Path integrals are introduced for Glauber dynamics of interacting Ising spins, equivalent to stochastic equations for local magnetizations. This enables us to perform quenched averages. For the Sherrington-Kirkpatrick model of spin-glasses the low-frequency dynamics is determined for all temperatures and fields.

A model of a two-dimensional Fibonacci lattice is presented. Numerical calculations show that there is a transition as a function of strength of potential from the regime of zero spectral measure for a strong potential to the regime of finite measure for a weak potential. The conductance fluctuates with the system size and in the strong-potential regime the fluctuation is of the order of ${\mathrm{e}}^2$/h, just like the universal conductance fluctuation in a mesoscopic random system.

ac-susceptibility and neutron-diffraction experiments show that ${\mathrm{Fe}}_{0.4}$${\mathrm{Mg}}_{0.6}$${\mathrm{Cl}}_2$ is a three-dimensional Ising spin-glass with a transition temperature ${\mathrm{T}}_{\mathrm{sg}=3.4\mathrm{}}$ K. Inelastic-scattering experiments show a sharp spin-wave peak at the zone center for all temperature T≲2${\mathrm{T}}_{\mathrm{sg}}$. This is the first direct observation of long-wavelength excitation in a spin-glass system. We suggest that it is due to the precession of spin clusters around the easy axis.

A nonlinear Hamiltonian model is presented for which exact analytic results can be obtained. It is shown that macroscopically distinguishable quantum states can be generated and detected by means of a homodyne detector. The vacuum fluctuations may inhibit their observability; however, this contribution can be subtracted.

The transition from quasiperiodicity to chaos is studied for the situation where the sine circle map becomes supercritical. The numerical results show convincingly that scaling behavior is present in this transition.

According to general relativity, the calculated rate of motion of lunar perigee should include a contribution of 19.2 msec/yr from geodetic precession. We show that existing analyses of lunar–laser-ranging data confirm the general-relativistic rate for geodetic precession with respect to the planetary dynamical frame. In addition, the comparison of Earth-rotation results from lunar laser ranging and from very-long-baseline interferometry (VLBI) shows that the relative drift of the planetary dynamical frame and the extragalactic VLBI reference frame is small. The estimated accuracy is about 10%.

A well-balanced hollow copper sphere freely floating and almost totally submerged in water is observed to move toward the nearby edge of a cliff. This observation is consistent with a substance-dependent, medium-range force postulated in a recent reanalysis of the Eötvös experiment. Further measurements with different elements and geometries will be required to establish definitely the existence, source, and description of such a new force.

We have placed a torsion balance (containing two Be and two Cu test bodies) on a hillside to search for intermediate-range forces that couple to baryon number. Our results constrain (at 1σ) the strength of such an interaction to be ‖α̃‖≤1×${10}^{\mathrm{-}4}$ for ranges 250≤λ≤1400 m and ‖α̃‖≤1×${10}^{\mathrm{-}3}$ for ranges 30<λ<250 m.

On the basis of a few assumptions as to the desired ingredients of a gauge theory in 2+1 space, the most general Abelian gauge theory is derived. It is seen to include in special limits (a) electrodynamics (both with and without the Chern-Simons term), (b) a recently proposed photonless gauge theory, and (c) a previously unknown model in which the parity-nonconserving term is associated with the (gauge-invariant) field strength rather than the gauge field itself. Some results for the commutation relations and propagators are given.

We observe that (2+1)-dimensional Yang-Mills theory admits an arbitrary bare mass. Radiative corrections are also analyzed.

A charge asymmetry has been observed in final-state jets from $e^{+}$$e^{\mathrm{-}}$ annihilation into hadrons at √s =29 GeV. The measured asymmetry is consistent with the prediction of electroweak theory. The product of axial-vector weak coupling constants, averaged over all quark flavors, is determined to be 〈$g_A^e$$g_A^q$〉=-0.34±0.06±0.05.

The asymmetry $A_{\mathrm{NN}}$ for pp elastic scattering has been measured at 800 and 650 MeV in the region of Coulomb-nuclear interference. The data have been analyzed to extract the real part of a spin-spin scattering amplitude. Results are compared with the predictions of forward dispersion relations. They disagree significantly at 650 MeV.

