The lifetimes of Rydberg atoms have been considered in micromaser theory. The difference from the usual micromaser theory [P. Filipowicz, J. Javanainen, and P. Meystre, Phys. Rev. A 34, 3077 (1986)] without level decay rates is discussed. It is shown that when the atom-field interaction time is large, the quantum collapse and revival are significantly different from the prediction of the usual micromaser theory. The relation between the photon fluctuation and the fluctuation of the population of the lower level after interacting with a maser field is also discussed. We found that the consistency of the sub-Poisson statistics of the lower-level population and photon number is violated.

Double-electron capture by slow (15–30 eV/u) ${\mathrm{Ar}}^{6+}$ ions from He has been studied by simultaneous measurements of postcollisional projectile energy-gain and angular distributions. The recorded spectra are interpreted with the aid of a semiclassical collision model. We find evidence for distinguishable one- and two-step double-electron capture in the energy region investigated.

A canonical generalization of the notion of sensitivity to initial conditions is developed for quantum dynamics and used to define the spectrum of characteristic exponents for quantum systems. It is then shown, under very general conditions, that there exists no positive characteristic exponent nor any sensitivity to initial conditions, however weak, in quantum dynamics. This result implies the nonexistence of chaos is quantum mechanics.

Motivated by the hypothesis that ‘‘self-organized criticality’’ is a common source of 1/f noise, we construct and analyze a class of nonlinear nonequilibrium models describing the dissipative dynamics of interacting particles injected stochastically at the system boundaries. We show that such noisy boundary problems may be analyzed by renormalization-group methods and find that the noise spectrum for the particle number is 1/f in all dimensions in the absence of an external driving force or noise. Addition of such a force or of bulk noise changes the spectrum to 1/${\mathit{f}}^2$, or 1/${\mathit{f}}^{3/2}$, respectively. These results explain several recent numerical experiments on dissipative transport.

I determine the critical behavior of a nonequilibrium three-dimensional lattice model exhibiting a phase transition to an absorbing state. I study the model in the vicinity of the critical point, and in the subcritical region, via time-dependent Monte Carlo simulations. The method used in the subcritical region is very efficient. The results for the directly measured critical exponents, ν=1.11±0.01, η=0.114±0.004, and z=1.052±0.003, are consistent with those of directed percolation. δ=0.732±0.004 is obtained from the hyperscaling relation 4δ+2η=dz, and β=0.813±0.011 from β=νδ. These results are the most precise so far for a three-dimensional model with directed percolation critical behavior.

We study numerically the behavior of some topological spiral defects, their dynamics being governed by a complex Ginzburg-Landau equation with space-dependent coefficients. We show that the interaction between a spiral and the gradients of the coefficients can counterbalance the repulsion between defects of identical sign and lead to topologically stable patterns. Configurations of several defects with the same topological charge have been observed recently in nonlinear optics experiments.

Microscopic solidification morphologies of binary systems are simulated with a Monte Carlo model that accounts for bulk diffusion, attachment and detachment kinetics, and surface diffusion. Through variation of interaction energies and undercooling, a broad range of microstructures is obtained, including eutectic systems and layered and ionic compounds.

A theoretical model is developed for the investigation of the adiabatic reflection of electrons from a spatially localized electromagnetic wave, taking into account the nonlinear trapping in the wave field. A complete analytic description of the adiabatic motion is given via the constancy of the Hamiltonian and the invariance of the adiabatic integral. The set of initial conditions for which reflection occurs is determined in detail as a function of the field amplitude and of the wave frequency for the case of electron-cyclotron waves in perpendicular propagation. The comparison with the results of the Lie transform approach is performed. It is found that trapping effects strongly modify the reflection process, giving rise to a substantial enhancement of the repulsive ponderomotive force. When trapping occurs, reflection is observed for a large set of initial conditions for which the perturbative approach predicts no reflection at any value of the perturbation.

