We employ a Monte Carlo method to study the effects of disorder and external bias on random walks. We find that general asymmetric hopping rates lead to subdiffusive behavior, i.e., vanishing diffusion at long times. When an external bias is imposed, a crossover to the drift behavior, i.e., a linear growth of the mean displacement, is observed at a critical value of the bias. The relation between this critical bias and the strength of the disorder is investigated.

Line-shape data have been obtained for the polarized Raman (Q branch) spectrum of ${\mathrm{N}}_2$ in the critical region. The high-resolution data were recorded under isochoric conditions at densities ranging from 0.6 to 2 times the critical density (${\rho }_c$) and at reduced temperatures [ε=(T-$T_c$)/$T_c$] in the range from 8×${10}^{\mathrm{-}5}$ to 7×${10}^{\mathrm{-}2}$. The spectra are shown to be inhomogeneously broadened for ε${<10\mathrm{}}^{\mathrm{-}3}$ on the critical isochore. This is consistent with the presence of long-lived spatial fluctuations in the molecular environment which can be described in terms of a probability distribution for local density. The results are shown to be consistent with a Gaussian distribution whose full width at half-maximum exhibits an exponential approach to a maximum value of ∼0.5${\rho }_c$ at the critical point.

We describe various phase equilibrium patterns occurring in multicomponent fluid model mixtures where several amphiphilic species are present. The characterization is based on the existing correspondence of states between the Furman, Dattagupta, and Griffiths (FDG) mixture of three components and a (mean-field) natural extension of the Wheeler-Widom model of bifunctional molecules. The shield region and the multicritical points appearing in the FDG and in the van der Waals binary-fluid models are reproduced in the mixture of amphiphiles through manipulations of composition. The diagrams obtained exhibit three- and four-phase equilibria associated with bulk liquids with structures analogous to those in mixed-micellar and bicontinuous middle-phase microemulsions.

Transient dynamics of spatial fluctuations of the director field in the pure twist Fréedericksz transition is studied. A nonlinear calculation is presented. Anomalous transient fluctuations are shown. Different stages of evolution and the domain of validity of linear theories are discussed.

Angular-momentum theory is formulated in terms of quantum action-angle variables. The quantum canonical transformation between the spherical polar and action-angle coordinates and momenta is constructed, and the Hamiltonian and energies in terms of the action variables are determined. Various sets of action-angle variables are considered.

We have used the beam-foil technique to measure the wavelengths of the 1s2s ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$–1s2p ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$,2 transitions in heliumlike Ne ix. The measured wavelengths are 1248.11±0.03 Å and 1277.75±0.05 Å for the J=2 and J=0 transitions, respectively. We compare our results with theory and with other measurements made with different techniques. The agreement is satisfactory and verifies the calculations of the relativistic and QED corrections in this two-electron system.

The nuclear-recoil terms contributing to the fine-structure splitting of 1sNL Rydberg states of helium are calculated. A great simplification resulting from the use of nonsymmetric Jacobi coordinates makes it possible to write the corrections to all terms in the asymptotic optical potential without additional computation. The isotope shifts between ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are displayed and evaluated.

The effect on the dielectronic recombination cross section of electric-field-induced mixing of high Rydberg-state (HRS) levels is determined, for both ${\mathrm{Mg}}^{1+}$ and ${\mathrm{Ca}}^{1+}$ target ions. After diagonalizing the energy matrix, ${\sigma }_n^{\mathrm{DR}}$ is calculated in the isolated resonance approximation as a function of n, the principal quantum number of the HRS electron. From this result, both the total cross section, ${\sigma }^{\mathrm{DR}\mathrm{\equiv }{\mathcal{J}}_{n_{\mathrm{}}{\sigma }_n^{\mathrm{DR}}}}$, and the total cross section integrated over energy, ${\Omega }^{\mathrm{DR}}$≡F ${\mathrm{de}}_c$ ${\sigma }^{\mathrm{DR}}$, are obtained. The agreement between theory and experiment for ${\Omega }^{\mathrm{DR}}$ is very good in the case of ${\mathrm{Mg}}^{1+}$, while roughly a factor of 2 discrepancy still exists for ${\mathrm{Ca}}^{1+}$.

We have carried out completely numerical molecular-orbital calculations (i.e., no linear-combination-of-atomic-orbitals basis sets or cellular approximations) on 13 first- and second-row dimers from ${\mathrm{H}}_2$ to ${\mathrm{Cl}}_2$ in the local-density approximation. The resulting ground-state bond lengths, dissociation energies, and vibrational frequencies are reported and compared with experimental values.

In this paper we exploit the Wei-Norman algebraic disentangling procedure to study the evolution of quantum states driven by a time-dependent Hamiltonian linear combination of the generators of the SU(1,1) group.

