The statistical nature of the real solutions of a set of αN random nonlinear equations constructed from N variables is examined, using analytical methods developed for neural networks. The nonlinearity of the equations is characterized by powers of the variables. The maximal α under which the equations have a real solution is found for various cases. The application of the results to physical systems is also discussed.

We present the theory for establishing a quantum standard of current. This is achieved by operating a scanning tunneling microscope at resonant tunneling through small metallic grains deposited on oxide layers, which exhibit Coulomb blockade. By adjusting the scanning period of the tip, a fixed number of electrons per oscillation can be made to tunnel. The current is directly related to the frequency and the electron charge.

We use seven years of millisecond pulsar-timing data to derive rigorous upper bounds on a cosmic gravitational-wave background. The energy density per logarithmic frequency interval near f=0.14 ${\mathrm{yr}}^{\mathrm{-}1}$ must be <9×${10}^{\mathrm{-}8}$ (68% confidence), or <4×${10}^{\mathrm{-}7}$ (95% confidence) of the density required to close the Universe. We detect a red-noise signal in the residuals for one pulsar. Its spectrum appears flatter than the ${\mathit{f}}^{\mathrm{-}5}$ power law expected for a gravity-wave background; likely noise sources include changes in the interstellar medium and pulsar rotational instabilities.

The neutron lifetime ${\mathrm{\tau }}_{\mathit{n}}$ has been measured by counting decay protons stored in a Penning trap whose magnetic axis coincided with a neutron-beam axis. The result of the measurement is ${\mathrm{\tau }}_{\mathit{n}}$=893.6±5.3 s, which agrees well with the value predicted by precise measurements of the β-decay asymmetry parameter A and the standard model.

The reactions ${\mathrm{\pi }}^{\mathrm{-}}$d→${\mathrm{\pi }}^0$X and ${\mathrm{\pi }}^{+}$d→${\mathrm{\pi }}^{+}$X are calculated within a relativistic three-body model and compared with recent data at 164.1 and 96.5 MeV, respectively. Contrary to expectations based on the impulse approximation, the differential cross sections of both reactions exhibit a strong suppression in the forward direction. It is shown that this suppression is due in the first case to the action of the Pauli principle on the two final neutrons, and in the second case to the orthogonality between the initial deuteron and final neutron-proton wave functions. The results of the full model agree well with the available differential cross sections at the two energies.

Coincident neutrons from the ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$${+}^{26}$Mg${\to }^{44}$Ca (${\mathit{E}}_{\mathit{x}}$=60 and 71 MeV) compound-nuclear reaction show an anticorrelation at small relative momentum, giving evidence for quantum-statistical interference in analogy to the optical Hanbury-Brown and Twiss effect. An average decay width of 60 keV is extracted from the measured energy correlations. The deduced extension of the neutron wave packets exceeds by far the nn scattering length, in accordance with the observed insignificance of the attractive nn final-state interaction.

Nine superdeformed bands in several nuclei of the mass-190 region all have transitions of the same or equivalent energies to within an average of about 1 keV–almost identical. Furthermore, it is found that transitions of the same energy do not always connect levels of the same spin, indicating noncollective angular momentum alignments that are all very nearly integers (0, 1ħ, or 2ħ). Possible explanations involving pseudospin are discussed.

We have observed Doppler-shifted x rays characteristic of Sb and Sn atoms in coincidence with ${}_{}{}^{108}{}_{}{}^{}\mathrm{Xn}$ evaporation residues resulting from the emission of four protons by the compound nucleus (CN) formed in the reaction ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$${+}^{54}$Fe. We have attributed the Sb x rays to atomic inner-shell vacancies which are created on the way into the nuclear reaction and filled before the emission of the last proton in the deexcitation cascade. The mean proton partial width of the nuclear states, formed at a mean excitation energy of 25±4 MeV by the evaporation of three protons by the CN, has been deduced.

Several series of doubly excited resonances have been observed in ${\mathrm{H}}^{\mathrm{-}}$ photodetachment, appearing as dips in the production cross section of excited neutral hydrogen. At least three resonances are clearly visible converging on each of the thresholds n=5, 6, 7, and 8. The data support recent theoretical calculations for the energies of doubly excited resonances and verify a Rydberg-dipole formula for the main resonance positions.

Adiabatic hyperspherical potential curves are calculated for very highly excited states of ${\mathrm{H}}^{\mathrm{-}}$ converging to H(n≤12). These potential curves reveal surprisingly weak channel interactions, manifested as extremely diabatic multiple curve crossings. We demonstrate that only resonances associated with the lowest ‘‘+’’ diabatic channel within each n manifold are observed in the recent experiments at Los Alamos (Harris et al.). A simple Rydberg-dipole formula gives the positions of all dominant resonances, permitting extrapolation to arbitrarily high quantum numbers.

