We study the Fubini-Study metric induced on the quantum evolution submanifold of the projective Hilbert space associated with the evolutions generated by a set of independent operators. It is shown that if the operators are Hermitian, then the off-diagonal components of the metric describe the correlations between them. Thus, not only the uncertainty but also the correlation acquires its geometrical interpretation. We also demonstrate this by using a squeezed state.

Numerical studies of the classical and quantum dynamics of a periodically driven anharmonic oscillator show that the only quasienergy states that are exponentially localized in the field-free energy space are those that are located in the regular region of classical phase space. All the quasienergy states located in the bounded chaotic region in phase space are extended states and do not show the strong quantum limitation of chaos due to the Anderson localization mechanism, which is characteristic of kicked systems.

The photoionization of gaseous ${\mathrm{CH}}_3$I below the first ionization potential has been studied as a function of pressure and temperature. Structural features that exhibit a Maxwell-Boltzmann temperature dependence are observed as far as 0.17 eV below threshold. They are identified as nd Rydberg transitions originating in excited vibrational levels of the electronic ground state and autoionizing, with Δν=-1 and -2, into the vibrational ground state of the ion. From these results along with the simultaneously measured absorption spectrum, we obtained the ${\nu }_2$ and ${\nu }_3$ vibrational frequencies of the d Rydberg states.

The Fano factor and W value in xenon have been measured with a gridded ionization chamber for 5.3-MeV α particles. We obtained a value for the Fano factor of 0.29±0.02 and the W value of 21.9±0.3 eV. This W value is nearly equal to those for α and β particles measured by Jesse and Sadauskis [Phys. Rev. 90, 1120 (1953); 97, 1668 (1955)]. The Fano factor is considerably larger than the value reported for x rays using a proportional scintillation counter. The reason for this difference is discussed.

The interplay between relativistic and electron correlation effects on the angular distribution of photoelectrons from strontium is studied by using the multiconfiguration relativistic random-phase approximation theory. Our results show a much shallower dip in the angular asymmetry parameter for photoelectrons from subshell 5${\mathit{s}}_{1/2}$ when double-electron excitations are included in the calculation. Measurements are called for to verify the effects.

Double-electron-excitation processes of He atoms by multiply-charged-ion impact have been theoretically investigated using the close-coupling method in the MeV/u energy regime. Hyperspherical wave functions are adopted to take full account of the strongly correlated motion of two atomic electrons in He. The Born series is used to analyze the results of cross sections obtained by the close-coupling method. The cross section of the process to the 2p2p ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$ state is found to show the most rapid increase as the projectile charge ${\mathit{Z}}_{\mathit{p}}$ increases, while that to the 2s2p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ state indicates the slowest in the double-electron-excitation processes to the (2l,2l’) manifold. For high ${\mathit{Z}}_{\mathit{p}}$ at 1.5 MeV/u, the 2p2p ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$ cross section becomes dominant in the excitation processes to the (2l,2l’) manifold. Physical interpretation based on the rovibrator model is given concerning the correlated motion of two atomic electrons.

High-resolution (∼0.1 eV) core-level photoelectron spectra of gas-phase ${\mathrm{SiH}}_4$, ${\mathrm{PH}}_3$, ${\mathrm{GeH}}_4$, and ${\mathrm{AsH}}_3$ have been recorded using monochromatized synchrotron radiation. These spectra, multiconfiguration self-consistent-field calculations of the vibrational profile, and the core-equivalent model all show that core-level vibrational structure decreases dramatically, both down a group of congeneric molecules and across a periodic row of isoelectronic molecules. The theoretical calculations also show that the Franck-Condon factors do not change for relatively shallow core levels (e.g., Si 2p,2s or Ge 3d,3p) but increase significantly for deep core levels (e.g., Si 1s).

We analyze the intensity fluctuation of multimode lasers by extending the linear-response theory of McCumber for single-mode lasers. In the two-mode case, we prove analytically that the rate equations allow for an additional dynamical oscillation frequency associated with the antiphase motion. This explains the self-organized collective behavior of two-mode lasers, i.e., that the total output behaves just like a single-mode laser. The linear stability predicts the scaling law for this time scale, which results quite generally through cross-saturation dynamics of population inversion. Experimental results in two different laser systems confirm these predictions.

We elicit an analytic approximation of the Q function of a damped anharmonic oscillator which is initially in a coherent state. We start with a Q function obtained by using a solution of the master equation. We find that multiphase coherent states can be observed in a damped anharmonic oscillator and determine the range of parameters for which it is possible.

