We agree with the preceding Comment by Maniak and Curtis [Phys. Rev. A 42, 1821 (1990)] that qualitative isoelectronic behavior of low-lying energy levels of sulfurlike ions with high nuclear charges, Z, can easily be understood using single jj configuration labels. However, such labels are, in general, useful only for high-Z ions. We do not recommend mixing numerical results from multiconfiguration calculations with those from single-configuration calculations because such a mixed usage may introduce artificial discontinuities in Z dependence, defeating the main advantage of studies along an isoelectronic sequence.

A recent paper [G. M. Palma and P. L. Knight, Phys. Rev. A 39, 1962 (1989)] has stated that the two-atom Dicke model exhibits phase-dependent population decay. In this Comment we show that population decay is invariant with respect to the input phase angle of squeezing in the two-atom Dicke model.

We clarify the nature of phase sensitivity in atomic decay in a broadband squeezed light field.

Resonances due to a resonant-excitation–double-autoionization process in the electron-impact ionization of ${\mathrm{C}}^{3+}$ ions are calculated using the R-matrix method. Twelve autoionizing states arising from the 1s2${\mathit{s}}^2$, 1s2s2p, 1s2${\mathit{p}}^2$, 1s2s3s, 1s2s3p configurations, together with the ground 1${\mathit{s}}^2$2${\mathit{s}}^2$S and excited 1${\mathit{s}}^2$2p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}^0$, 1${\mathit{s}}^2$3${\mathit{s}}^2$S, 1${\mathit{s}}^2$3p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}^0$, 1${\mathit{s}}^2$3d ${}_{}{}^2{}_{}{}^{}$D states, are included in the close-coupling expansion. These states are represented by accurate configuration-interaction wave functions. The present results are in good agreement with the recent crossed-beam measurement.

The effects of rotational-vibrational interaction, and of rotational coupling between the B 2p ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$ and C 2p ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }_{\mathit{u}}^{}{}_{}{}^{}$ electronic states, on the B–X fluorescence continuum of ${\mathrm{H}}_2$ associated with spontaneous dissociation were investigated spectroscopically using monochromatized synchrotron radiation for selective excitation of rovibronic states. The rotational shifts and perturbations in the modulated continua intensities observed agree well with close-coupling and Jeffreys-Wentzel-Kromers-Brillouin (JWKB) calculations also performed, and are explained in terms of nonadiabatic coupling effects and rainbow-interference structures. A straightforward experimental technique is described to detect mixed electronic states.

We report on a spin-echo phenomenon that is induced between Zeeman sublevels by two laser pulses close to an optical resonance. The echo formation is due to a Zeeman light shift during the second off-resonant pulse; this light pulse creates a fictitious magnetic field that leads to the phase reversal of the spins. Our experimental results on the ${}_{}{}^2{}_{}{}^{}$${\mathit{S}}_{1/2}$ sodium ground state are in good qualitative agreement with theoretical predictions.

A new fundamental thermodynamic property has been proved for classical electromagnetic zero-point radiation. Aside from a proportionality constant, classical electromagnetic zero-point radiation is shown here to possess the unique spectrum that is suitable for establishing a thermal equilibrium state with a set of fluctuating classical electric dipole harmonic oscillators at the temperature of absolute zero. As a consequence of this analysis, one can see that according to the fundamental thermodynamic definition of absolute zero temperature, the following traditional view in thermodynamics is an unnecessary thermodynamic restriction: namely, that all fluctuating motion and radiation must vanish at T=0 for classical physical systems. Indeed, as shown here, this restriction can violate the third law of thermodynamics if the spectrum reduces to zero by being proportional to T. The analysis in this article involves the calculation of (1) the change in internal energy, (2) the work done, and (3) the heat radiated for a quasistatic displacement of electric dipole nonrelativistic harmonic oscillators immersed in random classical electromagnetic radiation. The calculations include full nonperturbative evaluations of retarded van der Waals thermodynamic functions.

