obtain ${\mathit{Z}}^3$ terms. The time-ordering effects arise from virtual off-energy-shell intermediate states. As with second-order amplitudes for Thomas singularities in electron capture, the energy-nonconserving amplitude is connected to the second-order energy-conserving amplitude by a dispersion relation. Comparison is made with experiment.

We study hyperfine transitions in collisions between cold ground-state ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ atoms, which are of crucial importance for the decay of the atomic density in magnetic traps. For comparable densities we find the initial decay by exchange collisions to be roughly a factor of 10 more rapid than that in atomic hydrogen. The doubly polarized atomic gas that thus forms spontaneously in this initial process subsequently decays by dipolar relaxation with a rate that is about a factor of 5 larger than that in atomic hydrogen. The sensitivity of the calculated rate constants associated with uncertainties in the singlet and triplet potentials is discussed.

Unstable viscous fingers may be stabilized either by applying a local perturbation near the tip such as a bubble or a wire, or by providing a lattice anisotropy. The former case is a problem of singular perturbation that can be understood from the solvability theory by assuming a cusp at the contact point. An alternative way of understanding this problem is to relax surface tension locally near the perturbing region. We show that the cusp model requires a δ-function perturbation in the surface tension. We then show how the relaxation of this δ function into a Gaussian or an oscillatory function naturally provides a link between the two models. Apart from the numerical factor, we find that both models essentially predict the same scaling behavior. Next, we show that only the perturbations acting near the tip satisfy the solvability condition, thus providing a theoretical ground for modeling the lattice anisotropy by an oscillatory surface tension near the tip. This model enables one to quantify the strength of the lattice anisotropy and yields a simple relation between the tip radius ρ and the spacing between the grooves. Finally, we show why, regardless of the types of the local perturbations, the anomalous fingers that advance with speed U might be selected by the relation ρ${\mathit{U}}^2$≊const, the relation that holds for dendritic solidification.

We describe some properties for a phenomenological model of superdiffusion based on a generalization of the persistent random walk in one dimension to continuous time. The time spent moving to either increasing or decreasing x is characterized by a fractal-time pausing time density, ψ(t)∼${\mathit{T}}^{\mathrm{\alpha }}$/${\mathit{t}}^{\mathrm{\alpha }+1\mathrm{}}$, with 1<α<2. For this system it is shown that asymptotically p(0,t)∼1/${\mathit{t}}^{1/\mathrm{\alpha }}$. The form of the profile is shown to be Gaussian near the peak and to fall off like ${\mathit{tx}}^{\mathrm{-}(1+\mathrm{\alpha })}$ near the tails, and the survival probability is asymptotically proportional to exp(-Bt/${\mathit{L}}^{\mathrm{\alpha }}$). These results are confirmed by numerical calculations based on the method of exact enumeration.

A driven diffusive lattice gas is studied in a rectangular geometry: particles are fed in at one side and extracted at the other, after being swept through the system by a uniform driving field. Being periodic in the transverse direction, the lattice lies on the surface of a cylinder. The resulting nonequilibrium steady state depends strongly on this choice of boundary conditions. Both Monte Carlo and analytic techniques are employed to investigate the structure of typical configurations, the density profile, the steady-state current, and the nearest-neighbor correlations. As the temperature is lowered in a finite system, the simulations indicate a crossover from a disordered to an ordered state that is characterized by a backgammonlike pattern of alternating high- and low-density regions (‘‘fingers’’). For fixed strengths of the field and interparticle attraction, the average number of fingers is controlled by the ratio of the transverse to the longitudinal system size. Whether the crossover corresponds to an actual phase transition, where typical thermodynamic observables become singular, remains to be determined.

We propose a phenomenological model for microcrack nucleation in a solid under constant external stress. We argue that the kinetics of the crack nucleation process is qualitatively different from that occurring in simple metastable states such as supercooled liquids or supersaturated solutions. This difference is caused by irreversible processes such as surface diffusion that restructure microcrack surfaces. This restructuring inhibits microcrack healing and thus yields a microcrack nucleation rate that is much faster than that obtained by directly applying nucleation laws appropriate to metastable states in liquids or solutions.

There have been many studies of transport in an unbounded fractal medium. Here we discuss a number of quantities related to the concentration of reactants diffusing in fractal media in the presence of a trapping point. This investigation is suggested by an extension of the Smoluchowski model to calculate reaction rates in such media [M. von Smoluchowski, Phys. Z. 16, 321 (1915); 17, 557 (1917); 17, 585 (1917)]. Results, some analytic and some based on a scaling argument, are given for the flux into the trap, which is the analog of the reaction rate, in addition to the concentration profile in the neighborhood of the trap and the time dependence of the distance between the trap and the nearest untrapped particle. The results of our theory are found to be in good agreement with Monte Carlo and exact enumeration calculations for the concentration profile on a Sierpinski gasket and on an infinite percolation cluster at criticality. Some scaling and numerical results are reported for the situation in which the traps move in the presence of fixed particles.

Monte Carlo simulations have been performed on tethered networks possessing the connectivity of a b=2 Sierpinski gasket, both with and without self-avoidance. For networks without self-avoidance, the simulations are found to be in reasonable agreement with the theoretical prediction, ${\nu }_0$≊0.3685, and independent of the embedding dimension d. For networks with self-avoidance, the simulations give clear evidence for crumpling. The measured value for ν is in good agreement with the Flory theory and, to a lesser extent, the first-order ε expansion of an appropriately generalized Edwards model. The upper critical dimension, ${\mathit{d}}_{\mathrm{UC}}$, above which self-avoidance is irrelevant, is found to lie in the range 8<d<10, which is consistent with the theoretical prediction ${\mathit{d}}_{\mathrm{UC}}$≊8.6. The shapes of crumpled gaskets were also measured and found to be considerably more spherical than those of polymers.

It is proposed in this paper that when two processes compete with each other, one tends to create long-range correlations, whereas the other tends to destroy it; the limiting object usually consists of many length scales. In particular, it might have power-law correlation functions and spatial 1/f spectra. The basic features of this competing dynamical process with spatial degrees of freedom are captured by the model expansion-modification system [W. Li, Europhys. Lett. 10, 395 (1989)]. Many detailed properties of the system, both numerical and analytical, are discussed here. The implications of the proposed mechanism for power-law correlation functions to the evolution of mass distribution in the Universe and the evolution of prebiotic nucleotide sequences are also discussed.

This study tries to extend results observed in finite chains, like slowing-down effects and stretched-exponential decays, into the thermodynamic limit. An infinite chain of nonlinear oscillators is related to pairs of coupled anharmonic modes, where each mode is coupled to an infinite number of harmonic oscillators (thermal baths). For the model of the two coupled infinite chains, the analytical treatment leads very naturally to a ‘‘critical’’ energy below which slowing-down effects and stretched-exponential decays should appear. Also, the model yields a zero-energy threshold for the onset of energy sharing between modes, suggesting that chaos should set in for arbitrarily small energies of the Hamiltonian. The theory is confirmed by digital simulations. These results seem to support the phenomenology observed in models with finite degrees of freedom, suggesting that this behavior survives in the thermodynamic limit and it is perhaps a common feature of chains of coupled anharmonic oscillators.