A perturbation series of the distorted-wave Born type is developed in such a way that the slow decrease of the Coulomb potential in which the incoming and scattered particles move plays no role. We apply this approach to triple-differential cross sections for electron-impact ionization of helium at low and intermediate energies, where we use Coulomb waves with an effective charge for the incoming, scattered, and ejected electron, and show that even though these wave functions are known to satisfy the wrong Coulomb boundary conditions at infinity, they give reasonably and unexpectedly good agreement with experiment.

A noncompact, nonintegrable billiard of importance in cosmology—the infinite equilateral triangle on a space of constant negative curvature—gives rise to a natural noncompact integrable approximation, which is studied here quantum mechanically. The Weyl formula for the averaged spectral staircase contains a nonstandard logarithmic term due to the noncompactness of the billiard. For two symmetry classes we determine numerically the spectral staircase, the level-spacing distribution p(s), and the averaged ${\mathrm{\Delta }}_3$ statistic, and compare with analytical expressions that follow from Poisson statistics and semiclassical theory. The Poissonian result for the correlation function of ${\mathrm{\Delta }}_3$ is derived in closed form and also compared with the data.

An alternative concept of the basic invariants is introduced. The Lewis-Riesenfeld invariant theory is extended to obtain a generalized invariant formulation. The formulation is then used to establish four facts: (i) Any invariant for a quantum system can be constructed in terms of the basic invariants. (ii) It is possible to introduce a solution-generating technique by making use of the basic invariants. (iii) The path integral in the generalized invariant formulation reduces to an ordinary integral. (iv) The study of noncyclic evolution of a quantum system reduces explicitly to the study of the cyclic evolution. Finally, phase factors and general solution for the driven generalized time-dependent harmonic oscillator are studied as an illustrative example.

The ultimate sensitivity of interferometric gravitational-wave detectors requires extremely high light powers sensing the separation of test masses. Absorption of light at the optical components causes wave-front distortions via the thermally deformed substrates or via thermal lensing. The performance of thermally distorted interferometers is treated quantitatively, and the two schemes for increasing the optical path, the delay-line and Fabry-Pérot methods, are compared.

We extend the scope of the modified Riccati approach to partial solubility in quantum mechanics introduced in a previous work [L. D. Salem and R. Montemayor, Phys. Rev. A 43, 1169 (1991)]. With the use of adequate mappings u(x), we show the convenience of the modified Riccati approach to analyze potentials that can be written as rational functions on u. The necessary conditions for a Hamiltonian to be solvable are discussed in detail. By considering the exponential mapping u=${\mathit{e}}^{\mathrm{-}\mathit{x}}$, we construct a family of potentials related to the exactly solvable Morse oscillator. Within this family, we have identified a three-parameter quasiexactly solvable potential, which, depending on the value of its coupling constants, leads to a symmetric or asymmetric confining potential, with a single-well or a double-well structure. Explicit expressions for the energies and eigenfunctions are given for particular cases. The analytic continuation of the symmetric subset gives rise to a quasiexactly solvable periodic potential.

An information-theoretic inequality analogous to the well-known result of Bell [Physics 1, 195 (1964)] is formulated using the concept of information distance. This inequality, like Bell’s, is true for all local-hidden-variable theories, but not for quantum mechanics. The metric space structure of this new inequality suggests a reformulation of familiar Bell inequalities in terms of a ‘‘covariance distance.’’ Quantum nonseparability can be demonstrated through violations of these inequalities even in cases where the correlation between two systems is extremely weak. The connection between nonseparability and complementarity is also briefly discussed in this paper.

Three-body symmetrized vector hyperspherical harmonic functions, realizing irreducible representations of the permutation group of three particles, are constructed and expressed in terms of Wigner D functions. Matrix elements of arbitrary two-body potentials between these hyperspherical states, including their velocity-dependent parts, are calculated analytically and expressed through the sum of products of the Wigner 3-j symbols and explicitly written functions of the radial variable.