We describe a new sub-Doppler cooling scheme that cools atoms to nonzero velocity ${\mathit{v}}_{\mathit{r}}$. The atomic motion in a combined optical standing wave and constant magnetic field induces a velocity-selective magnetic resonance that produces strong cooling for negative laser detuning to ${\mathit{v}}_{\mathit{r}}$=${\mathrm{\omega }}_{\mathit{Z}}$/2k, with ${\mathrm{\omega }}_{\mathit{Z}}$ the Larmor frequency. In a one-dimensinal optical molasses transverse to a thermal Rb beam we observe the bunching of the atoms into two peaks corresponding to ±${\mathit{v}}_{\mathit{r}}$. We present a quantitative comparison between our theory and experiment and suggest some applications.

A two-photon coincidence experiment of the kind recently proposed by J. D. Franson [Phys. Rev. Lett. 62, 2205 (1989)] has been carried out with signal and idelr photons produced in the process of parametric down-conversion. The coincidence rate registered by the two detectors is found to exhibit a cosine variation with the optical path difference, with periodicity equal to the wavelength.

The task of electrical-impedance tomography is to invert boundary measurements for the conductivity distribution of a body. This inverse problem can be formulated so the primary data are the measured powers dissipated across injection electrodes. Then, since these powers are minima of the pertinent (dual) variational principles, feasibility constraints can be found for the nonlinear inversion problem. When power may be measured accurately, the existence of these dual variational principles implies that any exact solution must lie at a point of intersection of the two feasibility boundaries.

Spatiotemporal dynamics of multiple coupled laser systems are predicted as an example of distinct phenomena in high-dimensional nonlinear systems far from thermal equilibrium. Generic dynamics, including a self-induced phase turbulence which results in emitter partition noise, chaotic itinerancy between ruins of local attractors (supermodes) resulting from phase hopping, as well as superslow relaxation into equilibria, are found. It is shown theoretically that such inherent dynamics result from the destruction of phase locking of multiple emitters due to population dynamics.

We show that the Marangoni effect drives the fingering instability observed at the edge of an aqueous surfactant drop spreading on a thin film of water. A calculation of the unperturbed flow profile demonstrates that the spreading of the drop is controlled by the dynamics of a thin layer which develops in front of the drop. The surface-tension gradient in this region leads to the fingering instability via a mechanism mathematically similar to that in Hele-Shaw flow despite the very different underlying physics.

Detailed measurements of heat and particle transport are made on the TEXT tokamak by analyzing the dynamics of the postcrash sawtooth perturbation. Both the density and temperature perturbations are observed to be transported out through the confinement zone at the same rate and exhibit similar scaling with plasma parameters. The density and temperature sawteeth are in phase and highly correlated. These results suggest a strong coupling of plasma particle diffusion and heat flow.

A simple model of solvation is introduced to describe lower critical solution points in polymer solutions. Our theory predicts that physical bond formation between polymer segments and solvents can be a major cause of miscibility gaps showing a closed-loop or hourglass shape. Relative positions of upper and lower critical solution points are examined for the various molecular weights of the polymer. The result is compared with the observed phase diagram of polyethylene glycol in water.

A beam of ${\mathit{R}}^{\mathrm{-}}$ rotons, i.e., rotons which have oppositely directed group velocity and momentum, is reated by condensing an atom beam onto the surface of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. ${\mathit{R}}^{\mathrm{-}}$ rotons are identified by quantum evaporation and their time of flight. Measured signal shapes agree well with those modeled. Signal sizes are compared with those from atoms specularly reflected from the He surface, from which it is estimated that the quantum efficiency for the condensation or evaporation process is high and of the order of 0.5 for angles of incidence where mainly rotons are created. ${\mathit{R}}^{\mathrm{-}}$ rotons can specularly reflect from a solid-liquid He interface with high probability, if the interface is particularly good.

The interaction between an Ir tip and an Ir sample was investigated during normal tunneling operation of the scanning tunneling microscope. Force gradients compatible with metallic adhesion were observed within a range of 2 Å before making contact. Based on the theory of metallic adhesion, a scaling relation is derived which allows the tip geometry and the characteristics of the interaction to be accounted for in a systematic manner.

Structural models used in calculations of properties of substitutionally random ${\mathit{A}}_{1\mathrm{-}\mathit{x}}$${\mathit{B}}_{\mathit{x}}$ alloys are usually constructed by randomly occupying each of the N sites of a periodic cell by A or B. We show that it is possible to design ‘‘special quasirandom structures’’ (SQS’s) that mimic for small N (even N=8) the first few, physically most relevant radial correlation functions of a perfectly random structure far better than the standard technique does. We demonstrate the usefulness of these SQS’s by calculating optical and thermodynamic properties of a number of semiconductor alloys in the local-density formalism.