We believe that the criticisms of Nicolis and Balakrishnan [preceding Comment, Phys. Rev. A 46, 3569 (1992)] reflect a misunderstanding of the basis of our claims. Here, we repeat a number of points already made in our papers [Phys. Rev. A 43, 1709 (1991); 42, 1946 (1990); Phys. Rev. Lett. 64, 249 (1990)] in order to dispel ambiguity and misunderstanding.

By solving numerically the generalized Calogero-Moser equation corresponding to the model quantum Hamiltonian, we suggest an alternative interpretation of quantum irregular energy spectra from the viewpoint of nonlinear dynamics. The soliton-gas picture is shown to be effective in describing the Gaussian orthogonal ensemble–like spectra. The transition from Poisson to Wigner level-spacing distributions can be interpreted in the terminology of nonlinear dynamics such as soliton density and fluctuation of accelerations.

Relativistic many-body perturbation theory calculations of the energies of the 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$, 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$, and 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$ states of heliumlike ions with nuclear charges Z in the range 10–36 are presented. These calculations include Coulomb correlation corrections through third order, correlation corrections of first order in the Breit interaction and zeroth, first, and second order in the Coulomb interaction, together with second-order Breit-Breit corrections and first-order corrections for retardation of the Breit interaction. At Z=10, the calculated energies of the 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$, 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$, and 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$ states differ by 2.9, 0.02, and 0.3 ${\mathrm{cm}}^{\mathrm{-}1}$, respectively, from benchmark calculations based on variational wave functions. For higher Z, the difference between the present calculations and the benchmark calculations increases smoothly. Radiative and mass-polarization corrections are added to the many-body calculations and comparisons are made with measured 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_0$–2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$ and 2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_2$–2 ${}_{}{}^3{}_{}{}^{}$${\mathit{S}}_1$ intervals.

When a two-electron-like atom has one electron excited to a Rydberg state, and the other electron is then excited for a time that is short compared to the orbit time of the Rydberg electron, a ‘‘notch’’ is created in the Rydberg wave function, corresponding to that part which autoionized during the small time that the core was excited. This notch is initially localized in space and momentum, and follows a classical trajectory in momentum space. This transient-core-excitation method is a very efficient way to create notched atomic wave functions, and is demonstrated here using a long-pulse core excitation.

It is shown that the phenomenon of fractional revivals, which was observed in recent laser experiments on atomic wave packets, determines the long-time behavior of the Jaynes-Cummings model for a two-level atom interacting with a quantized cavity field. This provides an alternative mechanism for the generation of coherent superpositions of macroscopically distinguishable states of the field (so-called ‘‘optical Schrödinger cats’’) via resonant processes. The emergence of these states is associated with the appearance of atomic inversion revivals following each other 2, 3, 4, . . . times faster than the usual ones.

We present an application of a simple configuration-interaction approach to multiphoton ionization of magnesium, using a finite ${\mathit{L}}^2$-basis set constructed from a nearly complete set of one-particle frozen-core Hartree-Fock orbitals. The effects due to multielectron interactions to two- and three-photon processes at energies both near and away from the resonant structures dominated by singly excited intermediate states and doubly excited autoionization states are examined in detail. Our calculation has shown that the multiphoton spectra are mostly dominated by the resonant structures due to intermediate singly excited bound states. Such spectra are qualitatively different from the single photoionization spectrum, which often exhibits a strong presence of doubly excited autoionization structures. Our calculated results are in close agreement with other existing experimental and theoretical results for single- and two-photon ionizations.

A theory of a grating simulated echo (GTE) is developed. The GSE involves the sequential excitation of atoms by two counterpropagating traveling waves, a standing wave, and a third traveling wave. It is shown that the echo signal is very sensitive to small changes in atomic velocity, much more sensitive than the normal stimulated echo. Use of the GSE as a collisional probe or accelerometer is discussed.

Dispersion and peak likelihood—two performance measures recently used for the description of quantum phase—are compared in this Rapid Communication. The Susskind-Glogower phase operator represents the extremal quantum estimator with respect to both measures. The states with infinite peak likelihood and zero phase information explicitly demonstrate that peak likelihood is not relevant to the phase measurement, whereas dispersion represents a well-behaved performance measure of the phase variable. Peak likelihood restricts the lower limit of the variance of photon number, and the above-mentioned states represent the extremal states of the Shapiro-Shepard [Phys. Rev. A 43, 3795 (1991)] uncertainty relation.

We describe a method for calculating rates for multiphoton detachment or ionization of a two-electron system by a perturbative field. We have applied the method to ${\mathrm{H}}^{\mathrm{-}}$, and we present estimates of two- and three-photon detachment rates. In particular, we explore the ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}^{\mathit{e}}$ and ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$ Feshbach resonances below the n=2 and n=3 excitation thresholds of H; these resonances lie in the ‘‘excess-photon detachment’’ regime, where one photon is already sufficient to detach the electron.

The time-dependent Schrödinger equation for the helium atom with a model potential is solved on a numerical grid. The effects of intermediate-state resonance and of the ionization of the atom upon the harmonic generation are investigated. We also evaluate the contribution of the helium ion when the laser intensity is sufficiently high for most of the atoms to be ionized during the laser pulse. We find that the harmonics with order higher than 13 are due to the ion when the photon energy is 5.0 eV, while for photon energy 2.0 eV the atom produces up to about the 49th harmonic.

