An energy-dependent rovibrational-frame-transformation method, combined with the multichannel quantum-defect theory, has been applied to study the vibrational excitations of ${\mathrm{H}}_2$ by electron collision in the energy range below 5 eV. A class of nonadiabatic effects resulting from large collision time delay has been accounted for. Using a special set of short-range Born-Oppenheimer eigenstates, this approach does not explicitly introduce electron-molecule compound states. We show that the body-frame quantum-defect function ${\mathrm{\mu }}_{\mathit{l}=1\mathrm{}}$(ɛ,R), containing the information about the dynamical coupling of the incident electron and the molecular target, is all one needs to describe the scattering properties of the system.

Standard arguments used to justify the adiabatic approximation in barrier penetration problems at extremely low bombarding energies are critically examined. A simple model calculation is used to illustrate how the relative strength of the coupling to the intrinsic degrees of freedom may affect the validity of the adiabatic approach.

A close-coupling calculation with 1s, 2s, and 2p states has been carried out for the 1s-2s,2p excitations of hydrogenlike ions by electrons with an energy lower than 2.5 times the excitation energy. Differential cross sections show a strong dependence on both nuclear charge and impact energy, especially for the 1s-2s excitation. A scaling relation for differential cross sections is well satisfied for the 1s-2p transition. A comparison is made between the present result and other theoretical calculations.

The effect of many-electron correlations on anomalous scattering factors in Rayleigh scattering is studied, in the case of the Ar atom, using dispersion relations and the relativistic random-phase approximation (RRPA). The correlation effect changes the Ar 3s-subshell photoionization cross sections significantly compared with the corresponding independent-particle approximation calculations; thereby the anomalous scattering factors of Rayleigh scattering from this subshell also experience marked structural changes. But the Ar 3p subshells dominate the coherent total-atom scattering amplitude so that subshell structural changes in the Ar 3s subshell due to many-electron correlation effects are not seen in the total-atom scattering cross section or the total-atom anomalous scattering factors, which are the physical observables in Rayleigh-scattering experiments. One anticipates this outcome generally for closed-shell atoms, while in the case of open shells one can anticipate a greater importance for the many-electron-correlation effects.

We have measured the depolarized interaction-induced-light-scattering spectrum (DILS) of a metal vapor at low density. In this case, for mercury at temperatures T=673 and 723 K, the spectra show a large dimer band and an exponential wing. Comparison with theoretical calculations shows the inadequacy of the present knowledge of the pair potential of mercury and the possibility of using the DILS for the determination of the pair potential itself in metal vapors.

A method for the analysis of computer simulations of ultrafast dynamical processes in many-body systems is presented, based on a joint time-frequency Wigner-Ville distribution calculated from the evolving particle velocities. This quantity has the interpretation of a time- and frequency-dependent effective temperature, and the evolution of the distribution allows dynamical information about energy flow between modes and relaxation mechanisms of many-body systems to be obtained. This approach is illustrated for the example of vibrational relaxation of an ${\mathrm{I}}_2$ impurity in an argon cluster.

A temperature-size (T-N) phase diagram is derived for Na clusters of up to N∼1000 atoms. It is based on first-order pseudopotential calculations and the Lindemann criterion for melting. It contains three regions of stability: (1) a liquid (jellium) phase at temperatures above the melting line ${\mathit{T}}_{\mathit{M}}$(N); (2) a phase related to the body-centered-cubic structure at temperatures below the melting line; and (3) a close-packed structure at very low temperatures and sufficiently large N. The melting line drops to ${\mathit{T}}_{\mathit{M}}$(N)=0 for N<65. The phase diagram reduces asymptotically to the known phases of Na as N→∞, including the known martensitic transformation at T≊5 K.

The stability of dark solitary waves trapped in self-defocusing media that include gain and two-photon absorption is investigated. The stationary propagation of the dark solitary waves is found to be stable to a symmetric perturbation but unstable to an asymmetric perturbation. This contrasts with their bright counterparts, which are unstable to all perturbations.

We present the s-parametrized quasiprobability distributions for the negative binomial states. Marked changes in the quasiprobability distributions W(α,ε,s) are exhibited by states that are close to the random-phase coherent state (ε=0), as the parameter s is varied continuously from s=-1, corresponding to the Q function, to s=1, corresponding to the P function. However, states close to the thermal-noise state (ε=1) exhibit the usual Gaussian-like distributions for all values of s.

We rederive the normal-ordering theorem of Blow et al. [Phys. Rev. A 42, 4102 (1990)], which was later obtained by Barnett [Phys. Rev. A 43, 6418 (1991)] by functional differentiation, by virtue of the technique of functional integration within an ordered product (FIWOP). We also show that the FIWOP can be developed, if the corresponding functional integration is well defined, to deal with the squeezed state, P representation, and Wigner operator of the continuous mode of fields.