The pronounced l=0 selectivity of the (e,e’p) proton knockout reaction has been exploited to determine the relative occupation of the 3$s_{1/2}$ proton orbit in ${}_{}{}^{205}{}_{}{}^{}\mathrm{Tl}$ and ${}_{}{}^{206}{}_{}{}^{}\mathrm{Pb}$. This value, when combined with previous electron scattering data, enables us to extract in a largely model-independent fashion the absolute 3$s_{1/2}$ occupation probability in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. The depletion of the 3$s_{1/2}$ proton orbit is found to be (18±9)%, compatible with predictions of many-body theories.

We report the observation of the giant dipole resonance in Pb nuclei near A∼200 at excitation energies of 66, 88, and 103 MeV and with average angular momenta of 25ħ to 44ħ. The fits to the dipole strength distribution require two components indicating a strongly deformed nuclear shape. Using width parameters consistent with the ground-state systematics of heavy deformed nuclei gives $E_1$=11.9 MeV, $E_2$apeq215.6 MeV, and prolate deformation with βapeq20.3. These results are compared with a prediction for superdeformed shapes in ${}_{}{}^{196}{}_{}{}^{}\mathrm{Pb}$ at L=30ħ.

We discuss the asymptotic high–molecular-weight behavior of flexible, weakly repulsive polymer chains in melts, both through an analogy to an O(n) model of magnets and directly. We show that such polymers are slightly expanded in two dimensions so that in the limit of very high molecular weight, polymers interpenetrate strongly and the fraction of the monomers belonging to a polymer within the radius of gyration of that polymer tends to zero logarithmically. The molecular-weight or length-scale dependence of the radius of gyration, osmotic pressure, and end-end scattering function is given. The range of parameters for which this behavior is expected is discussed.

We introduce a stochastic process called a Lévy walk which is a random walk with a nonlocal memory coupled in space and in time in a scaling fashion. Lévy walks result in enhanced diffusion, i.e., diffusion that grows as ${\mathrm{t}}^{\mathrm{\alpha }}$,α>1. When applied to the description of a passive scalar diffusing in a fluctuating fluid flow the model generalizes Taylor’s correlated-walk approach. It yields Richardson’s ${\mathrm{t}}^3$ law for the turbulent diffusion of a passive scalar in a Kolmogorov -(5/3) homogeneous turbulent flow and also gives the deviations from the (5/3) exponent resulting from Mandelbrot’s intermittency. The model can be extended to studies of chemical reactions in turbulent flow.

We consider the interaction of counterpropagating pulses via a ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ nonlinearity, in an isotropic electrostriction medium. The polarization is taken into account and can vary through each pulse; group-velocity dispersion is neglected. We find a family of analytic solutions, termed polarization solitons, which play a central role in the dynamics. Upon interaction, the net effect on their polarization profiles is a rigid rotation in Stokes vector space. As special cases, they include the first nontrivial examples of polarization-transparent and orthogonally switched pulses.

Highly nonlinear phenomena are observed in Taconis oscillations which are spontaneous oscillations of gas columns thermally induced in a tube with steep temperature gradients. Near the overlapped region and the intersection of the stability curves for two different modes with incommensurate frequencies, we find that both modes can be excited simultaneously and competition between them leads to complex quasiperiodic and chaotic states. Experimental data are anlayzed by use of recent methods from the theory of nonlinear dynamical systems.

Recent theoretical work has suggested that the quasilinear description of the weak-warm-beam–plasma instability is incomplete. It has been argued that beam-mediated mode-coupling effects neglected in standard quasilinear theory play an important role, and that their average effect is a zeroth-order increase in the growth rate. We have experimentally observed strong mode-coupling effects when a weak warm beam interacts with waves on a slow wave structure. However, when we average the effects of the mode coupling we do not observe the predicted zeroth-order increase in the growth rate.

The vibrational Raman spectrum ${\mathrm{D}}_2$ has been found to exhibit a fine structure which is particularly distinct near the liquid-gas critical point (${\mathrm{T}}_{\mathrm{c}}$=38.3 K). No such structure was observed in the spectra of either ${\mathrm{H}}_2$ or HD. The effect is interpreted as arising from a high degree of local ordering in the ${\mathrm{D}}_2$ system.