An approximate solution to the steady-state version of the one-dimensional Fokker-Planck equation is obtained by (extending an approach due originally to Harris [J. Chem. Phys. 75, 3103 (1981)] and) using the ansatz that the solution, which has an explicit half-range character, can be approximated in each half of the velocity space by a truncated expansion in Hermite polynomials. The convergence of the expansion is studied and found to be remarkably rapid. With only a modicum of effort, the ninth-order approximation (i.e., the value based on an expansion containing nine terms) to the cardinal quantity in this context, viz., the extrapolated end point, is found to be 1.459 88, whereas the exact value is 1.460 35. . . .

The equilibrium and growth morphology of a crystal in a diffusion field are studied by means of a lattice-gas model in a unified way. In a closed system the crystal takes an equilibrium form, and its shape and size in two dimensions agree with those expected from the exact solutions of the corresponding Ising model. In an open system where a crystal is in contact with a gas reservoir, the crystal grows steadily. For a small crystal or at a small chemical potential difference Δμ between the gas and the crystal, the growth form is polygonal. Its growth rate and the size are interpreted by a single nucleation and growth mechanism. On increasing Δμ or for a large crystal, it becomes dendritic. Further increase of Δμ results in a fractal aggregate, which is, however, ‘‘compact’’ in a large scale due to the finiteness of the gas density.

An experimental and numerical analysis of the behavior of a two-delay differential equation is presented. It is shown that much of the system’s behavior can be related to the stability behavior of the underlying linearized modes. A new phenomenon, mode crossing, is explored.

Using the mathematics of spinors, the Bloch equations (ignoring relaxation) can be expressed as an ordinary differential equation of second order with complex variables. This form of the Bloch equations is more amenable to analytic solution than previous formalisms, and is useful in calculating the magnetization response to various amplitude and/or frequency-modulation excitation functions.

A recently discovered two-photon absorption process can produce novel features in spectra obtained with intense broadband radiation. Two mechanisms termed cooperative and distributive contribute to the effect, which involves synergistic photoabsorption by molecular pairs. In the former mechanism, each molecule of the pair absorbs a single photon; in the latter, two photons are absorbed by one of the molecules. In contrast to earlier suggestions, it is here shown that the distributive mechanism is far more significant over large intermolecular distances.

We consider the effect of dipole-dipole interaction on the quantum jumps in a system of two three-level atoms in a ssV configuration interacting with coherent fields. We show that the intensity-intensity correlation for the strong transition shows additional fluctuations for some interatomic separations between the atoms signifying three levels of fluorescence. It is argued that the intermediate level of fluorescence arises from the coupling between the symmetric and antisymmetric states caused by the dipole-dipole interaction.

In this Brief Report we analyze the limit of very weak damping of a quantum-mechanical Brownian oscillator. It is shown that the propagator for the reduced density operator of the oscillator can be written as a double path integral of the same form as that obtained in the high-temperature limit. As a direct consequence, we can write a Fokker-Planck equation for the reduced density operator of the weakly damped oscillator (at any temperature) involving only the damping and a generalized diffusion constant in momentum space.

The steady-state intensity fluctuations of a single-mode dye laser are investigated when the laser is operated far above threshold. An analytic expression for the variance of the laser intensity is obtained when both additive white and multiplicative colored noise are included in the laser model. The result is in excellent agreement with the measurements of Kaminishi, Roy, Short, and Mandel [Phys. Rev. A 24, 370 (1981)].

Under certain conditions the Hausdorff dimension of the two-scale Cantor set can be represented by the quasiweighted average of the Hausdorff dimensions of one-scale Cantor sets. This expansion of the Hausdorff dimension corresponds to the generally accepted idea that the multifractal is composed of infinitely many simple fractals.

The integral alignment $A_{20}$ was investigated for H(2p) excitation in slow (H-He${)}^{+}$ collisions. Pronounced differences are observed between ${\mathrm{H}}^{+}$-He and ${\mathrm{He}}^{+}$-H collisions; they are attributed to the different (singlet and triplet) spin channels which dominate the respective excitation process.

In this work, we present a more highly resolved spectrum of the transitions of ${\mathrm{C}}_2^{+}$. To avoid the difficulty of the observation of the B ${}_{}{}^4{}_{}{}^{}\Sigma _u^{\mathrm{-}}{}_{}{}^{}$-X ${}_{}{}^4{}_{}{}^{}\Sigma _g^{\mathrm{-}}{}_{}{}^{}$ emission spectrum of ${\mathrm{C}}_2^{+}$ by conventional methods, we used a technique based on fast-ion-beam laser spectroscopy which presents a very-high-resolution performance (120 MHz or less). Spin-spin and spin-rotation coupling parameters have been determined for the first time for both involved states.

A model of atomic ionization by smooth pulses is solved with bound-continuum and energy-dependent continuum-continuum (C-C) dipole coupling. The rotating-wave approximation for the C-C transitions is avoided. In contrast with the flat continuum result, our ionization rate is independent of the C-C coupling. We also derive the photoelectron energy spectra and show that counterrotating terms make important contributions. Relation to above-threshold ionization experiments with two frequencies is discussed.

