Resonant capture cross sections for the first excited state of the F ii ion (1${\mathit{s}}^2$2s2${\mathit{p}}^5$ ${}_{}{}^3{}_{}{}^{}$P) are calculated and the rate coefficients are evaluated at low energies involving excitation captures (Δn=Δl=0) to the singlet P state of the same configuration. The rates peak near the temperature kT=0.4 Ry, with the peak value of 2×${10}^{\mathrm{-}12}$ ${\mathrm{cm}}^3$/sec. This is nearly 100 times larger than that for the ground states with intermultiplet excitations. The resonant contributions to the collisional excitation are also estimated. They are three orders of magnitude larger than the capture cross sections, mainly because of the smallness of the fluorescence yields of the resonance levels.

The velocity distribution of the asymptotic populations in a typical collisional-redistribution experiment is calculated using a geometric semiclassical model. We find that the spherical symmetry of the collision is broken by the applied field leading to both superthermal and subthermal velocity distributions for moderate detunings to the red.

The dc Stark shift of the lithium D1 line has been observed using two visible diode lasers and an atomic beam. A heterodyne signal obtained from the two lasers permits a well-calibrated, high-precision measurement to be made. The scalar shift is found to be 4.6216(21) kHz/(kV/cm${)}^2$. We believe this result to be the most precise Stark shift measurement reported thus far.

Two-mode squeezing of a cavity field interacting with a three-level Λ-type atom is found for a field initially in a coherent state. Some phenomena are revealed, such as two-mode squeezing weaker than single-mode squeezing due to the mode coupling, and periodic recovery of squeezed states caused by two-photon processes.

An m-photon Jaynes-Cummings model is analyzed assuming the field to be initially in the squeezed vacuum state or in a more general squeezed state. Collapses and revivals of the Rabi oscillations in the atomic population inversion appear for a general squeezed input, but not for a squeezed vacuum input. The second-order coherence function is found to exhibit collapses and revivals for large initial average photon numbers. With a low-intensity input field and large m, one can achieve nearly steady-state squeezing.

Rashid [Phys. Rev. A 40, 4242 (1989)] proposes an approximate solution for the relativistic hydrogen atom in a laser field. The error he quotes is such that the solution becomes exact in the nonrelativistic limit. It is shown here to be in error.

An angular momentum J in a resonant-cavity electromagnetic field exhibits chaos in the time dependence of the expectation value of ${\mathit{J}}_{\mathit{z}}$. This fact is transparently demonstrated using the SU(2) generalized coherent-state picture. Using Hale’s averaging theorem, the mechanism of chaos is elucidated and found to be equivalent to a periodically modulated, near-separatrix, pendulum motion. The rotating-wave approximation is also elucidated, and its nonchaos is explained. The modulations that cause chaos result from virtual transitions, and the variance of ${\mathit{J}}_{\mathit{z}}$ initially grows exponentially.

We develop a continuum path-integral approach for the ferroelectric five-vertex model in arbitrary d dimensions by mapping it to a directed polymer problem. A renormalization-group approach with an ε=3-d expansion, 3 being the upper critical dimension, is used to study the polymer solution. The free-energy change due to the interaction of the chains has been computed to O(ε), and the exact expression for the second virial coefficient has been obtained. The fixed point of the problem is found to be exactly 2πε. By use of finite-size-scaling theory and thermodynamics, the exponents for the vertex model are obtained from those of the polymeric system as the specific-heat exponent α=(3-d)/2, and the incommensuration exponent β¯=(d-1)/2. The model is anisotropic with two length-scale exponents ${\nu }_{\mathrm{?}}$=1 in one direction and ${\nu }_{\mathrm{\perp }}$ =1/2 in the remaining d-1 directions. It is shown that there are no anomalous dimensions so that the exponents we obtain are exact.

We report numerical and analytical studies of the finite-size time scales in a system with microscopic stochastic dynamics that in the bulk limit corresponds to an evolution equation with an accumulation point of critical fixed points. Our results suggest that the finite-size behavior is dominated not by fluctuations but by the bottleneck statistical weights at near-fixed-point conditions in a finite-size system.

In this paper, a collective-coordinate description of a breatherlike solution of the perturbed sine-Gordon equation is considered. It is shown both numerically and analytically that the equations describing the evolution of the breather parameters are ill defined. This feature is shown to arise because the equations are obtained through a projection on a null vector. It is shown to be present also in collective-coordinate descriptions of the kink-antikink collision in the ${\mathrm{\phi }}^4$ model. Alternative Ansa$uml—tze hat do not cause singularities are presented.

We present the results of simulations of a two-dimensional mechanical model of a fault, which is a generalization of the one-dimensional model studied previously [Carlson and Langer, Phys. Rev. A 40, 6470 (1989)]. We incorporate both the lateral fault axis and the fault depth, and consider both cases of spatially homogeneous and depth-dependent velocity-weakening friction. Our main result is that in both cases for small- to moderate-sized events, the Gutenberg-Richter scaling exponent b is unity for a wide range of parameters, as observed in the one-dimensional model, and consistent with measurements for real earthquakes. In addition, in the depth-dependent friction model, we study the activity patterns as a function of depth. We observe that smaller events tend to be triggered near the surface, while on relatively shallow faults larger events tend to achieve their first appreciable velocities at depth, in agreement with certain trends observed in seismological studies of the hypocenter distributions of small and large earthquakes.

