We formulate the Blume-Capel spin-1 Ising model, with competing first- and second-neighbor interactions along the branches of a Cayley tree, in the infinite-coordination limit, as a discrete two-dimensional nonlinear mapping problem. The phase diagram displays multicritical points and many modulated phases. Mean-field calculations for the analogous model on a cubic lattice give the same qualitative results. We take advantage of the simplicity of the mapping to show the existence of complete devil’s staircases, at low temperatures T, with increasing values of the Hausdorff dimensionality $D_F$ with T. We show that there are regions of the phase diagram associated with positive values of the Lyapunov exponents of the mapping, and we give strong numerical evidence to support the existence of a strange attractor with a Lyapunov dimension $D_{\lambda }$>1. We also find a route to chaos, according to the scenario of Feigenbaum, with a reasonable estimate of the exponent δ.

We investigate the effects of pollution on a population that is on the brink of extinction. In the vicinity of the associated critical point, the temporal scales of the population density fluctuations are found to be completely governed by the diffusive behavior of the pollution density fluctuations. Moreover, the mean value of the population density is found to vanish with a larger power-law exponent in the presence of pollution density fluctuations. Results are obtained within a renormaliza- tion-group calculation to O(ε) (ε=4-d, d being the spatial dimension).

It is explicitly shown that the nonvanishing spacelike or timelike contributions to the Feynman propagator of quantum-field theory do not reflect any violation of local causality, such as propagation faster than light. An experiment is proposed to test the causality of quantum-field theory by measuring the broadening of a very short light pulse. For these pulses theory predicts a nondissipative behavior, with the pulse broadening only stemming from preparation and measurement uncertainties.

We establish a connection between a two-dimensional field theory using a classical solution which depends only on one of the coordinates, and the quantum-mechanical harmonic oscillator whose frequency is one-coordinate dependent.

The influence of the phase difference of the components of a bichromatic field on the dynamics of a two-level atom is studied in the framework of an analytical approach. We give a new, more adequate explanation of an experiment [R. E. Silverano et al., Phys. Rev. Lett. 55, 1070 (1985)] where strong phase effects were observed in the interaction of a fast atomic beam with a standing-wave field. It was shown that these effects are caused by interference of contributions of components of the bichromatic field in the amplitude of the upper state. There is excellent agreement between our analytical results and both experimental data and the results of numerical calculation.

The dynamics of the system of N two-level atoms in the free space is studied, when at the initial moment just one of the atoms is excited. It is shown that though the number of the field modes is sufficiently larger than the number of the atoms and all energy is transferred into radiation field for t→∞, the radiation suppression (in a broader sense) can be still observed.

Doppler-free spectra of linear and circular dichroisms for the hyperfine structures of Na $D_1$ and $D_2$ lines have been obtained by means of polarization-modulated optical pumping spectroscopy. The experimental results are compared with recent theoretical calculations based on velocity-selective optical pumping in a four-level atomic system.

We report on a new mechanism that can lead to line narrowing. We show that the line-broadening effects associated with a broadband source can be suppressed by irradiating the system with a coherent pump. We give explicit results for this suppression in spontaneous emission from a two-level system.

Using a simple three-state model for an atom or molecule in which two transitions are driven by two laser beams, we demand complete transfer of the occupation probability from state 1 to state 2 to state 3. This complete transfer is produced by two laser pulses, which may be concurrent. The minimum area required for complete transfer is considered, although ‘‘area’’ has no obvious definition for the three-state model. If the areas of the two separate pulses are calculated following McCall and Hahn, it seems that the minimum area for each pulse is π.

The coefficient of the square-gradient term, given by the second moment of the direct correlation function, is determined by three different length-scale parameters, each dominating a different range of the plasma coupling parameter Γ. It is the interplay between the relative contributions of these scales that provides the full form of the square-gradient term as a function of Γ.

In four recent papers Pradel et al. [Phys. Rev. Lett. 54, 2600 (1985); Phys. Rev. A 35, 1062 (1987)] and Monchicourt et al. [Phys. Rev. A 33, 3515 (1986); Chem. Phys. Lett. 152, 336 (1988)] give arguments claiming the observation of laser-assisted ionization of the short-lived collision complex formed during collisions of ${\mathrm{He}}^{\mathrm{*}}$(2 ${}_{}{}^1{}_{}{}^{}$,3S) with He. However, estimates of the relative sizes of the assisted and unassisted ion signals observed make it very unlikely that laser-assisted ionization has been observed in those experiments. Collisional excitation to higher ${\mathrm{He}}^{\mathrm{*}}$ states, followed by (single-photon) ionization of the excited states, seems a more likely explanation at all energies considered.

The energy spectrum of a charged particle bound by a short-range potential and subjected to an intense ac electromagnetic field is computed by using complex coordinates within the Floquet formalism. As the field strength is raised, additional discrete states appear and the lifetime of the states increase. The adequacy of a high-frequency model of the strong-field spectra is assessed.

