Current gradient-corrected density-functional approximations for the exchange energies of atomic and molecular systems fail to reproduce the correct 1/r asymptotic behavior of the exchange-energy density. Here we report a gradient-corrected exchange-energy functional with the proper asymptotic limit. Our functional, containing only one parameter, fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.

The quantization of a system subject to a force quadratic in the velocity and position dependence is carried out in the phase-space path-integral framework. The resulting Hamiltonian coincides with that obtained by using the Weyl-ordering canonical prescription.

Small extra Zeeman shifts measured in the ground states of ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ and ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ have previously been shown to be due to the hyperfine interaction to second order coupled with the Zeeman interaction to first order. Approximate theoretical calculations yielded effective frequencies for the two isotopes of 0.016 Hz/T and 0.18 Hz/T, respectively, in good agreement with experiments. We calculate exactly the same shift for the 1s and 2s states of ${}_{}{}^2{}_{}{}^{}\mathrm{H}$ by perturbation differential equations. For the 1s and 2s states the respective frequencies are 2.61×${10}^{\mathrm{-}5}$ Hz/T and 2.56×${10}^{\mathrm{-}5}$ Hz/T.

The muonic x-ray intensities of the Lyman series in pure silicon are investigated. The fitted data are compatible with a statistical initial angular momentum distribution of the captured muons. From a comparison with data measured in diamond, cubic boron nitride and in the two isoelectronic series ${\mathrm{F}}^{\mathrm{-}}$,Ne,${\mathrm{Na}}^{+}$ and ${\mathrm{Cl}}^{\mathrm{-}}$,Ar,${\mathrm{K}}^{+}$, we conclude that the calculated muon distribution reflects the symmetry of the electrons through which muon capture proceeds.

‘‘Cyclo-Raman resonance’’ of a single electron (i.e., cyclotron motion of an electron driven by optical fields) in the nth order at the cyclotron frequency ${\Omega }_c$ can be excited by biharmonic laser beams with their frequencies ${\omega }_1$ and ${\omega }_2$ such that ${\omega }_1$-${\omega }_2$≊n${\Omega }_c$. This effect exhibits hysteresis, ‘‘prohibited’’ and ‘‘allowed’’ orbits of excitation, phase multistability, and the optical Stark effect.

Using a molecular theory of harmonic generation developed within the framework of quantum electrodynamics, we prove that second-harmonic generation is forbidden in isotropic fluids to all levels of multipolar approximation.

We consider the evolution of configurations in a layered feed-forward neural network. Exact expressions for the evolution of the distance between two configurations are obtained in the thermodynamic limit. Our results show that the distance between two arbitrarily close configurations always increases, implying chaotic behavior, even in the phase of good retrieval.

Recently, attempts have been made to alter the equation of motion of a multiparticle system so that the temperature rather than the energy is constant. Nosé introduced a modified multiparticle equation of motion involving an auxiliary equation with a free parameter Q. We consider the Nosé-Hoover equation for a one-dimensional oscillator as the equation of motion for a coupled oscillator system with two degrees of freedom. For different values of Q, we consider the dynamics in the four-dimensional phase space by examining two-dimensional surfaces of section. We show that the overlapping of resonance zones causes a transition to large-scale irregular dynamics for a limited range of Q.

The strong-potential Born approximation to the single-electron capture amplitude in asymmetric ion-atom collisions is discussed in the context of a realistic atomic potential. When finalstate binding effects of the captured electron are neglected, a simple connection between the amplitude in the actual atomic-potential case and the one obtained employing a scaled-hydrogenic model is derived which involves the competing effects of an off-shell multiplicative term depending on the residual, target-ion charge and a phase factor containing the difference of the $s$-wave phase shifts for the two potentials.

Phase as well as amplitude dynamics in the complex laser Lorenz model have been studied, in contrast to previous studies limited to intensity (i.e., amplitude only). The topological nature of the chaotic intensity is not modified by a small detuning, although the electric field phase is dramatically altered, showing a steady drift with respect to the frequency of the corresponding steady-state solution in addition to small-scale modulation. For larger detunings at the same pump parameter, where one finds periodic intensity pulsations, there is a similar average drift in the phase leading to spuriously quasiperiodic representations of the attractor. After removal of this average drift (which amounts to a frequency shift) all dynamical variables, including the phase, have the same periodicity.

