The density-functional theory for ensembles of fractional occupation formulated by Gross, Oliveira, and Kohn [Phys. Rev. A 37, 2821 (1988)] has been applied. The excitation energies of several atoms have been determined using a parameter-free exchange potential of Gáspár [Acta Phys. Hung. 35, 213 (1974)]. The calculated excitation energies are in good agreement with the experimental values.

Electron-impact cross sections for exciting the oxygen molecule from the ground electronic level to the ns${\mathrm{\sigma }}_{\mathit{g}}$, np${\mathrm{\sigma }}_{\mathit{u}}$, nd${\mathrm{\sigma }}_{\mathit{g}}$, nf${\mathrm{\sigma }}_{\mathit{u}}$, np${\mathrm{\pi }}_{\mathit{u}}$, nd${\mathrm{\pi }}_{\mathit{g}}$, and nf${\mathrm{\pi }}_{\mathit{u}}$ Rydberg levels associated with the ${\mathrm{O}}_2^{+}$(B ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{\mathrm{-}}{}_{}{}^{}$) and ${\mathrm{O}}_2^{+}$(b ${}_{}{}^4{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{\mathrm{-}}{}_{}{}^{}$) cores are presented. For each Rydberg series of a given l, m, and ${\mathrm{O}}_2^{+}$ core state, the cross sections exhibit n dependence of the form ${\mathit{n}}^{\mathrm{-}\mathrm{\alpha }}$ with α varying from one series to another in the range of 1.47 to 4.60 in contrast to the more universal ${\mathit{n}}^{\mathrm{-}3}$ dependence for the hydrogen atom. The potential cusps at the two nuclear sites of the molecule make the Rydberg orbital density near the origin quite different from that of the hydrogen atom, thereby spoiling the simple ${\mathit{n}}^{\mathrm{-}3}$ dependence.

The individual cross sections σ(${\mathit{m}}_{\mathit{a}}$,${\mathit{m}}_{\mathit{b}}$) for the associative ionization process Na(3p,${\mathit{m}}_{\mathit{a}}$)+Na(3p,${\mathit{m}}_{\mathit{b}}$)→${\mathrm{Na}}_2^{+}$+e are calculated semiclassically over a wide velocity range. Qualitative comparisons are made with experimental results in which the colliding Na(3p) atoms have been excited by laser into specific ${\mathit{m}}_{\mathit{l}}$ states.

Excitation of the 3 ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }_{\mathit{u}–}^{}{}_{}{}^{}$X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$ transition in ${\mathrm{Cs}}_2$ by the 476.5-nm line of an argon-ion laser in the presence of inert gases results in emission from the 7${\mathit{p}}^2$${\mathit{P}}_{3/2}$ and 7 ${}_{}{}^2{}_{}{}^{}\mathrm{P}_{1/2}^{}{}_{}{}^{}$ atomic states of Cs. This verifies 6 ${}_{}{}^2{}_{}{}^{}\mathrm{S}_{1/2}^{}{}_{}{}^{}$+7p ${}_{}{}^2{}_{}{}^{}\mathrm{P}$ as the dissociation products of 3 ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }_{\mathit{u}}^{}{}_{}{}^{}$ and a dissociation energy of 4730.5±0.8 ${\mathrm{cm}}^{\mathrm{-}1}$ for the 7${\mathit{p}}^2$${\mathit{P}}_{3/2}$ limit or 4911.5±0.8 ${\mathrm{cm}}^{\mathrm{-}1}$ for the 7 ${}_{}{}^2{}_{}{}^{}\mathrm{P}_{1/2}^{}{}_{}{}^{}$ limit.

Total cross sections for electron scattering by CO molecules in the energy range 380–5200 eV have been measured with experimental errors of 3%. The present results have been compared with available experimental cross sections. No previous data have been found in the literature for impact energies above 500 eV. The dependence of total cross sections on electron energy is in agreement with the Born-Bethe approximation.

A consistent explanation of recent studies by Szabo and Muramoto [Phys. Rev. A 39, 3992 (1989); 38, 5928 (1988)] on the experimental test of modified optical Bloch equations is presented. It is shown that the observed peculiarities of optical transients in solids are connected with the mechanism of relaxation in systems with slow stochastic modulation. A theory of laser-modified relaxation and analysis of free induction decay (FID), hole burning, and rotary echo (RE) in such systems are presented. The universal character of the FID time dependence and field-independent RE decay is predicted.

The 3${\mathrm{}}^3$P–5${\mathrm{}}^3$S transition in atomic oxygen at 725.4 nm has been studied in a weak discharge using the optogalvanic effect with a cw tunable dye laser. The transition appears as a superposition of at least two components with different centroids and widths. The anomalous line shape is probably due to the long-range interaction of ${}_{}{}^3{}_{}{}^{}$P oxygen with ${}_{}{}^4{}_{}{}^{}$${\mathit{S}}_0$ oxygen ions.

