A recent and interesting experimental paper [B. McNamara, K. Wiesenfeld, and R. Roy, Phys. Rev. Lett. 60, 2626 (1988)] has refocused attention on the problem of stochastic resonance by presenting measurements of the singal-to-noise ratio (SNR) of a noise driven, periodically modulated bistable ring laser. We point out that the theoretical SNR, as defined in this and a previous work, is always infinity, because additive modulation leads to a δ function in the power spectrum of the output. Quantitative information on stochastic resonance is contained in the strength of this δ function relative to the noise background. We qualitatively reproduce the SNR data with an analog simulator using a standard quartic bistable potential. In this, as in previous experiments and simulations, a peak in the observed power spectrum is a reflection of the δ function, but the amplitude of the peak is rendered finite (and hence measureable) only because of the finite resolution of the measurement system.

In lattice gases the Boltzmann equation is not valid at low densities, if the collision rules admit reflections of unlike particles because of long-lived correlated ring-type collisions. This is shown for a simple mixture, a Lorentz gas, by comparing theoretical and molecular dynamics results for the diffusion coefficient.

Molecular-dynamics simulations of fluids composed of hard ellipsoids yield translational diffusional coefficients that deviate from the predictions of kinetic theory in the same way, but to a greater degree than, those of hard spheres. Surprisingly, however, the rotational diffusion coefficients are closely predicted by Enskog theory for all but the highest densities. However, for both motions, even at zero density, there are small deviations from kinetic theory, presumably due to chattering recollisions. Though the phase diagram is approximately symmetric between prolate and oblate ellipsoids of the same asymmetry, the dynamical properties are not. No existing theory explains these observations.

Mean-field methods of statistical physics are applied to replicator selection with N randomly interacting species and deterministic self-interaction u. We present the outcome of a replica symmetric calculation for the global maximum of the mean fitness which is a Lyapunov function of the system. The replica symmetric solution is stable and no further equilibrium states exist at least for u> √2 . On the other hand, in the low-u region the dynamics relaxes to states which differ from the replica symmetric result.

We report results of Monte Carlo simulations of diffusion on random two-dimensional substrates generated by N-step random walks. In contrast to a previous study by Dekeyser, Maritan, and Stella [Phys. Rev. Lett. 58, 1758 (1987); Phys. Rev. A 36, 2338 (1987)], we find the effective exponent ${\nu }_{\mathrm{eff}}$ for the mean-square displacement of the diffusion process to be a slowly varying function of N, with (1/2-${\nu }_{\mathrm{eff}\mathrm{\propto }1/\mathrm{n}\mathit{N}}$ as N→∞.

We have studied the effect of high pressure on the phase transitions in the seventh to tenth homologs of 4-alkoxyphenly-4’-nitrobenzoyloxybenzoates (DB.kO.${\mathrm{NO}}_2$). While pressure does not induce any new phases in k=7 or 8, it has a dramatic effect on k=10: triply reentrant behavior is seen over a narrow range of pressure, the sequence of transitions being the same as that observed in k=9 or DB.9O.${\mathrm{NO}}_2$ at atmospheric pressure. This is the first instance of pressure-induced multiply reentrant behavior in a single-component system. The observed sensitivity of the multiply reentrant behavior to molecular chain length and pressure is according to the predictions of the frustrated spin-gas model of polar liquid crystals.

We investigate the spatial correlation of a model of aggregation system with injection. This system is characterized by a single point on the f-α diagram (f=1,α=3) which is identical to the case of independent power-law distributions. The R/S analysis also shows no dependency. However, theoretically there exists a higher-order correlation which is difficult to detect but strong eneough to modify the exponent of mass distribution.

