The dynamics of an electron described by the one-dimensional tight-binding Hamiltonian with quasiperiodic (Fibonacci) modulation is studied numerically. The width of an initially localized wave packet is found to increase with time t in an overall power-law form ∼$t^{\alpha }$ (0<α<1). The exponent α continuously decreases with increasing strength of quasiperiodic modulation. Moreover, prominent hierarchical oscillations are found to occur in the case of strong modulation. These results are explained well by a renormalization-group argument.

In this paper we consider the two-dimensional symmetric model of dendritic solidification with capillary anisotropy in the limit of large undercooling. We show that capillary anisotropy is necessary to obtain steady-state solutions, and that it allows the system to select a particular value of the growth velocity. The results obtained are in complete agreement with what has been derived in the corresponding limit in the case of the boundary-layer model.

Diffusion-limited-aggregation (DLA) deposits with no branching (‘‘zeroth-order branching DLA’’) resemble a ‘‘forest of whiskers;’’ the fractal dimension $d_f$ of this forest is significantly less than that of normal DLA deposits. We study a generalization of this whisker model in which only first-order branching is allowed: attachment to the sides as well as the tips of the whiskers is permitted. Using various analysis methods, we find that $d_f$ may be only very slightly smaller than $d_f$ for conventional DLA (the full infinite-order branching case).

We consider three types of changes that attractors can undergo as a system parameter is varied. The first type leads to the sudden destruction of a chaotic attractor. The second type leads to the sudden widening of a chaotic attractor. In the third type of change, which applies for many systems with symmetries, two (or more) chaotic attractors merge to form a single chaotic attractor and the merged attractor can be larger in phase-space extent than the union of the attractors before the change. All three of these types of changes are termed crises and are accompanied by a characteristic temporal behavior of orbits after the crisis. For the case where the chaotic attractor is destroyed, this characteristic behavior is the existence of chaotic transients. For the case where the chaotic attractor suddenly widens, the characteristic behavior is an intermittent bursting out of the phase-space region within which the attractor was confined before the crisis. For the case where the attractors suddenly merge, the characteristic behavior is an intermittent switching between behaviors characteristic of the attractors before merging.

In all cases a time scale τ can be defined which quantifies the observed post-crisis behavior: for attractor destruction, τ is the average chaotic transient lifetime; for intermittent bursting, it is the mean time between bursts; for intermittent switching, it is the mean time between switches. The purpose of this paper is to examine the dependence of τ on a system parameter (call it p) as this parameter passes through its crisis value p=$p_c$. Our main result is that for an important class of systems the dependence of τ on p is τ∼‖p-$p_c$${\Vert }^{\mathrm{-}\gamma }$ for p close to $p_c$, and we develop a quantitative theory for the determination of the critical exponent γ. Illustrative numerical examples are given. In addition, applications to experimental situations, as well as generalizations to higher-dimensional cases, are discussed. Since the case of attractor destruction followed by chaotic transients has previously been illustrated with examples [C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 57, 1284 (1986)], the numerical experiments reported in this paper will be for crisis-induced intermittency (i.e., intermittent bursting and switching).

A new type of projection operator is used to derive homogeneous equations of motion for the reduced density operator of a system coupled to a bath. Crucial simplifications of these equations are obtained without assuming that the projection operator and the zeroth-order Hamiltonian commute. No factorization assumption for the initial density matrix is made. The applicability of the general formalism, which is valid also for nonergodic initial conditions, to physically relevant situations is investigated. It turns out to be particularly useful for the treatment of a system initially submitted to some constraints but otherwise in equilibrium. The relaxation towards the unconstrained equilibrium of a two-level system in contact with an Ohmic bath is treated as an example. The reduced equilibrium density operator of this system is obtained analytically for the case of extremely low temperatures. The result shows and it is then proved rigorously that the zero-temperature reduced density operator does not describe a pure state in general, except in the zero-coupling limit.

We study ultradiffusion in systems with an arbitrary distribution of energy barriers and nearest-neighbor hopping processes. As the effective temperature R is increased, we find power-law decay of the autocorrelation function with an anomalous R-dependent exponent for R<$R_c$. Furthermore, we observe singular crossover at $R_c$ to normal diffusion. The value of $R_c$ depends on the average branching ratio of the system. We have also discovered a set of trees for which the R dependence of the exponent departs from the expected value based on universality arguments. Analytical results and computer experiments for several systems are presented.

