We have observed the periodic motion of a parabolic electron wave packet. The wave packet was created by coherent excitation with 7-ps laser pulses of several parabolic states of atomic rubidium in a dc electrical field. The dispersion of the wave packet was small because the spacing between subsequent energy levels of the Stark map is almost constant. By measuring the photoionization yield in a pump-probe experiment, as many as 10 oscillations were observed.

The efficiency of cyclotron autoresonance maser (CARM) amplifiers with piecewise linear tapering of the magnetic field is analyzed. In the low-current limit, we find that increasing the magnetic field substantially enhances the efficiency if an effective detuning parameter is positive, while decreasing the magnetic field is advantageous when the detuning parameter is negative. For high-current, high-gain, CARM operation the efficacy of tapering is found to be reduced in a parameter regime where the saturation wave amplitude becomes of the order of an effective detuning parameter.

We present finite-difference numerical solutions of the time-dependent Navier-Stokes equations for propagating Taylor-vortex fronts into unstable Couette flow. The propagation velocities found are in excellent quantitative agreement with the theoretical predictions for normal fluids. Deviations of previous investigations reported in the literature can be explained in terms of transients. Agreement is found also for front propagation in magnetic fluids, where a magnetic field modifies the front velocity.

The reduction of the interbase hydrogen-bond force constants in a unit cell of B form poly(dA)-poly(dT) creates a local mode in the gap between 63.9 and 66.7 ${\mathrm{cm}}^{\mathrm{-}1}$. This mode emerges from the band with a zone-center frequency of 66.7 ${\mathrm{cm}}^{\mathrm{-}1}$. This band has a large h-bond stretch amplitude. Our calculations suggest that this local mode can be created by thermal fluctuations in the perfect homopolymer. We track the behavior of this mode with softening of the h bonds. As expected, we find that the mode shifts to lower frequencies as the bonds soften. The h-bond stretch amplitudes are found to increase with h-bond softening, up to a point, beyond which they decrease with further softening.

A phase-diffusion stochastic field with frequency fluctuations obeying Gaussian Markovian statistics is produced at microwave frequency and used to drive a two-level spin system. The system is tuned to the two-photon (TP) resonance and its TP-induced second-order response is measured as a function of the characteristic parameters of the frequency noise. It is found that, when the statistics of the driving field are varied from the fast- to the slow-modulation limit, the power spectrum of the nonlinear response of the system varies in a continuous way from a Lorentzian form toward a Gaussian one, and its relative width (normalized to the input spectral width) varies from 4.0±0.4 to 2.0±0.2. The experimental results are interpreted on the basis of a semiclassical calculation which takes into account the stochastic nature of the field. The effect of the filter action of the cavity modes is discussed. The relationship with previous experiments and theoretical calculations of TP absorption is also examined.

We analyze a discrete-time neural network with continuous state variables updated in parallel. We show that for symmetric connections, the only attractors are fixed points and period-two-limit cycles. We also present a global stability criterion which guarantees only fixed-point attractors by placing limits on the gain (maximum slope) of the sigmoid nonlinearity. The iterated-map network has the same fixed points as a continuous-time analog electronic neural network and converges to an attractor after a small number of iterations of the map.

We study a permeation process in a diffusion-limited regime. We derive general results that apply for this system without making any use of hydrodynamic rate equations, whose validity for diffusion-limited processes is in question. We support our theoretical conclusions by numerical simulations and discuss the applicability of hydrodynamic rate equations.

An experimental study of the dendritic growth of pivalicacid crystals in the presence of an external controlled Stokes flow is performed. A new experimental law, relating the value of product ${\rho }^2$V to the external flow velocity, is found.

The maximum-entropy method is here generalized to obtain many possible extrema of the uncertainty product corresponding to the generalized minimum uncertainty products recently discussed by Lahiri and Menon (LM) [Phys. Rev. A 38, 5412 (1988)]. Unlike the LM work, the present work applies to mixed states and leads to a new annealing algorithm for obtaining the extrema of the entropy functional.

