A quantum theory for a laser with inhomogeneously broadened active and absorber atoms is presented. Photon-number distributions are derived for both on- and off-resonance operation of the laser, and the results are compared with the results of earlier investigations.

We show how the general formulation of bilinear distribution functions may be profitably used to study the time dependence of the distribution functions considered by O’Connell, Wang, and Williams.

In a barium vapor pumped with laser light on the resonance transition at 553.5 nm the level 6p ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ is depopulated mainly by collisional processes. With neglect of this item, radiative lifetimes derived from fluorescence measurements come out systematically too short.

A representation of the kinetic-energy functional as the product of a homogeneous-gas functional and a Padé approximation in the density gradient is developed and shown to describe accurately the kinetic energy of atomic systems.

The time-dependent density-functional theory of Runge and Gross [Phys. Rev. Lett. 52, 997 (1984)] is reexamined on the basis of its limitations, and the criticisms raised by Xu and Rajagopal [Phys. Rev. A 31, 2682 (1985)] are addressed, within the imposition of natural boundary conditions of vanishing density and potential at infinity. Also, for a single-particle system characterized by an arbitrary time-dependent potential, the uniqueness of the density-to-potential mapping is established explicitly for both bound and scattering states.

Results of calculations using a novel numerical method for intense-field, low-order multiphoton ionization of hydrogen are reported and compared to previously published values. The technique involves the explicit numerical solution of the time-dependent Schrödinger equation using a finite-difference representation of the electronic wave function.

We present a calculation of the cross sections for two-photon bremsstrahlung in a Coulomb potential. The calculation was done in second-order nonrelativistic perturbation theory and in the dipole approximation. The potential was taken into account exactly by using the Coulomb Green’s function. The matrix element was integrated analytically as far as possible and then computed numerically quite accurately. Limiting cases are discussed. Results are presented here for a special emission geometry. These are compared with the recent experiment of Altman and Quarles, and large discrepancies are found.

We show that correlated-emission noise quenching can be achieved in a ring laser via a spatially modulated active medium. A gyroscope based on such a correlated-emission laser has a potential sensitivity superseding the usual quantum limit.

We report the first experimental observation to our knowledge of single-mode instabilities and chaos in a gain-modulated cw ${\mathrm{CO}}_2$ laser. With the use of detuning as a control parameter, chaos in this system has been found to occur through an intermittent route. We have identified certain regions of detuning over which the normal emission of the laser breaks down giving rise to periodic, quasiperiodic, or chaotic behavior.

The induced spectral broadening about a weak non-phase-matched 530-nm second-harmonic pulse is observed by propagating an intense primary 1060-nm picosecond laser pulse through ZnSe crystals. This broadening is attributed to the induced phase modulation of excitation states.

The influence of noise color on the phase diffusion in a ring-laser gyroscope is studied by use of a (formally) exact solution of the time-independent Fokker-Planck equation. Novel asymmetries in the distribution which develop with increasing noise correlation time are predicted and verified with an electronic model of the corresponding Langevin equation.

We found that for some highly nonlinear Schrödinger equations (as contrasted to the cubic equation) the criteria of stability of solitary waves against small and large perturbations do not coincide, which results in the existence of ‘‘weak’’ and ‘‘robust’’ solitons, respectively. We have shown that bistable solitons, predicted earlier by Kaplan, are robust for some particular nonlinearities and, therefore, physically feasible. We have also suggested a general criterion for robustness of solitons.

We examine a number of static and dynamic properties of an eight-mode model for convection in binary mixtures proposed recently by Cross. We find that the model allows richer dynamics than is observed in experiments. We also find differences between the bifurcations and fixed points of the eight-mode model and the five-mode model proposed earlier by Veronis [J. Max. Res. 23, 1 (1965)]. The effect of nonlinearities on the transient dynamics is similar to recent experimental observations. The bifurcations, fixed points, and dynamics are influenced significantly by the addition of an inhomogeneous ‘‘field’’ term to the model.