The eigenenergies of the hydrogen molecule are calculated in the alternant-molecular-orbital approximation. Emphasis is given to two-dimensional (2D) systems. Results for the 2D and 3D cases are compared and also with the singlet state of the variational Heitler-London approximation. Unlike what is observed in 3D, in 2D we found that in the ground-state electrons are highly correlated and that double occupancy is inhibited.

A model complex potential is employed to obtain integrated elastic cross sections, absorption cross sections, and total cross sections for positron scattering from argon atoms in 100–800 eV energy range. The total cross sections are found to be in good agreement with the experimental data for E≥300 eV and lower than the corresponding electron cross sections over the whole energy range.

Using a flow apparatus, the time dependence of 6$s^2$ ${\mathrm{}}^1$$S_0$–6s6p ${\mathrm{}}^1$$P_1$ (553.5 nm) resonance fluorescence in atomic barium has been studied following switch-on of cw laser excitation. It was found that the fluorescence decays with rates as great as 1.3×${10}^6$ ${\mathrm{s}}^{\mathrm{-}1}$. Assuming this can be ascribed to the pumping of atoms to the 6s5d ${\mathrm{}}^1$D and ${}_{}{}^3{}_{}{}^{}\mathrm{D}$ metastable levels, a value for the sum of the transition probabilities can be extracted.

First-order correlation functions of the electric field and photon-number probabilities in the case of a three-level atom interacting with two-mode radiation field are obtained to investigate the coherent properties of the stimulated emission under different initial conditions. It is found that double stimulation will cause the field to approach its initial coherent state and the oscillation of the photon-number probabilities to collapse and revive.

We demonstrate, in this article, another example of the usefulness of the nonrelativistic dipole approximation (NRDA) in predicting the angular distribution of Rayleigh scattering amplitudes scattered off K electrons. The real parts of the Rayleigh scattering amplitudes, obtained using Gavrila’s analytic Coulomb K-shell NRDA amplitudes in combination with a modified form factor, are compared with the amplitudes obtained from a numerical calculation based on a multipole expansion of the second-order S-matrix element; the present method of computing Rayleigh scattering amplitudes is found to be useful for photon energies below and not far above threshold.

The effective exponent for d=2 describing how the number of growth sites depends on the cluster size is found to depend on the ‘‘ensemble’’ used, i.e., whether the number of visited sites or the number of time steps is kept constant. The constant-site ensemble supports the Leyvraz-Stanley prediction, while the constant-time ensemble supports the Aharony-Stauffer prediction for the growth-site fractal dimension.

An elementary explanation is given for the boundary shadings observed in plots of chaotic attractors for the Feigenbaum map and the circle map. An explicit analytic representation of these phenomena is presented which provides the location of the boundaries and which side of the boundaries is shaded. For the Feigenbaum map, the same analytic expressions also yield the U sequence of periodic windows and their locations in the chaotic zone.

An analysis of the Rayleigh-Taylor instability in a spherical geometry is presented. Expanding any initial perturbation at a spherical surface between two fluids in spherical harmonics $Y_{\mathrm{lm}}$ and further assuming an exponential time growth of the expansion coefficients, an eigenvalue equation for the growth rate is obtained. The free-surface and jump boundary conditions are obtained from the eigenvalue equation. The eigenvalue equation is solved for solid spherical targets and analytical formulas for the growth rate of the instability are presented in the cases where the initial plasma density profile has a step function or exponential variation in space. An analytical expression for the growth rate is also presented for the shell targets and its variation with the aspect ratio of the shell is discussed.

Absolute intensities of certain resonance lines which are considered to be promising candidates for matched-line (photoexcitation) pumping of x-ray lasers are measured. Most are in the 3–8-nm wavelength range. A promising ${\mathrm{Na}}^{9+}$ candidate at 1.1 nm is also tested. The measured radiation is emitted from high-density plasmas formed near the surface of laser-heated slab targets of selected materials. It is concluded that gain-length products of 3 can be achieved with a driving-laser irradiance of ${10}^{12}$ W/${\mathrm{cm}}^2$ and with characteristic dimensions in the 10–100-μm range. Also, among the one-, two-, and three-electron ions tested, an apparent decreasing 2p→1s, 3d→2p, 3p→2s order of preference for resonance pumping transitions may exist, subject to limitations of the present measurement accuracy. One 3d→2p transition in a neonlike ion is proven to be a particularly poor pumping candidate; however, the 3s→2p transition appears to be more promising.

Numerical estimates of the time lag, the distribution function, and the flux of nuclei show that the differences between slow and fast quenches can be seen only if the critical nucleus has a comparatively large radius. In this case, a clear dependence on the quench rate appears, which hopefully might be observed in laboratory experiments and numerical simulations.