Using notions of supersymmetry, we present an exactly soluble model of anyons with both statistical and scalar interactions in 2+1 dimensions. We demonstrate that half-statistics particles with two spin flavors condense into a local singlet state which is both a charge superfluid and a ‘‘spin metal’’ in the sense that there is charge-pairing off-diagonal long-range order with gapless charge excitations, but a gap in the collective spin-mode spectrum. The present results shed considerable light on the mean-field theory of fractional statistics.

The axial oxygen contributions to the Cu K-edge, polarized, extended x-ray-absorption fine structure of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ are analyzed from 10≤T≤105 K, using a novel approach in which the radial distribution function is directly calculated from model potentials. The best fit is obtained with a double-well potential with two nearly equally populated O(4) sites 0.13 Å apart. The site separation decreases 0.02 Å in a region near ${\mathit{T}}_{\mathit{c}}$. This perturbation in the structure is accompanied by a large increase of the tunneling frequency of ∼80 K between the two wells, suggesting a coupling between superconducting fluctuations and nonlinear phonons.

We have derived the tilt and surface shape-equilibrium equations for tilted chiral lipid bilayers (TCLB’s) in analogy with cholesteric liquid crystals. On a cylindrical surface the field of tilt directions of TCLB molecules forms a right-handed helix with 45° gradient angle for ${\mathit{k}}_2$>0 or a left-handed helix with -45° angle for ${\mathit{k}}_2$<0, where ${\mathit{k}}_2$ is the cholesteric chiral curvature modulus. In addition, there exists another type of helical structure that looks like twisted strips or helicoids. We also show that on a spherical surface the tilt field has at least two singular points. These results explain the observed succession of transitions from a vesicular dispersion to a phase involving helical structures and then to tubes.

A statistical-mechanical theory of learning from examples in layered networks at finite temperature is studied. When the training error is a smooth function of continuously varying weights, the generalization error falls off asymptotically as the inverse number of examples. By analytical and numerical studies of single-layer perceptrons, we show that when the weights are discrete, the generalization error can exhibit a discontinuous transition to perfect generalization. For intermediate sizes of the example set, the state of perfect generalization coexists with a metastable spin-glass state.

The title statement is numerically shown for a globally coupled chaotic system. With an increasing number of elements, N, the distribution of the mean field approaches a Gaussian distribution, but the decrease of its mean-square deviation with N stops for large N. This violation of the law of large numbers is found to be caused by the emergence of a subtle coherence among elements, as is measured by the mutual information. With the inclusion of noise, the law of large numbers is restored. The mean-square deviation decreases in proportion to ${\mathit{N}}^{\mathrm{-}\mathrm{\beta }}$ with an exponent β<1 depending on the noise strength.

It is shown that critical behavior of systems with self-organized criticality can be explained as a Goldstone-mode phenomenon. The nonlinear interaction of the Goldstone mode causes the nontrivial critical exponents. Two more models are introduced with self-organized criticality features.

Variational upper bounds are derived for the escape rate of a particle trapped in a metastable well and interacting wth a dissipative medium. The theory leads to a reduced two-degrees-of-freedom Hamiltonian involving the unstable normal mode and a newly defined collective bath mode. Explicit treatment of strong nonlinearities or low-barrier systems present no special problem.

The magnitude of the gluon contribution to the proton spin induced by the triangle anomaly diagram in the quark axial current is estimated by means of a lattice QCD simulation (in the temporal axial gauge) of the polarized-proton matrix element of the anomalous current 〈ps‖${\mathit{K}}_{\mathrm{\mu }}$‖ps〉. The result of the simulation is that the fractional contribution of the gluon anomaly to the proton spin, -(3α/2π)Δg, is less than 0.05 in magnitude. This is much too small to affect the basic interpretation of the E.M.C. experiment, namely that the quark spins are responsible for very little, if any, of the proton spin.

We report on measurements of the ${\mathit{K}}_{\mathit{L}}$ Dalitz decay ${\mathit{K}}_{\mathit{L}}$→${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$γ. The results are based on a sample of 919 events. Through an evaluation of the form factor, we have established evidence for a nonvanishing contribution due to the ${\mathit{KK}}^{\mathrm{*}}$γ coupling. We have determined the branching ratio to be B(${\mathit{K}}_{\mathit{L}}$→${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$γ)=(9.1±0.$4_{\mathrm{-}0.5}^{+0.6\mathrm{}}$)×${10}^{\mathrm{-}6}$.

A many-body calculation of the parity-nonconserving amplitude for the 6${\mathit{s}}_{1/2}$→7${\mathit{s}}_{1/2}$ transition in atomic cesium with an error of order 1% is presented, ${\mathit{E}}_{\mathrm{PNC}}$=-0.906[9] (${\mathit{Q}}_{\mathit{W}}$/-N)i‖e‖${\mathit{a}}_0$×${10}^{\mathrm{-}11}$. Using this result to determine ${\mathit{Q}}_{\mathit{W}}$ from high-precision measurements of the transition leads to a quantitative test of the standard model. The various sources contributing to this transition are discussed and their uncertainties estimated. A discussion of radiative corrections with emphasis on the role of the top-quark mass is given.