We consider a generalized sandpile model where the particle addition and toppling are formulated in terms of mappings. In this way, the toppling rules and toppling conditions of the system can also be completely general. Even under these extremely relaxed conditions, we can still find an if and only if condition for the existence of an absolute steady state. Moreover, such a kind of absolute steady state often exhibits self-organized criticality. Our model is a superset of both the original Bak-Tang-Wiesenfeld sandpile and the Abelian sandpile models. Finally, we shall demonstrate the importance of both the particle-addition methods and the boundary conditions to the self-organized critical phenomena of a physical system.

We consider several simplified models of breath figures in one dimension. For all these models, the combined effects of growth and of coalescence of droplets lead to a scale-invariant regime with a stable distribution of the distances between droplets. We show that at the mean-field level there exist one-parameter families of such stable distributions, each distribution being characterized by its decay at infinity. We explain how the mean-field theory can be improved by taking into account the effect of pair or higher correlations. For some models one can check that the pair and higher correlations are factorized, meaning that correlations are absent and that therefore the mean-field theory is exact. Finally, we show that a very simple model of domain growth related to spinodal decomposition, the one-dimensional Potts model in the limit of an infinite number of states, also possesses a one-parameter family of stable distributions analogous to what we obtained for breath figures.

The Feynman rule of any quantum system explicitly depends on the initial time when it is prepared. Assuming that the initial state is in equilibrium, the complete diagrammatical rule is applied to the field-theoretical time-dependent model Hamiltonian. The explicit calculations up to the lowest nontrivial order are performed for the typical nonequilibrium processes. The equation of motion is derived by the inversion method, which is equivalent to the Legendre transformation. The subjects discussed are the calculation of the damping term, the change of the internal energy due to the adiabatic or the nonadiabatic change of the external source, and the resulting temperature shift of the system.

Ordinary diffential equations of continuous dynamical systems, or at least of equivalent systems, can be reconstructed from numerical scalar time series. Methods are exemplified for a Rössler band. Equivalent systems are standard and inverse systems, which are systematically investigated. Validations rely (i) qualitatively on comparisons between phase portraits and (ii) quantitatively on comparisons between generalized dimension spectra. By-products of the work are an information-compression scheme for time-series encoding and the introduction of squeezed systems that facilitate evaluations of generalized dimensions of small order q<1.

We consider an ultrasmall Josephson junction driven by a classical time-periodic current. The whole system is isolated and free of dissipation. Charge quantization of Cooper pairs on the junction capacitor requires the quantization of the system, otherwise described by classical pendulum equations. Our investigations of the Floquet operator show that under certain conditions level repulsion of those quasienergies occurs that corresponds to the chaotic classical regime. This leads to a decrease of the spectral density in the low-frequency region constituting a quantum effect related to classical chaos.

Various models for fragmentation and partitioning phenomena are developed using methods from permutation groups and combinational analysis. The appearance and properties of power laws in these models are discussed. Several exactly soluble cases are studied. An application to nuclear fragmentation and clusterization is given. A connection with Ewens’s approach [Theor. Popul. Biol. 3, 87 (1972); Mathematical Population Genetics (Springer, Berlin, 1979)] to genetic diversity is mentioned. Applications to the social behavior of a vervet monkey troop and to the group behavior of people are given.

An extension of Nelson’s stochastic mechanics to the finite-temperature equilibrium states allows one to describe the quantal harmonic oscillator in equilibrium with a thermal bath in terms of a temperature-dependent diffusion process. The stochastic process is called a ‘‘thermal-mixture diffusion process’’ for the harmonic oscillator. In this paper, by the use of a regularization of the classical Kepler problem, a thermal-mixture diffusion process associated with the Coulomb potential in ${\mathit{openR}}^{\mathit{n}}$ (n=2,3,5) is derived from one associated with the harmonic oscillator in ${\mathit{openR}}^{\mathit{N}}$ (N=2,4,8), which reduces to Nelson’s ground-state process for the quantal Kepler system at zero temperature.

Stratified percolation patterns result from hierarchical cascades with continuous overlap. The pattern construction is a hybrid process, combining continuum percolation with random curdling. Stratified percolation is a correlated percolation with fractal dimensions that can be continuously tuned. The percolation threshold is found to vary with changing correlations. The density of percolating sites is approximately log-normal and can be described by a multifractal. Trends in the f(α) curves are studied as fractal dimensions are changed. The finite-size-scaling properties are investigated using Monte Carlo real-space renormalization. Because the patterns have features at all length scales, stratified percolation has intrinsically small-cell renormalization properties. However, the small-cell properties can be removed by transforming the occupation fraction into an equivalent occupancy for standard uncorrelated continuum percolation. The transformed threshold is approximately invariant with respect to changing correlations and is close to the standard value of ${\mathit{a}}_{\mathit{c}}$=0.7 for isotropic continuum systems. Stratified percolation has a correlation length exponent of ν=1.33±0.05.