Two typical motions of dislocations, climb and glide, and their mutual interactions are studied experimentally in a layered pattern of electrohydrodynamical convective rolls of nematic liquid crystals under well controlled initial conditions. It was found that two kinds of forces acted on the dislocations with opposite Burgers vectors. The first kind is a pattern-selection force under which the dislocation moves at constant velocity. The second kind is an attractive interaction force. When dislocations are approaching each other, the effective length of the latter is of short range, typically of the order of the wavelength of the pattern.

We analyze some nontrivial cooperative adsorption-desorption models that exhibit trivial random steady states. The subtle balance in dynamical processes maintaining these steady states is elucidated. In addition, we analyze the complicated kinetics of the approach to the steady state.

We show that it is possible to transfer energy efficiently between two laser beams of comparable intensity by means of the near-resonant nonlinear response of an atomic vapor. The coupling is due to stimulated Rayleigh scattering and occurs when the frequency difference between the two beams is approximately the inverse of lifetime of the excited atomic state. We have measured the coupling between two beams from an Alexandrite laser tuned near the $4^2$$S_{1/2}$→$4^2$$P_{3/2}$ potassium transition and found that one of the transmitted beams can contain up to 85% of the total incident energy.

The immersion energy of an inert-gas atom or ${\mathrm{H}}_2$ molecule into jellium is calculated using an electron-gas approximation. Our modification of the energy functional of Gordon and Kim [J. Chem. Phys. 56, 3122 (1972)] includes a correction to remove the self-exchange term from the exchange energy and adjustments to take into account the nonuniformity of the system. The calculated ratio of the immersion energy to the jellium density varies about a factor of 2 over five orders of magnitude variation in jellium density and agrees relatively well (within a factor of 2) with the result of previous density-functional approaches in the low-density limit; the Gordon-Kim model is not reliable, however.

Some time-dependent physical systems do not admit, in the general case, either an invariant or auxiliary equation. The study of these systems is then in general made easier by space-time transformation of coordinates. This is true for the case for a rectangular well with a moving wall, which generalized canonical transformations reduce, in the path-integral formalism, to the case of a variable-frequency oscillator with fixed walls. The variable-frequency harmonic oscillator is an example where the invariant and the auxiliary equations can be calculated. All calculations are done in phase space.

This paper adopts the hypothesis that the absence of macroscopic quantum fluctuations is due to a certain universal mechanism. Such a mechanism has recently been proposed by Ghirardi et al. [Phys. Rev. D 34, 470 (1986)], and here we recapitulate a compact version of it. Károlyházy [Nuovo Cimento 52, 390 (1966)] showed earlier the possible role of gravity and, along this line, we construct here a new parameter-free unification of micro- and macrodynamics. We apply gravitational measures for reducing macroscopic quantum fluctuations of the mass density. This model leads to classical trajectories in the macroscopic limit of translational motion. For massive objects, unwanted macroscopic superpositions of quantum states become destroyed in very short times. The relation between state-vector and density-operator formalisms has also been discussed. We only anticipate the need for elaborating characteristic predictions of the model in the region separating micro- and macroscopic properties.

In the power-series solution of the separated two-center equations for ${\mathrm{H}}_2^{+}$, determining eigenparameters by recursion in the stable direction (from high to low order) encounters severe numerical limitations in the case of large internuclear distance and high spatial dimension or, equivalently, high angular momentum. We find this can be overcome by use of recursion in the unstable direction (from low to high order), thereby greatly improving the accuracy of the eigenparameters obtained. For instance, for the ground electronic state with angular momentum ‖m‖=0 and dimension D=67 (equivalent to ‖m‖=32 for D=3), the improvement in accuracy is about five orders of magnitude for the energy and about eight orders for the separation constant related to the Runge-Lenz vector. The source of this seemingly paradoxical behavior is revealed by examining the divergent solution for each recursion direction. The method is useful for determining the eigenparameters only; recursion in the stable direction must still be used to determine the eigenfunctions.

Slater-type basis sets are commonly used to perform nonrelativistic and relativistic variational calculations. A major limitation of this method is that no more than about 14 powers per nonlinear parameter can be used while working in double-precision arithmetic without entering into numerical difficulties. Even for moderate-size basis sets, large numerical errors are introduced. We introduce a variational method based on the orthogonality properties of the Laguerre polynomials. All the matrix elements of the Dirac Hamiltonian are calculated in closed form, therefore avoiding numerical cancellations and vastly increasing the speed of the calculations. As a result, full double-precision accuracy is maintained with very large basis sets. Results for sets with 75 powers are given as examples. The method is applied to a new, very accurate relativistic calculation of the two-photon decay rates for hydrogenic ions. This calculation resolves a discrepancy between the previous calculation of Parpia and Johnson [Phys. Rev. A 26, 1142 (1982)] and that by Goldman and Drake [Phys. Rev. A 24, 183 (1981)] in favor of the latter.