A linear equation of motion for the state vector is presented, in which an anti-Hermitian Hamiltonian that fluctuates randomly is added to the usual Hamiltonian of the Schrödinger equation. It is shown how the resulting theory describes the continuous evolution of a state vector to an ensemble of reduced state vectors while retaining important physical features of the Ghirardi, Rimini, and Weber [Phys. Rev. D 34, 470 (1986)] theory of spontaneous localization, in which the state vector reduction occurs discontinuously. A novel aspect, compared with ordinary quantum theory, is that the state-vector norm changes with time. The squared norm of each state vector is interpreted as being proportional to the probability possessed by that state vector in the ensemble of state vectors. This interpretation is shown to be consistent with the independent Markovian evolution of each state vector.

An empirical model for the correlation energy ($E_c$) of atoms is proposed. The method, a perturbation applied to the Roothaan Hartree-Fock atomic functions, requires the reevaluation of the two-electron integrals due to the introduction of a ‘‘soft’’ Coulomb hole whose magnitude is calibrated semiempirically. We have tested it by computing the total correlation energy, the first ionization potentials for atoms helium through xenon, by considering excited states of the ground-state configuration for Z=3 to Z=18 and the electron affinity for fluorine, chlorine, bromine, and iodine ions.

In this paper we present a realization of the concept, first put forth by V. Efimov [Few Body Dynamics, edited by A. N. Mitra et al. (North-Holland, Amsterdam, 1976)], of enhancing the Efimov effect by placing the three particles in a medium whose parameters vary. We do this in the context of equilibrium statistical mechanics by incorporating three-body potentials and subsequently writing their contribution to the cluster series in terms of effective, density-dependent, two-body potentials. We then perform approximate partial summations of the cluster series expressing the sums in terms of cluster coefficients involving the effective potentials. From the high-temperature expansion of the corresponding equation of state for a model system, we find that, at the Efimov point, behavior resembling that of a first-order phase transition appears.

The first through fourth derivatives of the statistical total energy in the generalized exchange local-spin-density-functional (LSD-GX) theory with respect to the occupation number are given, and used to calculate electronegativities, hardnesses, first and second ionization potentials, and electron affinities for some atoms. The effects of the Coulomb correlation and relaxation correction on the calculations of ionization potentials and electron affinities are discussed. Comparing the results with experiment, it is shown that the Gazquez and Ortiz relaxation model in the LSD-GX scheme [Gazquez and Ortiz, J. Chem. Phys. 81, 2741 (1984)] is a powerful method for calculating the first and second ionization potentials of atoms, but not for calculating electron affinities, since correlation is more important than relaxation in the calculation of the electron affinity.

We discuss three different formulations of the Coulomb approximation that allow us to avoid numerical difficulties encountered with the standard one in the case of transitions between highly excited states. A common feature of these alternative (though not equivalent) methods is the fact that the radial multipole matrix elements are expressed in terms of standard or generalized hypergeometric functions. The recurrence relations satisfied by the latter can be used to bypass the loss of accuracy resulting from dramatic cancellations among their individual terms.

Sakharov has proposed a suggestive model in which gravity is not a separately existing fundamental force, but rather an induced effect associated with zero-point fluctuations (ZPF’s) of the vacuum, in much the same manner as the van der Waals and Casimir forces. In the spirit of this proposal we develop a point-particle–ZPF interaction model that accords with and fulfills this hypothesis. In the model gravitational mass and its associated gravitational effects are shown to derive in a fully self-consistent way from electromagnetic-ZPF-induced particle motion (Zitterbewegung). Because of its electromagnetic-ZPF underpinning, gravitational theory in this form constitutes an ‘‘already unified’’ theory.

The aspect of conservation of spin polarization in electric-dipole transitions is addressed for hydrogenic ions in a nonrelativistic time-dependent perturbation theory. The results show that for direct transitions the polarization is highly conserved. The depolarizing influence of the spin-orbit interaction on the initial spin orientation is only of the order of (αZ${)}^2$ or less for hydrogenic ions.