The Wigner phase-space representation of thermal excitations used in thermo-field-dynamics (TFD) is investigated. The phase-space description is obtained by introducing a reduced density operator in which the fictitious degrees of freedom of TFD are traced over. A new closed-form expression for the Wigner function of the harmonic oscillator thermal excitation is derived, thereby showing that the thermal excitation may be described as a temperature-dependent radial spreading of the coordinates and momenta in phase space. The population distribution in these stationary excitations is determined and shown to reduce to a Boltzmann distribution for the thermal vacuum only.

An alternative algorithm for the numerical analysis of fractal structures and measures is presented, which consumes computer time and memory only quasiproportionally to the size of the input data set. This efficient tool is applied to various deterministic and random multifractals, in particular to the growth probability measures of diffusion-limited aggregation clusters in two- and three-dimensional embedding space.

We analyze transitions between stable equilibrium states of a nonlinear stochastic mean-field model by means of Brownian dynamics simulation techniques. We have considered, in particular, the region of parameter space for which analytical approximations are not suitable. Two types of transitions have been considered, corresponding to either a sudden or gradual variation of the noise strength. Several time regimes can be clearly identified during the transition process.

We study the dynamics of classical particles interacting with attractive Gaussian potentials. This system is thermodynamically not stable and exhibits negative specific heat. The results of the computer simulation of the dynamics are discussed in comparison with various theories. In particular, we find that the condensed phase is a stationary solution of the Vlasov equation, but the Vlasov dynamics cannot describe the collapse.

Relaxation oscillations are very commonly found in nature. When modulated by an external field, such systems show phase-locked, quasiperiodic, or chaotic behavior, dependent on the specific parameters. We present an exact analysis for a triangular modulated relaxation oscillator and determine the parameter-space phase diagram. We identify critical lines associated with qualitatively different transitions to chaos and complete phase locking (CPL). One transition is related to overlapping of phase-locked regions and is also identified as the transition from quasiperiodicity to chaos described by a noninvertibility of the Poincaré map. Another is a nonchaotic transition to a CPL regime, where a gap appears in the Poincaré map. Also, we find a sudden transition between this CPL regime and a regime where all attractors are chaotic. The critical lines separating the different regimes are found and attributed to either a horizontal or vertical line segment in the Poincaré map. Moreover, we find analytically a number of scaling relations for the phase-locked stability intervals on and nearby the critical lines. We also comment on the situation when the modulation is sinusoidal and when damping is present.

We propose an analog apparatus simulating a standard Josephson junction, which allows easy experimental manipulations and measurements. We center our attention on the onset of chaotic responses, in particular on its dependence on the different physical parameters, and we obtain quite good agreement with other existing data. Great attention is also paid to compare the results with the theoretical threshold of chaos we deduce from Melnikov’s method: The agreement is globally as good as possible, taking into account the approximations and the validity of the method; in particular, we obtain a description of the behavior of the threshold for small frequencies, and of the important role played by the dc bias term. We also discuss, both theoretically and experimentally, the case of a Josephson junction to which a periodic modulating term has been added.

We show that in the trace formula of Gutzwiller [J. Math. Phys. 8, 1979 (1967); 10, 1004 (1969); 11, 1791 (1970); 12, 343 (1971)] and Balian and Bloch [Ann. Phys. (N.Y.) 60, 401 (1970); 63, 592 (1971); 69, 76 (1972); 85, 514 (1974)], applied to systems of two degrees of freedom, the Maslov index arising in the contribution from each periodic orbit is equal to twice the number of times the stable and unstable manifolds wind around the periodic orbit. As a consequence, we find that the Maslov index of a periodic orbit is equal to the Maslov index defined by either its stable or its unstable manifold. In this way it becomes apparent that the Maslov index occurring in the trace formula is an intrinsic property of the periodic orbit, being independent of the coordinates used to find it. In contrast to the case of torus quantization applied to integrable systems, where only even Maslov indices appear, we find that odd Maslov indices can arise in the trace formula of chaotic systems. These odd Maslov indices arise in the contributions of periodic orbits that are hyperbolic with reflection.