We perturb the one-dimensional nonlinear Schrödinger equation with a time-independent spatially periodic potential with a period large compared to the spatial width of solitons present in the system. A collective-coordinate approximation maps the system to a nonintegrable many-particle dynamics with an effective Hamiltonian, which we derive under the assumption that we can neglect three-soliton collisions as well as two-soliton collisions with vanishing relative velocity. We give an estimate for the power radiated by a single soliton in the presence of the perturbation and show that radiative effects can be neglected for perturbations with sufficiently small amplitude and large spatial period. We show that the nonintegrability of this perturbed nonlinear Schrödinger equation manifests itself already in the two-soliton sector. We use the effective many-particle Hamiltonian to investigate soliton depinning. The effective Hamiltonian results are compared with numerical simulations of the full perturbed equation.

We propose a simple discrete model to study the nonequilibrium fluctuations of two locally coupled (1+1)-dimensional systems (interfaces). Measuring numerically the tilt-dependent velocity we construct a set of stochastic continuum equations describing the fluctuations in the model. The scaling predicted by the equations is studied analytically using dynamic-renormalization-group theory and compared with simulation results.

We find that the discrete sandpile type of models in finite dimension under a uniform particle addition must result in 1/${\mathit{f}}^2$ or 1/(f+a${)}^2$ power spectrum depending on the existence of particle conservation law or not. However, their continuous counterparts may exhibit 1/f instead. This difference in power spectrum behavior can be expoained in terms of rate of relaxation of the system in the continuous models.

In this Rapid Communication, a novel simple monatomic liquid, possessing the distinctive icosahedral inherent local order, is reported. It has been generated by a special form of pair potential employed in a molecular dynamics system of 16 384 particles, and remained stable within a wide range of temperatures explored. Pronounced stability of this model with respect to crystalline nucleation has been tested in a very long run under supercooling which was found to enhance its icosahedral inherent structure. The inherent structure factor exhibits an anomalous long-wavelength maximum which is interpreted as being indicative of the tendency for icosahedral clustering.

Expressions for the hard-sphere nearest-neighbor probability distribution, ${\mathit{P}}_{\mathrm{NN}}$, and the associated mean nearest-neighbor distance, 〈${\mathit{r}}_{\mathrm{NN}}$〉, in D=1 to 3 dimensions, which were recently derived by Torquato, Lu, and Rubinstein [Phys. Rev. A 41, 2059 (1990)] are compared with earlier results of Reiss and Casberg [J. Chem. Phys. 61, 1107 (1974)] and Macdonald [Mol. Phys. 44, 1043 (1981)]. Full agreement is found for the D=1 results, where an exact solution can be found. But no such solution is possible for D=2 and 3. The equation of state, ${\mathit{P}}_{\mathrm{NN}}$, and 〈${\mathit{r}}_{\mathrm{NN}}$〉 can all be calculated from knowledge of the central function ${\mathit{G}}_{\mathit{D}}$, a conditional probability depending on both density and distance, r, from a particle center. The consequences of several different approximations for ${\mathit{G}}_{\mathit{D}}$ are explored for hard disks and spheres. In spite of the much more approximate ${\mathit{G}}_{\mathit{D}}$ functions used by Macdonald compared to those of Torquato, differences in the resulting ${\mathit{P}}_{\mathrm{NN}}$ responses are relatively small even at high densities, and the differences in 〈${\mathit{r}}_{\mathrm{NN}}$〉 predictions, the quantities of primary experimental value, are entirely negligible. Although the original D=2 Torquato expression for ${\mathit{P}}_{\mathrm{NN}}$ was not properly normalized, a sign correction restores normalization and leads to close agreement with the earlier work. For D=3, numerical results show that simple approximation of ${\mathit{G}}_3$ by the contact value of the ordinary radial distribution function, a quantity independent of r, yields results for ${\mathit{P}}_{\mathrm{NN}}$ very close to those of Torquato, and the corresponding 〈${\mathit{r}}_{\mathrm{NN}}$〉 results are completely indistinguishable.

We show that the Eckhaus instability for traveling waves is of convective nature and does not directly lead to absolute instability. As a consequence spiral waves remain stable in a larger range than expected previously, transition to defect-mediated turbulence can be delayed beyond the Benjamin-Feir limit, and the occurrence of phase turbulence can be made plausible. We calculate the onset of absolute instability using the complex Ginzburg-Landau equation and verify the results by simulations.

Experimental evidence of two distinctive mechanisms of transition from localized (LTW) to extended (ETW) traveling waves in convecting binary mixtures is presented. Both are related to the convectively unstable nature of LTW, and reflect its different manifestations. In short cells the mechanism which is responsible for the LTW instability is related to the transition from convective to absolute instability. In long cells and negative enough values of the separation ratio ψ, transition from LTW to ETW occurs due to the interaction of convectively growing perturbations and LTW. Crossover between the two mechanisms is demonstrated.

We consider a dynamic entropy of a Rayleigh-Bénard flow which varies with the characteristic scales ε of the process. Such an ε entropy is used to distinguish and classify the different dynamic regimes recently observed in this system: oscillation, chaos, and soft, hard, and developed turbulences. Moreover, data analysis of an experimental time series reveals a scaling behavior of the ε entropy in a hard turbulent regime, demonstrating that this notion of entropy is suitable to describe dynamic processes with a heirarchy of characteristic instabilities.