For purely repulsive $r^{\mathrm{-}\nu }$ potentials the three-dimensional linear Boltzmann equation is solved for two limiting cases. In the Rayleigh limit ($m_A$→∞) the Boltzmann collision operator reduces to the Fokker-Planck differential operator, which is independent of the potential index ν. In the Lorentz limit ($m_A$→0) the eigenvalue problem of the Boltzmann collision operator is solved analytically yielding speed-dependent eigenvalues and the Legendre polynomials as eigenfunctions. For the particular case of a hard-sphere interaction potential (ν=∞) the Lorentz collision operator reduces to the well-known projection operator, which averages the distribution function over all directions in velocity space. Either of the above limits allows an analytical solution of the Boltzmann equation for the dynamical self-structure factor $S_s$(q,ω) in terms of a scalar continued fraction. Finally, for the particular case of a Maxwell interaction potential (ν=4), the dependence of $S_s$(q,ω) on the mass ratio $m_A$/$m_B$ is studied using our previous result of the infinite matrix-continued-fraction representation of $S_s$(q,ω).

It turns out that for $m_A$/$m_B$→0 and $m_A$/$m_B$→∞ the matrix-continued-fraction representation of $S_s$(q,ω) converges to the same values as do the respective scalar-continued-fraction representations mentioned above. From a physical point of view two interesting results should be mentioned here: First, it turns out that in the Lorentz limit the dynamical self-structure factor does not approach the well-known Lorentz line shape in the hydrodynamic limit (q→0), which means that the two limiting processes, $m_A$→0 and q→0, must not be interchanged. Second, by scaling $S_s$(q,ω) to the customary dimensionless quantity R(q,x), the dependence of R(q,x) on both the potential index ν and the mass ratio M:=$m_A$/($m_A$+$m_B$) is rather weak. This statement, however, is only true for mass ratios M>0.05, whereas for very small mass ratios (M<0.05) one observes for all potential indices a strong dependence of R(q,x) on the mass ratio.

We study the temporal approach of a cluster size distribution to its asymptotic scaling form. By enforcing consistency between the distribution’s zeroth moment derived from both the Smoluchowski equation and the scaling distribution ansatz, we find values for the scaling exponents w and z in terms of the scaling exponent τ and the kernel homogeneity λ which are not equivalent to their asymptotic, scaling forms. The predicted values do agree well, however, with intermediate time values found in simulations by Kang, Redner, Meakin, and Leyvraz [Phys Rev. A 33, 1171 (1986)]. By enforcing consistency between all moment orders, the asymptotic exponent values are found. These results imply the lowest-order moments approach their scaling values quickest.

A variational calculation for the (ddμ${)}^{+}$ muon molecular ion has been carried out. Muon-helium sticking probabilities are obtained for the (J=1, ν=0) and (J=1, ν=1) states. Despite the very different method used for the three-body wave-function calculation, the present sticking probabilities agree within 2.5% with a previous calculation which uses the adiabatic representation three-body wave function.

We consider the Boussinesq theory for convection in a rectangular box with imposed constant, negative, vertical heat and salt gradients. We analyze the bifurcation of two-dimensional convection steady states near a double instability point defined by a critical value of the thermal Rayleigh number and geometrical aspect ratio. We find that for thermohaline convection the interaction of the two lowest pure-mode steady states does not produce the tertiary bifurcation of periodic solutions because the direction of bifurcation of the modes is always the same, either both supercritical or subcritical. On the other hand, we find that the interaction can produce the secondary bifurcation of mixed-mode steady states, and that jump transitions between multiple, stable, pure-mode steady states are possible. We also find that the mixed-mode steady state is always unstable in the parameter ranges considered.

We have applied both angular and energy distribution measurements of the collision-induced dissociation of a-few-keV ${\mathrm{H}}_3$${\mathrm{}}^{+}$ in He to estimate the binding energy of the triatomic molecular ion ${\mathrm{H}}_3$${\mathrm{}}^{+}$. Our measured value of 6.3±0.5 eV below the dissociation energy agrees well with previous theoretical predictions and experiment.

The local-plasma model for the stopping mean excitation energy I(0) of Lindhard and Scharff is used to investigate the effects of target density. The use of the Thomas-Fermi electron density produces a universal curve for I(0)/Z, where Z is the nuclear charge number, as a function of the target density. Experimental data for I(0) are shown to be in good agreement with this predicted curve. A simple formula is derived for I(0) in the limit of high target density. This approach is known to predict a similar curve for the charge dependence of I(0)/Z for atomic ion targets. Numerical comparisons and an asymptotic formula for the large-charge limit are presented for this case.