A systematic variation in the line-intensity ratios of Gai– and Zni–like Pr (Z=59) to Dy (Z=66) ions has been observed in spectra emitted by atoms injected in a low-density high-temperature tokamak plasma. This variation is shown to be correlated with the progressive closing of the autoionizing channels through the excited 3${\mathit{d}}^9$4${\mathit{s}}^2$4p4f configuration in the Gai–like ionization state as Z increases.

The ${\mathrm{H}}^{\mathrm{-}}$ ion is modeled by an effective one-electron potential specified by a regularized three-dimensional δ-function potential. With the help of quasienergy methods, the multiphoton-detachment rate of this model ion by a plane-wave field of arbitrary elliptical polarization can be expressed as a one-dimensional integral that has to be evaluated numerically. The results exhibit a pronounced dependence on the polarization of the laser: circular polarization yields a rate that depends smoothly on frequency and intensity with barely noticeable thresholds. In contrast, linear polarization generates marked thresholds as well as structure in between. All of the calculated thresholds closely obey the Wigner threshold law. There is good agreement with the available data where the ponderomotive energy is kept constant while the frequency varies.

Well dynamics within the quantum Kramers model is studied. The validity of the approach based on linear-response theory for the bath of normal modes is explored by including the second-order terms in the classical equations of motion (EOM) for the stable modes. The effect of nonsecular terms describing the linear interaction between the stable modes vanishes upon averaging over the distribution of initial positions and velocities of stable modes. By accounting for the secular terms, the classical EOM’s for the stable modes are reduced to those of forced oscillator with time-dependent frequency. An exact expression for the transition probability kernel is derived using the known quantum-mechanical solution for the model. The time-reversal symmetry of EOM ensures that the kernel satisfies the detailed-balance condition. The corrections to the linear-response-theory results for the kernel and for the average energy loss and its dispersion are exponentially small for the high-frequency modes due to the slow (adiabatic) variation of the frequency. They are important in the case of the continuum spectrum of the bath, when the dominant contribution is due to the low-frequency modes. The results demonstrate the validity of the perturbative approach in the study of well dynamics.

We present a numerical study of the two-wave system that reveals the occurrence of stochasticity for a limited range of the perturbation only, beyond that it disappears. We refer to this type of stochasticity as ‘‘intermediate stochasticity.’’ Using a Fourier analysis, it is found that intermediate stochasticity is closely associated with the mode-locking phenomenon taking place in the system. A theoretical analysis of this phenomenon, based on an extension of the Krylov-Bogoliubov theory of slow variation parameters, which is appropriate to strongly nonlinear equations, is presented. This analysis explains the main qualitative features of the numerical observations.

We study a two-state quantum-mechanical system, equivalent to a 1/2-spin dipole, with frequency ${\mathrm{\omega }}_0$, linearly interacting with a set of quantum oscillators. The corresponding discrete nonlinear Schrödinger equation (DNSE) has been given an analytical solution by Kenkre and Campbell [Phys. Rev. B 34, 4959 (1986)]. We show that in the strong-coupling limit their analytical expression is recovered from our microscopic approach when the thermal and quantum fluctuations of the bath of oscillators are neglected. To take into account the influence of thermal and quantum fluctuations on the prediction of the DNSE in the strong-coupling limit, we adopt a straightforward procedure based on the direct evaluation of 〈${\mathrm{\sigma }}_{\mathit{x}}$(t)〉, under the assumption alone that the frequency ${\mathrm{\omega }}_0$ is very weak. A special initial condition is used, with 〈${\mathrm{\sigma }}_{\mathit{x}}$(t)〉=1 and the oscillator at equilibrium in the corresponding effective potential. It is shown that in the strong-coupling limit this expression coincides with the noninteracting-blip approximation of Leggett et al. [Rev. Mod. Phys. 59, 1 (1987)] and the result of the equivalent projection approach of Aslangul, Pottier, and Saint-James [J. Phys. (Paris) 46, 2031 (1985); 47, 1657 (1986)]. Then, this expression is used to study the special case where the 1/2 spin interacts with only one oscillator at zero temperature. It is shown that the fast oscillations predicted by Kenkre and Campbell in the strong-coupling limit are damped by a Gaussian-like relaxation process provoked by the quantum fluctuations of the oscillator, which eventually lead to the destruction of the trapped state. These collapses are followed by periodical revivals reminiscent of those observed in quantum optics.