We show that the two-photon phase coherence of parametrically generated photon pairs, which is at the origin of squeezed-light generation, can be directly probed using an intensity-correlation measurement. The resulting intensity correlation leads to a new violation of Bell's inequalities, which could be experimentally tested.

The statistical properties of the time delay between the switch on and the attainment of a fixed value of the output power in single-mode semiconductor lasers are analyzed and discussed. In particular, we show that the only parameter needed to describe the process, when the laser is initially operated quite below threshold, is the value of the stationary output power of the final state, a result supported by recent experimental measurements.

By combining the technique of exploding foils with inner-shell photoionization, we predict that lasing can occur for x rays below 50 Å in Cu-like ions. As an example, we work out the case for Cu-like iodine (${\mathrm{I}}^{24+}$) which should lase on the ${3d}^9{4s}^2\to {3d}^{10}4p$ doublet calculated at 24.565 and 26.026 Å with integrated line energies comparable to the selenium x-ray laser.

We report measurements of the convective heat transport near the onset of convection in a normal ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixture for values of the separation ratio $\psi$ between -0.044 and -0.010. For $\psi \lesssim -0.018\mathrm{}$, the first bifurcation was to a relatively large-amplitude time-dependent state with characteristic frequencies over an order of magnitude smaller than predicted by linear-stability analysis. The onset of the time dependence was intermittent and not hysteretic. Above onset, the frequency spectrum of the time dependence either contained discrete frequencies or not, depending on $\psi$.

Using high-resolution laser Doppler velocimetry, we have experimentally obtained comprehensive results concerning the oscillatory onset of free convection (relevant critical Rayleigh numbers and the associated periods of oscillations are in agreement with theoretical predictions), the stable monoperiodic oscillatory states (traveling waves) just past the critical point, and the transition towards steady states for greater Rayleigh numbers. Our most striking result is obtaining, when decreasing the imposed Rayleigh number below the critical point, stable biperiodic oscillatory states (modulated traveling waves).

We study the motion of a reaction front formed by a process, $A+B\to C$, in which the reagents are transported by diffusion and the reaction kinetics is of second order. A scaling description valid in the long-time limit is derived analytically, and it is found that the center ($x_f$) and the width ($w$) of the front scale with time as $x_f\sim \sqrt{t}$ and $w\sim t^{\frac{1}{6}}$, while the production rate of $C$ at $x_f$ is proportional to $t^{\frac{-2\mathrm{}}{3}}$.

Ab initio self-consistent all-electron spin-polarized calculations have been performed for the ground-state properties of the ${\mathrm{Fe}}_2$ molecule using the local-spin-density approximation. A Gaussian orbital basis is employed and all the two-electron integrals are evaluated analytically. The matrix elements of the exchange-correlation potential are computed numerically. The total energy, the binding energy, the equilibrium distance, vibrational frequency, and the ground-state configurations are reported and compared with other calculations and experimental results.

The generalized-exchange local-spin-density-functional theory with self-interaction correction has been used to calculate negative ions. The effect of the Fermi hole in the negative ions is discussed. The results are compared with experiment, Hartree-Fock, and other theoretical methods. It is shown that relaxation and correlation effects are very important for the negative ions.

The purpose of this work is to provide a quantitative underpinning to the qualitative understanding of the various physical effects which play a role in the spectra of many-electron atoms. Shielding and exchange contributions are studied, as functions of the principal quantum number n, the orbital angular momentum l, and the nuclear charge Z, for neutral alkali-metal atoms in the Dirac-Fock (DF) approximation. Fine-structure effects and valence-state correlation corrections to the DF approximation are also considered for these atoms. Breit interaction and correlation corrections are discussed for the core states of noble gases. Previous numerical computations of these various contributions to atomic energy levels by others are extended to provide a larger data set to serve as a basis for the study of estimates and trends.

Equations are derived for the calculation of the relativistic propagator for a multielectron atom consisting of n spin-1/2 point fermions of different masses. A Hamiltonian is found whose eigenfunctions approximately diagonalize the propagator. This Hamiltonian reduces to that found by Salpeter [Phys. Rev. 87, 328 (1952)] for two fermions (the hydrogen atom) and appears to have the proper structure to reduce to the nonrelativistic Coulomb Hamiltonian in that limit. Formulas are presented for calculating improvements to the propagator to any order.