We report on the observation of a strong optical dipole force which is exerted on atoms in a bichromatic standing light wave as a result of nonlinear wave-mixing processes. This force can substantially exceed the upper limit of the spontaneous light force and, in contrast to the dipole force in monochromatic standing-wave fields, acts with constant sign on a macroscopic spatial scale.

We have demonstrated (47±8)% squeezing of vacuum-fluctuation noise using a Josephson-parametric amplifier operated at 19.16 GHz. The amplifier was operated at 30 mK and has a double-sideband noise temperature of 0.446 K. This is comparable to the vacuum noise floor hν/2k=0.460 K.

The modulation instability of a two-dimensional field with a saturable self-focusing nonlinearity is investigated numerically. We show that approximate recurrence to an initial homogeneous field occurs, but oscillation around the exact recurrence is observed. This pseudorecurrence arises only for a restricted range of spatial modulation frequencies.

We present fluorescence spectra showing that the spontaneous-emission spectrum of a molecule in front of a mirror is not invariant on propagation. We also calculate the cross-spectral density of this light source and show that it does not obey Wolf’s scaling law [Phys. Rev. Lett. 56, 1370 (1986)].

The transition from traveling-wave to stationary convection in a binary-fluid mixture is studied as a function of Rayleigh number. The experiments are conducted in an annular container, which provides periodic boundary conditions in the direction of the wave motion. In agreement with the predictions of recent theories, the transition is shown to be continuous with no measurable hysteresis. The functional dependence of the wave phase velocity on Rayleigh number is in agreement with the predictions over the entire traveling-wave branch.

L-shell absorption of germanium transitions has been exploited for the first time to diagnose the low-temperature, high-density region of multilayered targets irradiated by 0.35-μm laser light at irradiances around ${10}^{14}$ W/${\mathrm{cm}}^2$. A detailed atomic-physics package has been used to relate the observed absorption wavelengths to the ionic distribution from Ge vii to Ge xx and to the electron plasma parameters. Results show time-dependent temperature variations closely following the driving-laser pulse shape, in agreement with hydrocode simulations.

The localized motion of hydrogen in scandium has been studied by quasielastic neutron scattering. The results reveal that the quasielastic linewidth has a pronounced minimum near 100 K and rises at lower temperature with approximate ${\mathit{T}}^{\mathrm{-}1}$ dependence, indicative of nonadiabatic behavior that can be associated with weak coupling of hydrogen to the metal conduction electrons. This is the first such observation in a pure-metal–hydrogen system. The simultaneous determination of the elastic incoherent structure factor is interpreted in terms of labile and nonlabile hydrogen configurations in a manner consistent with recent estimates of pairing and activation energies in the rare-earth–hydrogen systems.

In a critical system contained between parallel plates, it is known that the magnetization and energy density profiles close to one wall are modified due to the presence of the other wall. In addition, there is a long-range force between the walls. It is shown that the ratios of the ampiltudes governing these effects are universal, and moreover, independent of the boundary conditions at either wall. Their values are proportional to the scaling dimension of the density under consideration. Results are also given for the effects of local curvature of the wall on the density profiles. These results are shown to be a consequence of the conformal invariance of the critical system.

Using a scanned point-source, point-receiver technique based on laser generation and piezoelectric sensing, we have observed pronounced anisotropy in the amplitudes of ultrasonic waves propagated in silicon single crystals. The source of this anisotropy can be attributed to focusing of acoustic-ray vectors brought about by the elastic anisotropy of the medium. We present our results in the form of scan images that contain a wealth of structures corresponding to reflection and mode-conversion processes. Head waves are also clearly identified for the first time in a single-crystal specimen. The transduction process also has an important influence on the radiation pattern, and is responsible for the almost complete extinction of certain wave modes. Our results are well accounted for with Monte Carlo ray simulations, and are consistent with the known phonon-focusing pattern of silicon.

We report the first measurement of magnon thermal conductivity in monodomain single crystals of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in the U2D2 antiferromagnetic phase. The magnon mean free path λ was found first to rise rapidly upon cooling below ${\mathit{T}}_{\mathit{N}}$ and then more slowly at low temperatures, depending on the sample. The temperature dependence is consistent with magnon umklapp scattering at high T, i.e., λ proportional to ${\mathit{T}}^{\mathrm{-}2}$ exp(Δ/${\mathit{k}}_{\mathit{B}}$T), with Δ/${\mathit{k}}_{\mathit{B}}$ determined to be 5.8(±0.3) mK. The limiting low-temperature values of λ varied from 0.3 to 3 μm.