We use a dynamical two-chain model to study anomalous transport in chainlike systems (like polymers) with a statistical distribution of transition rates. Temporal disorder (resulting from energetic or spatial randomness) is taken into account in the framework of continuous-time random walks. The interchain and intrachain transitions are characterized by different waiting-time densities. The effective current along the chains is studied as a function of the interchain and intrachain waiting-time densities. The approach presented here allows an exact expression for the Laplace-transformed effective current and for higher moments of the effective probability distribution of the walker. The general scheme can be applied to a model consisting of N chains and also to higher-dimensional lattices.

In a preceding publication [Z. Y. Chen, P. C. Albright, and J. V. Sengers, Phys. Rev. A 41, 3161 (1990)] a procedure for constructing a thermodynamic free energy of fluids was proposed that incorporates crossover from singular behavior at the critical point to regular behavior far away from the critical point. In the present paper this procedure, based on an approximate solution of the renormalization-group theory of critical phenomena, is further extended so that it can be used in conjunction with a six-term classical Landau expansion. The resulting thermodynamic free energy yields a satisfactory representation of the thermodynamic properties of fluids in a large range of temperatures and densities around the critical point, as is demonstrated by a comparison with experimental thermodynamic-property data for carbon dioxide, steam, and ethane.

The class of Fokker-Planck equations considered in this paper bridges the gap between the generalized Verhulst-Landau process and the Rayleigh process, which were apparently unrelated up to now. The equations are solved analytically for the transition probability density function of the underlying stochastic processes. The solution method uses operational calculus, and simultaneously produces all components of the spectral problem: spectrum, eigenfunctions, and their normalization. The general results obtained are benchmarked with the known results for the above-mentioned processes by inserting suitable parameters.

Nonlinear dissipative mapping is applied to determine the trajectory of a two-dimensional die thrown onto an elastic table. The basins of attraction for different outcomes are obtained and their distribution in the space of initial conditions discussed. The system has certain properties in common with chaotic systems. However, a die falls to rest after a finite number of impacts, and therefore the system has a finite sensitivity to the initial conditions. Quantitative measures of this sensitivity are proposed and their variations with the initial momentum and orientation of the die investigated.

A method is presented for the study of first-passage-time statistics in one-dimensional disordered media. We introduce a projection-operator formalism that allows the calculation of an averaged backwards master equation. A generalized Dynkin’s equation is also presented. We apply this approach to the random-trap model. The exact mean first-passage time to leave a finite domain is calculated for weak disorder. To study strong disorder we introduce a mean-field-like approximation that gives exact results at long times. Long-time tails in the survival probability and in the first-passage-time distribution are found, predicting a divergent mean first-passage time for the case of strong disorder. Our findings confirm numerical results found previously.

We obtain the generalized susceptibility for the motion of a charged oscillator in a harmonic potential well in the presence of a uniform external magnetic field, and linearly coupled to a heat bath, by using the generalized quantum Langevin equation we obtained in an earlier paper. The result is then used to calculate the autocorrelation function of the position operator of the oscillator by the fluctuation-dissipation theorem. The free energy of the oscillator is then obtained in terms of the determinant of the susceptibility matrix. Applications are made to two types of heat baths: the Ohmic case and the case of blackbody radiation. As a special case (no heat bath) of our general formalism, a well-known eigenspectrum result is obtained but in a simple and rather novel fashion.

We introduce and investigate a family of exactly self-similar nonrandom fractal measures, each having stretched exponentially decreasing minimum probabilities. This implies that τ(q) is not defined for q<0 and that ${\mathit{q}}_{\mathrm{bottom}}$=0 is a critical value of q. Since the partition function does not scale for all values of q, these measures are not multifractals in the restricted sense due to Frisch and Parisi [in 2 Turbulence and Predictability of Geophysical Flows and Climate Dynamics, Proceedings of the Enrico Fermi International School of Physics, edited by M. Ghil, R. Benzi, and G. Parisi (North-Holland, New York, 1985), p. 84] and to Halsey et al. [Phys. Rev. A 33, 1141 (1986)]. However, they are exactly self-similar, hence are multifractals in a much earlier and more general meaning of this notion [B. Mandelbrot, J. Fluid Mech. 62, 331 (1974)]. We show that in these measures the ‘‘free energy’’ τ(q) is singular at q=${\mathit{q}}_{\mathrm{bottom}}$, in the sense that τ(q)=-1+${\mathit{c}}_{\lambda }$${\mathit{q}}^{\lambda }$+${\mathit{c}}_1$q+${\mathit{c}}_2$${\mathit{q}}^2$+O(${\mathit{q}}^3$), where 0<λ is a ‘‘critical’’ exponent. For λ≤1, the transition in the f(α) is smooth (i.e., of infinite order), while for λ>1, the transition order is ≥2. We then use a new sampling method to study problems arising in the study of such transitions in case of undersampling.