The formula Γ=4${\mathrm{\sigma }}_{\mathrm{tot}}$${\mathit{v}}_{\mathit{e}}^{+}$‖ψ(0)${\mathrm{\Vert }}^2$ gives the decay rate for the singlet positronium atom into two photons in terms of the total cross section for the unbound (on-mass shell) annihilation ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$→2γ and the ${\mathit{e}}^{+}$${\mathit{e}}^{+}$ bound-state wave function at the origin and leads to the results m${\mathrm{\alpha }}^5$/2 to lowest order in α. We show how this same result can be found by treating the electron and positron as bound (off their respective mass shells). This solves the problem of how to find this decay rate when faced with a relativistic wave function that is mildly singular at the origin.

Improved estimates of the nonrelativistic stationary nucleus correlation energies of the ground-state atomic ions with three to ten electrons and Z up to 20 are derived by combining experimental data and improved ab initio calculations. Unlike previous work in this area, we focus on the correlation contribution to individual ionization energies, computed by comparing experimental data with relativistic complete-valence-space Hartree-Fock energies.

One way to reduce the large degeneracy of the hyperspherical-harmonic basis for solving few- and many-body bound-state problems is to introduce an optimal basis truncation called the potential-harmonic (PH) basis. In this paper we introduce various potential-harmonic truncation schemes and assess their accuracies in predicting the energies of the helium and ${\mathrm{H}}^{\mathrm{-}}$ ground states and the excited 2 ${}_{}{}^1{}_{}{}^{}$S level of the helium atom. We first find that the part of the PH basis that accounts for one-body correlations gives a better ground-state energy for He than Hartree-Fock (2.8790 a.u. versus 2.8617 for Hartree-Fock and 2.9037 exact). When an orthogonal complement is introduced to the basis to account for e-e correlations, we find that the error in the binding energy is 0.000 25 a.u., and 0.000 15 a.u. for ground-state and excited helium, and 0.000 35 a.u. for ${\mathit{H}}^{\mathrm{-}}$. Furthermore, the PH truncation is about 99.9% accurate in accounting for contributions coming from large values of the global angular momentum. This PH scheme is also much more accurate than previous versions based on the Faddeev equations. The present results indicate that the PH truncation can render the hyperspherical-harmonic method useful for systems with N>3.

The relativistic configuration-interaction method with analytical relativistic Hartree-Fock-Roothaan (RHFR) basis functions for atomic systems is presented. One-electron functions used for constructing configuration state functions (CSF’s) are obtained with the RHFR method in which the large and small components of the radial part of a four-component wave function are expanded in terms of an analytical basis set consisting of Slater-type orbitals. Numerical application of the method to neonlike atomic systems is carried out. It is shown that calculated excitation energies with the method are in good agreement with experiment. The Z-dependent behavior of the optical oscillator strengths for various electric-dipole transitions from the ground state in the systems is also given.

A detailed analysis is presented for the evaluation of atomic integrals of the form F${\mathit{r}}_1^{\mathit{i}}$${\mathit{r}}_2^{\mathit{j}}$${\mathit{r}}_3^{\mathit{k}}$${\mathit{r}}_{23}^{\mathrm{-}2}$${\mathit{r}}_{31}^{\mathit{m}}$${\mathit{r}}_{12}$ ${}_{}{}^{\mathit{n}}{}_{}{}^{}$${\mathit{e}}_1^{\mathrm{-}\mathrm{\alpha }\mathit{r}}$-β${\mathit{r}}_2$-γ${\mathit{r}}_3$d${\mathbf{r}}_1$ d${\mathbf{r}}_2$ d${\mathbf{r}}_3$, which arise in several contexts of the three-electron atomic problem. All convergent integrals with i≥-2, j≥-2, k≥-2, m≥-1, and n≥-1 are examined. These integrals are solved by two distinct procedures. A majority of the integrals can be evaluated by a reduction of the three-electron integrals to integrals arising in the atomic two-electron integral problem. A second approach allows all integrals with the aforementioned indices to be evaluated by the use of Sack’s expansion [J. Math. Phys. 5, 245 (1964)] of the interelectronic separation, which leads to a reduction of the above nine-dimensional integrals to a set of three-dimensional integrals. A discussion is given for the numerical evaluation of the three-dimensional integrals that arise.