For the microwave-driven stretched hydrogen atom (SHA) a time-dependent transformation is introduced, which renormalizes Floquet states to include the effect of the permanent dipole moment. The criterion of Hose and Taylor is used to identify the level mixing in the SHA. A differential formula is given for dipole transition matrix elements.

The interpretation of the dynamical scaling indices for transient chaos is given. The spectrum of these scaling indices is calculated in an exactly solvable example of chaotic repellers and, by means of a perturbative method, in a class of chaotic attractors in crisis. An approximate form of the universal spectrum related to the universal chaos function is derived. We point out a degeneracy in the spectrum appearing in an intermittent situation.

The correlation-integral method of Grassberger and Procaccia is generalized to yield the whole spectrum of dimensions $D_q$ and entropies $K_q$ from a measured time series with a numerical effort which is only insignificantly larger than that needed to determine the original correlation integral. It is shown that our method yields reliable numerical results for the tent map and for the Mackey-Glass equation.

Electron spectra from simultaneous electron transfer and ionization (TI) are reported for 300-keV ${\mathrm{H}}^{+}$-He, -Ne, and -Ar collisions. The results are compared with theoretical calculations based on different theoretical approaches, treating TI either within the independent-electron model or as a double-scattering mechanism.

Motivated by the Coulomb-field result that the derivative of the density ρ(r) for an arbitrary number of closed shells is directly proportional to the s-state density ${\rho }_s$(r), we have explored for closed-shell atoms a convolution relation between ${\rho }_s$(r) and ∂ρ/∂r. This relation is most readily expressed in K space, and we thereby establish certain relations between the scattering factors f(K) and $f_s$(K) corresponding to total density and s density, respectively. The method is illustrated by using near-Hartree-Fock accuracy data of Clementi for closed-shell atoms Ne and Ar. For the Hartree-Fock theory, it is shown that at large r, ${\rho }_s$(r)∝$r^{\mathrm{-}4}$ρ(r). Use is made in the convolution representation of the electron-nuclear potential energy of the closed-shell atom and the second derivative ${\partial }^2$ρ/∂$r^2$ evaluated at the nucleus.

The adiabatic Σ electronic terms of highly excited states of the He–alkali-metal atom systems are determined as the roots of a transcendental equation whose only required inputs are the alkali-metal quantum defects, the $e^{\mathrm{-}}$-He s-wave phase shifts and, of course, the internuclear distance R. The results obtained for relatively low excited states are in reasonable agreement with more elaborate calculations. It is found that the notion of adiabatic quantum defects requires R(a.u.)≲2n, n being the principal quantum number. The method is generalized to the case where a small external electric field scrE is present. Then the energy levels strongly depend on the angle between scrE and the internuclear axis. Numerical applications to He-H are presented.

Formulas for the matrix elements of the spin-dependent interactions, such as spin-spin, spin-other-orbit, and effective electrostatic spin-orbit, were constructed for $l^N$l’ configurations, including the two special cases N=1 and 4l+1. Since these interactions are described by two-electron operators, they comprise, in analogy with the electrostatic interaction, both direct and exchange parts. For each of these interactions, 12 angular momenta participate in the orbital part, as well as in the spin part, of the corresponding matrix element. In the formula representing the direct part, both orbital and spin angular momenta are connected according to the identity of Arima, Horie, and Tanabe; in this identity, a double sum of three 6j symbols and one 9j symbol is expressed as a simple product of one 6j symbol and one 9j symbol. In the exchange part, all orbital (spin) angular momenta are grouped in one 12j symbol of the first kind, according to a newly discovered identity; in this identity, the 12j symbol is expressed as a double sum of three 6j symbols and one 9j symbol. All the above-mentioned results were also reproduced by using graphical methods. It can thus be concluded that the identity of Arima, Horie, and Tanabe and the new identity, respectively, represent the symmetry properties of the direct and exchange parts of the two-electron spin-dependent interactions. For the purpose of obtaining simple and closed formulas in the special case N=4l+1, namely, for configurations comprising a hole and an electron, additional new identities were constructed.