A nonsymmetric four-dimensional volume-preserving map (i.e., two nonsymmetrically-coupled two-dimensional area-preserving Hénon maps) is numerically studied. In this map it is found that the universality classes of period doubling are identical to those previously found in the symmetric four-dimensional volume-preserving maps, reported by J. M. Mao and R. H. G. Helleman [Phys. Rev. A 35, 1847 (1987)]. This is the first time a global picture of period doubling in more general, nonsymmetric, four-dimensional volume-preserving maps has been given. Also, a simple analytic renormalization is presented for the new Feigenbaum constants.

The stochastic differential equation of Nelson’s stochastic mechanics is integrated numerically for several simple quantum systems. The calculations are performed with use of Helfand and Greenside’s method and pseudorandom numbers. The resulting trajectories are analyzed both individually and collectively to yield insight into momentum, uncertainty principles, interference, tunneling, quantum chaos, and common models of diatomic molecules from the stochastic quantization point of view. In addition to confirming Shucker’s momentum theorem, these simulations illustrate, within the context of stochastic mechanics, the position-momentum and time-energy uncertainty relations, the two-slit diffraction pattern, exponential decay of an unstable system, and the greater degree of anticorrelation in a valence-bond model as compared with a molecular-orbital model of ${\mathrm{H}}_2$. The attempt to find exponential divergence of initially nearby trajectories, potentially useful as a criterion for quantum chaos, in a periodically forced oscillator is inconclusive. A way of computing excited energies from the ground-state motion is presented. In all of these studies the use of particle trajectories allows a more insightful interpretation of physical phenomena than is possible within traditional wave mechanics.

The formalism of sensitivity analysis for stochastic differential equations is adapted and extended to the framework of stochastic mechanics. Thus a methodology is provided for analyzing the dependence of expectations of functionals of the stochastic mechanical diffusion process on parameters defining the system. This should prove useful in numerical simulations employing the latter theory. We take into account the fact that in stochastic mechanics typically a probability distribution of initial positions (rather than the initial position itself) is prescribed. The expression for a sensitivity density with respect to a drift variation depending only on time is shown to follow from the Ito-Girsanov formula, which is also employed to develop new formulas for sensitivity densities with respect to position-dependent drift variations. As an example to verify these techniques, the sensitivity coefficients of the harmonic-oscillator correlation function with respect to the angular frequency and the diffusion constant are calculated; the results coincide with those obtained by direct differentiation.

To test the connection between chaotic classical motion and quantum spectral and overlap statistics, we examine a schematic three-orbital shell model. This system is novel in that the quantum phase space is compact and the momentum dependence of the classical Hamiltonian is nonstandard. We find good agreement with the expected behavior of the spectral statistics and reasonable agreement for the overlap distributions. Also, there is evidence that the eigenvector statistics are more sensitive to the details of the classical dynamics than are the eigenvalues.

A real-space renormalization-group method is applied to the drift-diffusion-limited aggregation proposed by Meakin [Phys. Rev. B 28, 5221 (1983)]. The effects of particle drift on the diffusion-limited aggregation (DLA) are investigated. The aggregation process is transformed from DLA to the ballistic process with increasing drift effect. It is found that at a finite drift velocity the aggregate is compact with a surface fractal dimension between the DLA and ballistic aggregation results with increasing drift effect. The crossover from a fractal structure at short length scales to a compact structure at longer length scales is shown. The multifractal scaling properties of the growth probability distribution on the growing perimeter are found to be described by the set of generalized dimensions and the α-f spectra.

Electromagnetic wave propagations in a helical cholesteric liquid crystal and a chiral smectic-C liquid crystal are studied for the case of normal incidence. Both the exact and generalized geometrical-optics-approximation (GGOA) solutions are obtained. The two solutions are in close agreement when the period of the structure is not comparable to the wavelength of the incident wave. In particular, for a liquid crystal with small optical anisotropy, the analytic expressions for the exact solution are identical to the corresponding GGOA solutions when the pitch of the helical structure is either much smaller or much larger than the wavelength of the incident wave. With the use of the exact solution, the polarization and total internal reflection as well as the optical rotation power and circular dichroism are discussed. The results on optical rotation power in a cholesteric liquid crystal for an incident wave far from the reflection band agreed with the results obtained by de Vires and by Mauguin [S. Chardrasekner, Liquid Crystals (Cambridge University, Cambridge, England, 1977)] under the respective applicable conditions.

A number of different effective Fokker-Planck equations have been proposed to describe systems driven by colored noise. Herein we show that the effective Fokker-Planck equation obtained from the path-integral technique is identical to that obtained from other techniques at the same level of approximation. Recently reported differences thus arise not from the use of different formalisms but merely as a consequence of different approximations.

The microscopic approach to solid-state nucleation [J. Salik, Phys. Stat. Solidi B 142, K19 (1987)] is applied to the case of monolayers. A criterion for cluster stability is derived and used for analyzing the stability of square monolayer clusters on a two-dimensional square lattice. The nucleation and growth behavior is found to be similar to that predicted by the classical theories only when the binding energy is high enough or the temperature low enough. Computer simulations show that this conclusion can be generalized to clusters of random shapes.

We consider a simple model of the flux in a rf superconducting quantum-interference device (SQUID) ring subjected to an external periodic magnetic field. The dynamic equation describing the flux response of the SQUID is solved analytically in the absence of damping and external driving terms. We then introduce these terms as small perturbations, and construct, for this system, the Melnikov function, the zeros of which indicate the onset of homoclinic behavior. For the parameter values under consideration, excellent agreement is obtained between our theoretical predictions and numerical calculations of the stable and unstable (i.e., time-reversed) solution manifolds. A chaotic attractor is shown to appear somewhat above the homoclinic threshold.