It is shown that the angular distribution of $E1\mathrm{}$ photoelectrons from oriented nonlinear molecules exhibits circular dichroism. The study, based upon a general expression that is obtained by taking full account of the transformation properties of the point-symmetry group of the target, reveals that, unlike the case of fixed linear molecules, (i) it may arise even if there is only a single photoelectron continuum, (ii) all terms, interference or otherwise, in $-L\le M(=m-m^{\prime })\le L$ with $L$ both even and odd contribute, and (iii) there are in general no restrictions on the experimental arrangement for it to be observable in nonlinear systems. This discussion has been illustrated by ionization in the $6a_1$ orbital in an oriented C${\mathrm{Cl}}_4$ molecule.

We have measured numerous transitions from the $E$, $F$ state of ${\mathrm{H}}_2$ to the singlet $\mathrm{np}$ Rydberg states with an accuracy of 0.01 ${\mathrm{cm}}^{-1\mathrm{}}$. The data have been analyzed to obtain values for the ionization potential of ${\mathrm{H}}_2$ relative to the $v=0\mathrm{}$, $N=0\mathrm{} \mathrm{and} 1$ levels of the $E$, $F$ state. By combining these results with previous measurements of the $E$, $F$ state, a value of 124 417.524±0.015 ${\mathrm{cm}}^{-1\mathrm{}}$ is obtained for the ionization potential of ${\mathrm{H}}_2$. This result is in good agreement with previous work but nearly an order of magnitude more accurate, and is very close to the best theoretical value.

We investigate theoretically the statistical properties of the bad-cavity laser with field and population fluctuations. This system is equivalent to the stochastic Toda oscillator, whose probability distribution obeys the Kramers equation with a position-dependent diffusion coefficient. An approximate probability distribution function is calculated in the stationary state by the method of the orthogonal polynomial expansion. We predict novel statistical features of the laser intensity resulting from the power tail of the intensity distribution. Diverging intensity moments and the deviation of the photon-counting statistics from the Poisson type are also given.

The emission of strongly driven two-level-like Ba atoms into the modes of an optical cavity has been studied as a function of cavity tuning and Ba density. At low densities, the cavity-mode emission viewed as a function of cavity tuning is identical in form to the three-peaked Mollow emission spectrum. At high densities, however, the cavity-mode emission is strongly amplified (attenuated) when the cavity is tuned to the frequency of one (the other) Mollow sideband. It is predicted that modest increases in Ba density will cause lasing to occur in this system.

A simple prescription for scaling diatomic potentials so that they have a common dissociation limit and fixed curvature near the minimum is used to examine 35 diatomic potentials which are known over relatively large fractions of their well depths. These global comparisons reveal greater similarity, particularly among chemically related molecules, than might be predicted from spectroscopic properties that are based on derivatives of the potential near its minimum.

We report the results of a neutron interferometry experiment where for the first time (to our knowledge) a phase shift of a neutron de Broglie wave induced by moving matter has been successfully measured. This experiment is the quantum-mechanical analog of the optical Fizeau effect. The observed phase shift is caused by the motion of matter itself, and not by the motion of its boundaries. The experimental results are found to be in good agreement with the theoretical predictions. Some unexpected and previously unreported neutron wave interference effects observed during the experiment are also reported.

We have used a superconducting quantum interference device to measure all components of the small magnetic field inside a coaxial capacitor that is being charged at a low frequency (695 Hz). The expected result is that $B_z$ and $B_{\rho }$ should be 0 and that $B_{\phi }$ should increase linearly from the end of the capacitor. This prediction depends upon Maxwell’s displacement current ${\mathrm{J}}_D$ being strictly equal to (1/4π)∂D/∂t in the annular region between the electrodes. Anomalous fields would arise if $J_D$ twisted a little in going from one electrode to the other. We find no evidence for such a twist. $B_{\phi }$ is as predicted; $B_{\rho }$ and $B_z$=0 everywhere to within a few percent of $B_{\phi }$. Our results show that the displacement current flows within Δφ=22° of the radial direction. We have also searched for a B field that is in phase with the charge (rather than the current) and for fields which vary as the second harmonic of the charging frequency. The former search is interpreted to show that in a traveling TEM wave B is perpendicular to E to within 0.8×${10}^{\mathrm{-}8}$ rad. The latter search is loosely connected to nonlinear electromagnetic effects such as those provided by axions.

The approximations needed to treat the resonant formation of the compound molecule [(dtμ)dee${]}^{\mathrm{*}}$ as a line-broadening process are examined. The necessary criteria for applying the impact (Lorentzian) approximation are shown to be seriously violated under the usual conditions of muon-catalyzed fusion. Neither the condition for binary collisions nor the requirement that the detuning not be too large holds. A much more appropriate description is the many-body quasistatic approximation, which is valid for large detunings at any density and for practically the whole profile at high densities. The convenient factorization of the three-body rate into a convolution of a two-body rate with a broadening factor is shown to hold within some approximations, but the broadening factor itself depends on the transition being considered.