Two box-counting algorithms for the determination of generalized fractal dimensions are described. Results of application of the algorithms to Euclidean curves, quadric islands, Koch symmetric and asymmetric triadic snowflakes, and split snowflake halls introduced by Mandelbrot [Fractal Geometry of Nature (Freeman, New York, 1983)] are described. Comparison to analytic results for the model curves is provided and the effectiveness of the algorithms is discussed.

A metric-affine geometry about the Uhlenbeck-Ornstein (UO) process and about a random walk (RW) is investigated. It is found that the time development of the UO process is a geodesic motion in the metric-affine space spanned with two parameters, the mean and standard deviation, and that the time development of the RW is an expansion of a spherical space spanned with jump probabilities.

Motivated by recent studies of Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)], we study self-organized criticality in models of ‘‘running’’ sandpiles. Our analysis reveals rich temporal structures in the flow of sand: at very short time scales, the flow is dominated by single avalanches. These avalanches overlap at intermediate time scales; their interactions lead to 1/f noise in the flow. We show that scaling in this region is a consequence of conservation laws and is exhibited in many examples of driven-diffusion equations for transport. At very long time scales, the sandpiles exhibit system-wide discharge events. These events also obey scaling and are found to be anticorrelated. We derive the ${\mathit{f}}^{1/2}$ mean-field power spectrum for these events and show that a threshold instability of the model, coupled with some stochasticity, is the underlying origin of the long-time anticorrelation.

We consider a directed polymer on a square lattice confined inside a parabola with boundaries Y=±${\mathit{Cx}}^{\mathrm{\alpha }}$. Generalizing standard transfer-matrix methods, an effective transfer operator was introduced that takes into account slow variation of the size of the system in the y direction. By an exact calculation the effect of the confinement is found to be relevant and irrelevant for α<1/2 and >1/2, respectively; in the former case the thermodynamical functions have a stretched-exponential behavior around the critical point. For α=1/2 the geometrical constraint is marginal, and the critical exponents are nonuniversal.

Well-behaved dynamical properties have been found in a parametrically damped pendulum. For various dampings, all minimum forcing amplitudes E for chaos to occur are at the forcing frequency Ω=1.66, and all minimum E for a stationary solution to be unstable are identical (E=2) and at Ω=2 in the Ω-E state space. Between these two frequencies, the variation to chaos along stability boundaries (where the stationary solution becomes unstable) is solely Ω dependent and insensitive to dampings. These two frequencies separate parameter regions with distinct dynamical behaviors. For Ω<1.66, the route to chaos is due to an inverse boundary crisis while for Ω>1.66, it is associated with period doubling. For Ω<2 the transition from stationary solution to periodic solution is a jump, while for Ω>2 it is a Hopf bifurcation.

A classical phase-space structure of a strongly chaotic Fermi resonant system is studied. An alternative method to construct the Poincaré surfaces of section is used. The method includes the location of the Farey-tree families of the hyperbolic periodic orbits. The Farey-tree organization of resonances provides a very useful decomposition of the phase space. The structure of periodic orbits trapped within resonances can be characterized in two ways: first, it can be described in terms of the islands-around-islands picture; second, one can utilize the relationship between the homoclinic orbits of the main resonances and the topology of the adjacent periodic orbits. We show that there exists a one-to-one correspondence between these two classifications.

The description of an infinite number of time correlations associated with band-splitting phenomena in chaotic systems is executed by means of the order-q power spectrum ${\mathit{I}}_{\mathit{q}}$(ω) which was recently introduced with the aim of elucidating various aspects of time correlations in a dynamical (temporal) fluctuation. By sweeping the value of the parameter q, various parts of dynamical fluctuation are singled out. Just before the band splitting, the temporal evolution of the state variable intermittently switches between two bands. Because of the long-time correlation, the order-q power spectrum exhibits a critical behavior. It will be shown that this is described by the dynamic scaling law ${\mathit{I}}_{\mathit{q}}$(ω)=${\mathrm{\kappa }}^{\mathrm{-}1}$I(q/κ,ω/${\gamma }_{\mathit{q}}$) with ${\gamma }_{\mathit{q}}$=κγ(q/κ), where κ is a characteristic value of q, which tends to zero as the system approaches the band-splitting point, and ${\gamma }_{\mathit{q}}$ is the width of ${\mathit{I}}_{\mathit{q}}$(ω). Numerical results are compared with theoretical ones due to a simplified Markovian stochastic model.

It has been shown that the appropriate setting of data windows is crucial to a successful estimation of a time-series correlation dimension using the Grassberger-Procaccia algorithm [Physica 9D, 189 (1983); Phys. Rev. Lett. 50, 346 (1983)], and it has been proposed that the first minimum of the corresponding mutual-information function may be an appropriate window value. We have tested this hypothesis against data generated by the Rössler equations, the Lorenz equations, and a three-dimensional irrational torus. We conclude that mutual information is not consistently successful in identifying the optimal window.