In this paper, we study first the connection of the k orthonormalized eigenstates of ${\mathit{a}}^{\mathit{k}}$ with coherent states, then, according to the higher-order squeezing defined by Zhang et al. [Phys. Lett. A 150, 27 (1990)], study the properties of the higher-order squeezing of k orthonormalized eigenstates. Our results show that the k orthonormalized eigenstates can be represented as a linear superposition of k coherent states, and that all of them are minimum uncertainty states of the operators ${\mathit{Z}}_1$(N) and ${\mathit{Z}}_2$(N) (N=mk, m=1,2,3, . . .) for even and odd k, and all of them have the Nth-order squeezing [N=(m+1/2)k, m=0,1,2, . . .] for even k.

We study the effect of quenched disorder on the behavior of tethered membranes. We consider D-dimensional membranes in a d-dimensional embedding space using expansions in ε=4-D and 1/d. Disorder is introduced via a random spontaneous curvature, such as would be caused by impurities that break the symmetry between the sides of the membrane, and via a random preferred metric. The presence of random spontaneous curvature is found to stiffen the long-wavelength bending rigidity, giving rise at temperature T=0 to a disordered flat phase associated with a new fixed point of the renormalization group. This phase is characterized by anomalous statistical and elastic properties similar to those found previously for pure membranes at T≠0, but due here to quenched disorder rather than thermal fluctuations.

The influence of weak external noise on the Lorenz model has been studied in parameter ranges where it is characterized by pairs of nonsymmetrical periodic attractors. The investigations, based on electronic analog and digital techniques, have shown that the noise can give rise to pronounced zero-frequency spectral peaks of complicated shape and to chaos.

Statistical properties of time-dependent wave functions for classically chaotic bound and scattering systems with two degrees of freedom are studied numerically and analytically. For comparison, two-dimensional systems that are classically nonchaotic are also studied numerically. Our numerical results show that the wave functions for chaotic systems become spatially irregular after some characteristic time, whereas no evident irregularities are observed in the nonchaotic systems. Spatial fluctuations of irregular wave functions are shown to be reproduced quite accurately by the random plane-wave superposition approximation. This approximation predicts that the real and imaginary parts of an irregular wave function are uncorrelated Gaussian stochastic functions with the same spatial pair correlation function, which is expressed through a Bessel function. To assess this prediction, distribution functions and spatial pair distribution functions for each of the real and imaginary parts, which must be Gaussian for Gaussian stochastic functions, are computed numerically and found to be close to Gaussian. Analysis of the widths of the numerical pair distribution functions enables us to obtain a pair correlation function that is, in accordance with prediction, well approximated by the Bessel function.

Ordinary differential equations of continuous dynamical systems, or at least of equivalent systems, can be reconstructed from numerical scalar time series. Corresponding methods have been previously discussed for a Rössler band. This paper is devoted to the case of the Lorenz system. Several kinds of equivalent systems are being investigated, and a classification of them is being introduced. Validations may rely (i) qualitatively with comparisons between graphical displays of exact and corresponding reconstructed attractors and (ii) quantitatively with comparisons between invariants such as generalized dimension spectra.

We present here a brief summary of results on so-called ‘‘exotic’’ directed lattices having nonregular periodicity. Such lattices, e.g., the Archimedean nets, are characterized by different site types and a spread of coordination numbers. The evidence adduced here shows that the exponent structure for the growth of animals and trees on such lattices is of the form predicted, with ${\mathrm{\theta }}_0$ for trees equivalent to θ for unrestricted animals, independent of the periodicity property. This supports the general form ${\mathrm{\theta }}_{\mathit{c}}$=${\mathrm{\theta }}_0$-c, for cycles c=0. We quote values for the growth parameter (or inverse critical fugacity) λ for bond trees and animal growth on selected directed lattices. The convergence of such series is well known to be subject to the influence of subdominant singularities in addition to θ, and we report on results obtained using the second-log-derivative scheme for the lattices of interest. Recent results from percolation studies for the alternating nets [H. J. Ruskin, Phys. Lett. A 162, 215 (1992)] have proved particularly encouraging for the Archimedean lattices, with z̃=2.498+-0.010, but uncertainties for the honeycomb were found to be large. Investigation of the site-to-bond ratios for animals and trees on the honeycomb gives somewhat smoother series behavior, which, though subject to confluence effects, supports a much lower value of the effective coordination number. We quote z̃=1.450+-0.050.