The convergence of the Born and Coulomb-Born approximations for the electron-impact excitation cross sections of positive ions was examined both formally and by sample calculations on several lithiumlike ions. It was found that the convergence of the two approximations with increasing energy is not necessarily monotonic and may not occur until many tens of threshold units. An analytic expansion of the Coulomb partial waves, in terms of spherical Bessel functions, indicates that partial-wave collision strengths in the two approximations do not necessarily converge in the limit of high angular momentum, although agreement at high incident energies occurs for all partial cross sections. Criteria for the use of the Born approximation for highly ionized atoms are discussed.

Multiconfiguration Dirac-Fock energies are compared with experiment for the 4s-4p transitions in Cu-like ions and the 4$s^2$ ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$–4s4p ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ transition in Zn-like ions for Au, Pb, Bi, Th, and U. The Coulomb, Breit, and QED contributions to these transitions are tabulated for selected ions in the range Z=50–92. Results show that the agreement between theory and experiment is good enough to show the importance of QED corrections in the spectra of these highly stripped ions. Contrary to earlier findings by Seely et al. [Phys. Rev. Lett. 57, 2924 (1986)] we find no significant differences between the observed and calculated transition energies after finite-nuclear-size corrections are included.

This is an addendum to our previous publication [Phys. Rev. A 36, 143 (1987)] dealing with cross-correlation–induced resonances in four-wave mixing. The temporal fluctuations of the source lead to well-resolved Hanle resonances in forward four-wave mixing which is in contrast to the dephasing-induced resonance in the same geometry.

In a previous publication [R. H. Enns, S. S. Rangnekar, and A. E. Kaplan, Phys. Rev. A 36, 1270 (1987)], it was demonstrated numerically that the generalized nonlinear Schrödinger equation (GNLSE) describing one-dimensional optical pulse propagation displays nondestructive collisions between bistable solitonlike pulses for a variety of nonlinear models including the model f(I=‖${\mathit{E}}^2$‖)+μ(I/${\mathit{I}}_0$)+(I/${\mathit{I}}_0$${)}^{\mathit{n}}$/[1+(I/${\mathit{I}}_0$${)}^{\mathit{n}}$] for n≥3. Here I is the intensity, E the complex electric field amplitude, μ and $I_0$ are real positive constants, and n takes on positive integer values. In this paper, we report that the GNLSE passes the analytical Painlevé test for the above model. Explicit formulas for the first few coefficients in the Painlevé expansion, as well as the compatibility conditions, are given for n≥3. Thus there exists at least one physically reasonable form of the GNLSE for which bistable solitons exist.

We use a numerical technique to study the time development of squeezing and antibunching resulting from the interaction of coherent light with a two-photon medium. While we find that enhanced squeezing occurs for short time, the squeezing is eventually revoked. We also find that antibunching develops but also is eventually revoked.

Absolute excitation rate coefficients for Fe xvi and Ni xvi ions ions are measured spectroscopically in the Texas Experimental Tokamak. Previous measurements for the 3d-3p transition array of Cu xvii are verified and the measurements are extended to the 3s3$p^2$→3$s^2$3p transition array of this ion. The experimental rate coefficient for the 3d-3p transition array of Fe xiv is 6.2×${10}^{\mathrm{-}9}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$ at an electron temperature near 160 eV and for Ni xvi and Cu xvii, the values are 4.2×${10}^{\mathrm{-}9}$ and 3.8×${10}^{\mathrm{-}9}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$, respectively, at an electron temperature near 240 eV. For the 3s3$p^2$ ${}^2$$P_{3/2}$→3$s^2$3p ${}^2$$P_{3/2}$ transition array, the experimental excitation rate coefficient for Fe xiv is 8.2×${10}^{\mathrm{-}9}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$ at an electron temperature near 160eV and for Ni xvi and Cu xvii the value is 5.5×${10}^{\mathrm{-}9}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$ at an electron temperature near 240 eV. The uncertainty in these results is estimated to be ±50% (one standard deviation). Computed values of absolute excitation rates in a distorted-wave approximation and Mewe’s semiempirical formula are found to be in good agreement with the experimental values.

On the basis of Monte Carlo (MC) data from newly performed simulations for classical one-component plasma (OCP) as well as those from earlier work, we examine critically the validity of the center-of-mass correction through comparative studies on how the computed values of the excess internal energies depend on the number N of the MC particles. It is thereby concluded that the correction cannot be justified for the fluid OCP; an alternative internal-energy formula is derived.

The beat-wave excitation of plasma waves in a counterstreaming electron beam is studied, and the consequences for particle acceleration are discussed. Both the plasma-wave length and the pump-depletion length can be significantly longer than that in the plasma beat-wave accelerator. Thus the single-stage energy gain of the accelerated particles is greatly increased, whereas the injection energy for particle trapping is greatly reduced; this allows the possibility of ion acceleration.