For functions with power-law singularities we consider series expansions whose coefficients have been determined by Monte Carlo simulation. In many practical problems the relative noise of the coefficients is constant or slowly increasing with the order. We modeled real Monte Carlo expansions by test series with known singularity structure where noise with different strength and form is imposed on the coefficients. The efficiency of different standard methods of series analysis (ratio method, Padé approximants, differential approximants) has been tested together with smoothing methods based on repeated partial summation of the series. We found the Padé method to give reasonable estimates and its accuracy is independent of the smoothing, while the estimates of the ratio and the differential approximant methods are greatly improved when smoothing is applied. Indeed, we found the ratio method with optimally selected smoothing to give the most reliable results.

We study a power-series expansion for a conserved quantity K in the case of the two-dimensional Hénon-Heiles potential. An alternative technique to that of Gustavson [Astron. J. 71, 670 (1966)] is applied to find the coefficients in the expansion for K. The technique is used to determine twelve orders for the conserved quantity K, more than twice as many as that calculated by Gustavson. We investigate the degree of constancy of our truncated K in regions where the motion is known to be chaotic and also where it is nonchaotic.

A master equation is constructed that provides a stochastic description underlying the logistic map. In an appropriate macroscopic limit, the underlying master map (equation) yields the logistic map. It also describes intrinsic fluctuations associated with the logistic map. When the logistic map parameters are chosen so that the map produces a chaotic trajectory, the variance of the associated fluctuations diverges. This means that the distribution function determined by the master map becomes very broad and that the logistic map no longer results from averaging with respect to the master map distribution function. Numerical examples of this behavior and its interpretation are discussed.

We investigate the origin of long-range spatial correlations in certain anisotropic translation-invariant stationary nonequilibrium states of systems with conservative dynamics. We consider both lattice-gas models with anisotropic but reflection-invariant stochastic dynamics and driven diffusive systems described by a Ginzburg-Landau equation with an electric field E. Carrying out perturbation expansions about an equilibrium state with short-range correlations we find that, in general, the spatial correlations in the stationary state decay only via a power law; the spatial decay thus reflects the well-known diffusive decay in time for systems with conservative dynamics. The typical spatial decay of the pair correlation behaves like the electrostatic potential produced by a quadrupole charge density at the origin. Exponential decay of spatial correlations, so familiar from equilibrium, appears here as the exception; it occurs generically only when there are special constraints on the dynamics, such as detailed balance and possibly spatial symmetry. The paradigm for this generic long-range behavior or self-organized criticality is found in the solutions of the linear Langevin equation describing the behavior of fluctuations of a conserved macroscopic variable. The fluctuating hydrodynamics underlying such a description is justified here rigorously for the macroscopic scaling limit of certain lattice-gas models.

A simple surface-reaction model based upon the oxidation of carbon monoxide on a catalytic surface, introduced by Ziff, Gulari, and Barshad (ZGB) [Phys. Rev. Lett. 56, 2553 (1986)], has been extended in order to include diffusion of the adsorbed particles (both O and CO). The ZGB model is a nonequilibrium model exhibiting both a first- and a second-order phase transition. The effects of diffusion on the behavior of the model has been explored by means of computer simulations. The main effect of diffusion is to change the positions of the phase transitions and increase the rate of ${\mathrm{CO}}_2$ formation. Fast diffusion causes the second-order transition to disappear from the system. Simple explanations of these changes are given. The extended version of the ZGB model has furthermore been studied by mean-field theory in the pair approximation. This approach gives qualitatively correct predictions about the effects of diffusion and yields quantitative predictions in good agreement with simulation results in the vicinity of the first-order transition.