With the use of Feynman’s laws for combining quantum-mechanical amplitudes, expressions for the n-particle states in terms of the single-particle states (for noninteracting particles) are derived rather than postulated. The usual direct-product form for distinguishable particles and the symmetric (antisymmetric) combination of direct products for identical particles emerge as the only forms consistent with the quantum-mechanical laws for compounding amplitudes.

We consider the system of equations obtained by Davydov from the Fröhlich Hamiltonian through the use of a coherent-state Ansatz. We obtain equations of motion which, although entirely equivalent to the usual Davydov system, allow the dynamics to be analyzed in a more transparent way. In the continuum limit the exact equations reduce to the usual nonlinear Schrödinger equation. Initial states and the soliton formation process are discussed, and time and length scales governing soliton coherence properties are determined. In order to address the case of intermediate wavelengths, where the discreteness of the underlying lattice has significant consequences for soliton motion, we formulate a modified nonlinear Schrödinger equation which resolves a number of difficulties implicit in the usual nonlinear Schrödinger equation.

We show that the known equivalence between the regularized Kepler potential -k/(x⋅${\mathrm{x})}^{1/2}$ and the free motion on the sphere also holds in one dimension. Consequences for the classical and quantum situations are worked out; the disappearance of the quantum ground state is checked through numerical calculations with a cutoff potential.

The electron excitation function for the metastable states of molecular nitrogen has been analyzed to reveal the excitation cross section for the E ${}_{}{}^3{}_{}{}^{}$ ${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$ metastable state of ${\mathrm{N}}_2$. This cross section has been placed on an absolute scale by a normalization technique based on the argon metastable-atom excitation cross section. The resultant cross section is dominated near threshold by a strong, narrow negative-ion resonance. The general features of the near-threshold cross sections are entirely consistent with a number of recent excitation functions for the E state but not with previously published absolute values.

Recent papers on electron-${\mathrm{N}}_2$ scattering by Rumble, Stevens, and Truhlar [J. Phys. B 17, 3151 (1984)] and Weatherford, Brown, and Temkin [Phys. Rev. A 35, 4561 (1987)] have suggested that Hartree-Fock (HF) wave functions may not be accurate for calculating potentials for use in studying electron-molecule collisions. A comparison of results for electron-${\mathrm{H}}_2$ scattering using both correlated and HF wave functions is presented. It is found that for both elastic and inelastic collisions and for all energies considered (up to 10 eV) the HF wave functions yield results in excellent agreement with those obtained from the more accurate wave functions.

Cross sections for the ionization of lithium atoms from the 2S as well as from the 2P level resulting from collisions with hydrogen molecules were derived from the effective ionization of a 30-keV lithium beam. Population of the 2P level by collisions and by optical pumping was used; only the latter technique, however, proved to yield reliable results. The measurements are compared with simple theoretical estimates.

A study of the elastic scattering of positrons from the ground (1 ${}_{}{}^1{}_{}{}^{})$ state of helium has been carried out using a distorted-wave approximation method involving the distortion of the positron projectile by static and polarization potentials in both the initial and final channels. Results for the differential and total cross sections are reported and compared with previously reported results.

We have measured the absorption profiles of the Mg–rare-gas (3s ${}_{}{}^1{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$–4s ${}_{}{}^1{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$) collision-induced molecular bands. The experimental results for the Mg-He and Mg-Ne profiles are compared with a semiquantitative theoretical model based on model potential curves and an assumed transition dipole-moment function. Reasonably good agreement is obtained supporting our interpretation for the nature of these collision-induced absorption bands.

Resonant-transfer-excitation (RTE) cross sections are calculated for K-shell excitation in ${\mathrm{Ca}}^{17+}$+He, ${\mathrm{Ca}}^{17+}$+${\mathrm{H}}_2$, and ${\mathrm{S}}^{13+}$+He collision systems, and the results are compared with experiments. The RTE cross sections are obtained in the impulse approximation by averaging the corresponding dielectronic-recombination cross sections over the momentum distribution of the target electrons. Agreement is excellent for ${\mathrm{S}}^{13+}$, but there are discrepancies in the ${\mathrm{Ca}}^{17+}$ case.

The accuracy of ab initio effective optical and model polarization potentials has been assessed for ${}_{}{}^1{}_{}{}^{}\mathrm{S}$, ${}_{}{}^1{}_{}{}^{}\mathrm{P}$, ${}_{}{}^3{}_{}{}^{}\mathrm{S}$, and ${}_{}{}^3{}_{}{}^{}\mathrm{P}$ electron-hydrogen scattering where essentially exact results are available. These studies demonstrate that effective optical potentials can be used to provide highly accurate phase shifts for low-energy scattering where polarization effects are quite important and can be used to study the characteristics of Feshbach resonances. In addition, we find that the better-than-adiabatic dipole model polarization potential provides reasonably accurate results for this open-shell system.

We have observed the deflection of Rydberg atoms towards a metallic surface by the van der Waals force. Cs and Na atoms in states of principal quantum number n were sent between two parallel gold-coated mirrors, spaced by a gap w (2.1 μm≤w≤8.5 μm). We measured the value $n_m$ at which the transmission cuts off and from the variation of $n_m$ versus w, we obtained a measure of the atom-surface interaction. For $12<n<30$ this interaction is 3–4 orders of magnitude larger than for ground-state atoms, and it obeys the scaling laws of the Lennard-Jones model.