A modified version of the maximum-entropy principle is applied to distributions associated with special quantum states. In this way, it becomes feasible to make statistical inferences concerning the ground-state wave function and the associated potential from the sole knowledge of a few relevant mean values. The scheme is illustrated for the case of anharmonic and Morse potentials and yields excellent results.

The general time-dependent quantum two-level system is shown to admit an exact invariant. This leads to a classical formulation of the problem, which is then solved by standard techniques of Hamiltonian mechanics. Berry’s phase and nonadiabatic corrections to it emerge as an asymptotic limit of the exact dynamics. A novel connection between Berry’s phase and Hannay’s angle is shown to exist in this case.

Annihilation and creation operators in quantum mechanics are constructed in the framework of Nelson’s stochastic mechanics. Employing Ito’s stochastic calculus, annihilation and creation operators were found to be written as (1/√2ω)[d/dt,∂/∂Ḃ(t)] and (1/√2ω)[d/dt,∂/∂B${̇}^{\mathrm{*}}$(t)], respectively, where Ḃ(t) is a Gaussian white noise and B${̇}^{\mathrm{*}}$(t) is a time-reversed Gaussian white noise. The operators were shown to have proper commutation relations and to provide a Hamiltonian which has an eigenvalue equation desired in the {N} representation as should exist in conventional quantum mechanics. Therefore, the present formulation provides a correspondence between stochastic mechanics and conventional quantum mechanics.

We demonstrate the use of angular momentum graphs, based on those of Yutsis, Levinson, and Vanagas [Mathematical 1 Apparatus of the Theory of Angular Momentum (Israel Program for Scientific Translation, Jerusalem, 1962)], adapted for the unitary group approach to the theory of many-particle systems. Using a variant of the standard Gel’fand state labels, we show that graphical representations of generator matrix elements in U(n) parallel the SU(2) vector-coupling approaches of Drake and Schlesinger [Phys. Rev. A 15, 1990 (1977)] and Paldus and Boyle [Phys. Scr. 21, 295 (1980)]. The graphs are constructed using the U(n) Clebsch-Gordan coefficients. Fundamental subgraphs, such as occur in the evaluation of operator matrix elements, are expressed in terms of U(n) Racah coefficients and generalized 3n-j coefficients. The results are anticipated to be of interest to high-energy physicists and to others concerned with systems of particles involving spin higher than (1/2.

The rate coefficients for charge transfer from ${\mathrm{H}}_2$ molecules to ${\mathrm{O}}^{2+}$ and ${\mathrm{O}}^{3+}$ ions have been measured at eV energies using an ion-storage technique. A single rate coefficient k(${\mathrm{O}}^{3+}$,${\mathrm{H}}_2$) =(7.15±0.15)×${10}^{\mathrm{-}9}$ ${\mathrm{cm}}^3$/s characterizes the ${\mathrm{O}}^{3+}$,${\mathrm{H}}_2$ interaction, but the attenuation of the stored ${\mathrm{O}}^{2+}$-ion number due to charge transfer in a mixture of ${\mathrm{O}}_2$ and ${\mathrm{H}}_2$ gases exhibited a double time constant. Analysis employing the time dependence of the ${\mathrm{O}}^{2+}$-ion metastable-level mean lives resulted in the charge-transfer rate coefficients k(${\mathrm{O}}^{2+}$${(}^3$P),${\mathrm{H}}_2$) =(1.71±0.15)×${10}^{\mathrm{-}9}$ ${\mathrm{cm}}^3$/s and k(${\mathrm{O}}^{2+}$${(}^1$D),${\mathrm{H}}_2$) =(9.6±0.6)×${10}^{\mathrm{-}9}$ ${\mathrm{cm}}^3$/s. The mean energy of the ${\mathrm{O}}^{2+}$ ions was 1.25(0.5) eV, while the ${\mathrm{O}}^{3+}$ ions were at 2.15(0.5) eV. The relationships to electron capture from H and from ${\mathrm{O}}_2$ by these ions are discussed.

