The singular-point analysis for two Hamiltonian systems with three degrees of freedom is performed. The connection with their chaotic behavior is discussed. To characterize the chaotic behavior we have calculated the one-dimensional Lyapunov exponent.

We investigate special types of solutions of the hydrodynamical version of a generalized Schrödinger-Langevin equation (GNLSLE), derived in an earlier work, via stochastic mechanics. Within the same scheme of stochastic differential equations, we decompose the stochastic process associated with the GNLSLE into two independent processes: a classical Langevin-type process and a pure quantum Nelson-type process.

Experimental studies revealed that liquid water bound between lecithin bilayers becomes increasingly viscous with decreasing interbilayer distance. Percolation calculations do indeed show that cluster formation and thus viscosity are favored with decreasing interbilayer distance.

The quantum mechanics of an oscillator interacting with a field in the limit of zero damping (λ+0) and infinite field extension (Λ→∞) depends on the order in which the limits are taken. If the limit λ→0 is taken after the limit Λ→∞, one obtains Gaussian wave functions for all stationary states (m=0,1,2,. . .) of the particle. These Gaussians do have the correct standard values for the variances 〈${\zeta }^2$${〉}_n$ but otherwise obviously differ from the standard harmonic-oscillator result. The latter arises only if the zero-damping limit is taken before the infinite-system limit.

We give numerical evidence and prove that for a class of maps of the circle onto itself, relevant to the study of nonlinear forced oscillators, the structure of the basins of attraction within a region of bistable dynamics is not altered by the occurrence of bifurcations. For each value of the parameters of the map, the boundary between the basins is a Cantor set; we show that the homeomorphism between these Cantor sets varies continuously with these parameters.

In the Thomas-Fermi model, the energy of an atomic ion with N electrons and nuclear charge Z differs from the neutral-atom energy by an amount which, in the situation of weak ionization (N≲Z), is proportional to (Z-N${)}^{7/3}$. A simple but highly precise method is presented for the computation of the corresponding coefficient.

We point out that the Hamiltonian for the periodically pulsed harmonic oscillator considered by Hogg and Huberman [Phys. Rev. A 28, 22 (1983)] preserves ordinary coherent states under time evolution. The expectation values of x and p then follow the classical motion in phase space.

We have examined the new method of Nauenberg to obtain analytic solutions for the nonzero orbital angular momentum l bound eigenstates of atoms with the exponentially screened Coulomb potential model. We found that the method is useful only for the case with l=0. Thus, the question of obtaining the analytic solution for the case with l≠0 is still open.

Recently, Shivamoggi [Phys. Rev. A 31, 1728 (1985)] considered the modulational instability of a right-hand circularly polarized electromagnetic wave along an external magnetic field. He claims that a strong magnetic field might suppress the modulational instability of field-aligned circularly polarized electromagnetic radiation. In this Comment, we wish to point out that there are serious errors in Shivamoggi’s paper.

Polarizing microscopy and optical rotatory power measurements are used to determine the phase diagram for highly chiral mixtures of chiral and racemic cholesteric S-(+)-4-(2-methylbutyl)phenyl-4-decyloxybenzoate (CE6). In addition to the two blue phases previously reported for this system (BP I and BP II), the new results reported here contain information on the stability of the third blue phase (BP III).

We have measured the yield of convoy electrons in coincidence with the emergent ionic charge state $q_e$ for heavy ions in equilibrium-thickness C foils. The data extend the range of previous measurements to include higher-Z projectiles and lower energies. The dependences found range from an approximately $q_e$-independent yield for ${\mathrm{O}}^{\mathrm{q}+}$ projectiles to a dependence which peaks near $q_e$=9 for ${\mathrm{Si}}^{\mathrm{q}+}$ and $q_e$=11 for ${\mathrm{Cl}}^{\mathrm{q}+}$ projectiles, respectively. We have been able to interpret the observed $q_e$ dependences in terms of primary-electron-loss events in the foil.

We have measured convoy electrons produced by the passage of deuterium particles through thin carbon foils in coincidence with emerging particles in both charge states, ${\mathrm{D}}^{+}$ and ${\mathrm{D}}^0$. The energy spectrum of electrons coincident with emerging ${\mathrm{D}}^{+}$ ions exhibits the characteristic convoy-electron cusp shape centered about the projectile velocity. The energy spectrum of electrons coincident with emerging ${\mathrm{D}}^0$ particles also exhibits a peak at the projectile velocity, but its shape appears to be qualitatively different from the e-${\mathrm{D}}^{+}$ coincidence spectrum. We suggest that e-${\mathrm{D}}^0$ coincidences are the result of neutralization of ${\mathrm{D}}^{+}$ particles (accompanied by convoy electrons) between the sites of congies and agree very well with recent measurements, in the energy range where channel coupling and autoionizing transitions are not important. Comparison is also made with a calculation carried out within the local-density random-phase approximation.

The photoionization cross sections of the singly excited Ba states 6 snl ${}_{}{}^1{}_{}{}^{}$L with n=5-9 and l=0-2 have been calculated in the Hartree-Slater approximation over a broad energy range. Our results establish some systematic trends of these cross sections as functions of photon energy and the quantum numbers n and l. Our data for 6s5d extend previous preliminary predictions to higher photon energies and agree very well with recent measurements, in the energy range where channel coupling and autoionizing transitions are not important. Comparison is also made with a calculation carried out within the local-density random-phase approximation.

Photoelectron angular distributions have been measured for two-photon ionization of rubidium atoms both when the first photon was in resonance with the 4d ${\mathrm{}}^2$D state via an electric quadrupole transition and when it was detuned from it. Angular distributions have also been obtained for the first and second above-threshold ionization (ATI) photoelectron peaks. Tuning to the 4d ${\mathrm{}}^2$D resonance creates a large enhancement of the two-photon ionization photoelectron signal but causes only a modest increase in the ATI signal.

In the recent successful demonstration of a soft-x-ray laser in neonlike selenium, the 3p-3s, J=0-1 transition, which had been predicted to show very high gain, did not appear to be amplified. Most previous calculations have assumed that the dominant pumping mechanism is electron collisional excitation, and have neglected the effects of ionization and recombination on the kinetics of neonlike levels. In this work, we studied the effects of collisional ionization and three-body, radiative, and dielectronic recombination, connecting the three fluorinelike ground states to the lowest 89 levels of neonlike Se. Our results show that dielectronic recombination is a significant process for populating the J=2 upper laser levels, and must be considered to model accurately the excited-state kinetics of the neonlike ion.

The intrinsic linewidth of a cw free-electron laser is calculated, and the result compared to the ordinary atomic laser. A classical (i.e., nonquantum) linewidth is obtained for a free-electron laser operating in the classical regime.

First-passage time statistics for non-Markovian processes have heretofore only been developed for processes driven by dichotomous fluctuations that are themselves Markov. Herein we develop a new method applicable to Markov and non-Markovian dichotomous fluctuations and calculate analytic mean first-passage times for particular examples.

Both high-resolution heat-capacity and tilt-angle measurements have been carried out near the smectic-A–chiral–smectic-C transition of p-(n-decyloxy)benzylidene-p-amino-(2-methlbutyl)cinnamate (DOBAMBC). The extended mean-field theory, suggested by Huang and Viner, for the smectic-A–smectic-C (or chiral–smectic-C) transition, requires a unique relationship between the tilt angle and the anomalous part of the heat capacity. Here we demonstrate this relationship by our experimental results on both heat capacity and tilt angle. This provides a strong additional support for the extended mean-field model in describing the smectic-A–chiral–smectic-C transition.