Absolute cross sections for the ejection of electrons by proton impact that are differential in the angle and energy of the electrons have been measured for helium, neon, and krypton. The primary energy ranged from 7.5 to 150 keV, the angles from 10° to 160°, and the measured energies from 1 to 550 eV. These data along with earlier data on argon are used to study the systematics of proton-impact ionization of the rare gases. An analytical model is employed to correlate and systematize the cross-section differential in ejected-electron energy. For low-energy collisions the angular distribution of electrons ejected into the forward hemisphere is found to be independent of the electron energy and largely independent of the target. The Massey adiabatic criterion yields results for the energy of the maxima of the electron-ejection functions, in disagreement with experiment. Doubly differential cross sections for neon calculated from the distorted-wave Born approximation show only fair agreement with experimental data. A method of determining electron multiplier efficiency based on Poisson statistics is described.

Rydberg states (${\Sigma }_g^{\mathrm{-}}$, ${\Sigma }_u^{\mathrm{-}}$, ${\Pi }_g$, and ${\Pi }_u$) of ${\mathrm{O}}_2$ that converge to the $B^2$${\Sigma }_g^{\mathrm{-}}$, $b^4$${\Sigma }_g^{\mathrm{-}}$, and $c^4$${\Sigma }_u^{\mathrm{-}}$ excited states of the parent ${\mathrm{O}}_2^{+}$ ion have been calculated. The Rydberg electron wave functions are expanded by one-center basis functions that are solutions of an electron moving in a sphericalized potential of the parent-ion core. The Rydberg energy levels are obtained by diagonalizing the full Hamiltonian which includes both the spherical and nonspherical parts of the potential. Rapid convergence of the expansion is assured because the basis functions are already a good approximation to the Rydberg-state wave functions. The calculations cover (nl) from (3,0) to (10,7) and m=0 and 1 using two internuclear distances, R=1.2 Å and the equilibrium distances of the parent excited ${\mathrm{O}}_2^{+}$ states. The results are compared with photoabsorption and electron-impact energy-loss experiments. Good agreement is seen for the ns${\sigma }_g$, np${\sigma }_u$, and np${\pi }_u$ series but the nd${\sigma }_g$ states exhibit larger discrepancies.

A calculation of the total cross section for direct electron-positron pair production by heavy ions is described. It combines the use of the Weizsäcker-Williams method for low-energy transfers and existing calculations for high-energy transfers. Higher-order corrections to the total cross section are calculated based on the Weizsäcker-Williams method and existing results for pair production by photons.

Absolute cross-section measurements are presented for the double ionization of ${\mathrm{Xe}}^{8+}$ by electron impact from below threshold to 1500 eV. A search for direct double ionization indicates that this process is small or negligible compared to the single-electron processes which contribute to double ionization. The presence of a high percentage of metastable target ions in the interaction region of this experiment significantly affects the interpretation of the measured cross sections and indicates the potential importance of selected metastable ions in plasmas.

Electron-impact excitation cross sections for outer-subshell transitions in ${\mathrm{Ca}}^{+}$, ${\mathrm{Sc}}^{2+}$, ${\mathrm{Ti}}^{3+}$, ${\mathrm{Cr}}^{5+}$, and ${\mathrm{Fe}}^{7+}$ are calculated in the close-coupling and distorted-wave approximations. Coupling effects, beyond the first-order perturbation included in the distorted-wave approximation, are found to decrease rapidly as one moves to higher Z along the potassium isoelectronic sequence. Only for ${\mathrm{Fe}}^{7+}$, however, are the close-coupling and distorted-wave results in agreement to 10% or better for all the excitations studied.

We report differential and momentum-transfer cross sections for elastic scattering of electrons by ${\mathrm{NH}}_3$ for collision energies from 2.5 to 20 eV. These cross sections were obtained in the fixed-nuclei static-exchange approximation using the Schwinger variational principle. Although fixed-nuclei cross sections for electron–polar-molecule collisions are inherently divergent at small angles, such results can provide useful estimates of the differential cross sections at intermediate and larger angles. The agreement at intermediate and larger scattering angles between the calculated and relative experimental cross sections, which are available at 8.5 and 15 eV, is good. The differential cross sections also show evidence of a weak d-wave enhancement around 8 eV. A significant feature seen in these cross sections, particularly at 15 and 20 eV, is their substantial backward peaking beyond 120°.