It is shown that Berry’s phase is equal to the integral of a symplectic 1-form of the effective action of a quantum theory along closed trajectory in the phase space, corresponding to configurations with cyclic evolution. In classical approximation this is just the Fp dq term in the classical action.

Simon’s exterior-scaling procedure is applied to model systems within the framework of the finite-basis-set approximation. We show that if the basis-set functions are scaled when r>$r_0$, a variational solution is obtained by adding the term 1/2δ(r-$r_0$)[d/dr-λ] [1-exp(-2iΘ)] to the Hamiltonian, where λ is the logarithmic derivative of the resonance wave function at $r_0$. Two computational methods are proposed. One is an ab initio linear variational iterative procedure, whereas in the second one λ is semiclassically estimated during the iteration procedure and all the variational calculations are carried out for r≤$r_0$ and therefore are exactly Θ independent. An illustrative numerical application is presented.

Exact density-phase relations have been derived for a three-level independent-particle problem. The density can explicitly be written in terms of the phase functions ϑ and cphi and their derivatives. The Euler equation of the density-functional theory has been derived for the ground state of the C atom. The one-body potential V can be obtained from the phase functions ϑ and cphi. The differential form of the virial theorem of March and Young [Nucl. Phys. 12, 237 (1959)] has been generalized for particles moving in a common local potential V and having different azimuthal quantum numbers.

Provision is made for the existence of excited target states and projectile continuum-continuum coupling, within the framework of the interacting resonance theory of electron-ion recombination described previously [Phys. Rev. A 36, 4662 (1987); 38, 1820 (1988)]. This ‘‘extended’’ theory makes explicit what was merely implicit in these earlier works. Dielectronic recombination probabilities, which include the effects of interaction and interference between resonances, are derived for two model systems: (a) A target ground state supporting two coupled projectile continua, and one excited target state as a closed channel; (b) a ground and first excited target state, each supporting one projectile continuum, and a second excited target state as a closed channel. Explicit calculations are performed for model (b), wherein are included Rydberg series of fully interacting resonances built on each of the two excited target states. The probability of excitation from the ground to the first excited target state is also obtained for model (b). This probability includes the effect of the interaction and interference between resonances, as well as the interference between resonance and direct excitation processes.

A detailed analysis is given for the study of positronium (Ps) formation in $e^{+}$+H collisions in the presence of a homogeneous, single-mode laser field, considering full interaction. The projectile–laser-field interaction and the dressing effect on the target hydrogen atom and the Ps atom in the final channel are considered to first order. The field is treated classically in the dipole approximation to calculate the dressing effect. We consider the dressing effects of the hydrogen atom and the Ps atom for the field directions both parallel and perpendicular to the incident momentum (scr${\mathrm{E}}_0$∥${\mathrm{k}}_i$ and scr${\mathrm{E}}_0$⊥${\mathrm{k}}_i$). The dressing effects are shown to produce significant modifications of the differential cross section. The differential cross sections for Ps formation with and without the dressing are presented for no-photon and one-photon (l=0,±1) exchange at 50, 75, 100, and 200 eV energies with laser-field amplitude ‖scr${\mathrm{E}}_0$‖=0.02 a.u. and the angular frequency ω=0.074 a.u.

A theory is developed, valid within the accuracy of the first-order Born approximation, of the scattering of electromagnetic fields that applies under much more general conditions than do the current theories. The incident field is assumed to be statistically homogeneous and stationary, of arbitrary state of coherence, of arbitrary state of polarization, and to have arbitrary spectrum. The medium is assumed to be linear and spatially and temporally random, with the randomness being characterized by an ensemble that is statistically homogeneous, isotropic, and stationary. The analysis is not restricted to scattering from a medium in thermal equilibrium and applies in both off-resonance and near-resonance regions of the medium.