A generalization of the Euclidean diffusion equation is proposed for diffusion on fractals on the basis of a scaling argument, a renormalization-group theory for the Green's function, and numerical tests. Conjectures on the applicability to natural fractals (such as porous media) are presented.

Strong quasielastic features have been found in light scattering from diamond in the frequency range 0 to ± 200 GHz and have been investigated as a function of wave-vector transfer ($Q$) and temperature ($T$). The evolution of a relatively narrow Lorentzian component (∼ 10 GHz) demonstrates for the first time the manner in which a two-phonon difference spectrum in the collision-free regime (low $T$ and large $Q$) develops into entropy-fluctuation scattering in the collision-dominated regime (high $T$ and low $Q$).

Yield curves of molecular and fragment ions desorbed from covalent adsorbates on metals by photon-stimulated adsorbate-core excitation show distinct resonances, whose symmetries can be determined from polarization dependences. Threshold resonances for shakeup excitations followed by spectator Auger decay are particularly desorption efficient. The influences of Coulomb localization of the multiply valence-excited final state, its repulsive nature, and its separation from the substrate are discussed.

Previous time-of-flight experiments at 20-meV He beam energies, which provided the dispersion curve of Rayleigh surface phonons, have been extended to 90-meV energies on NaF(001) along $〈100〉$. Despite a large multiphonon background from the Rayleigh phonons it has been possible to detect small peaks due to optical surface phonons. The results provide the first direct experimental evidence in the dispersion curves of microscopic surface optical modes.

By employing an $S$-matrix theory for evanescent waves, we have calculated the repulsive potential between a helium atom and corrugated metal surfaces. $P$-wave interactions and intra-atomic correlation effects were found to be very important. The corrugation part of the interaction potential is much weaker than predicted by the effective-medium theory. Application to Cu, Ni, and Ag (110) surfaces gives good agreement with experiment without any adjustable parameters.

We study the effect of Anderson localization in dirty superconductors. The scale dependence of the diffusion in the vicinity of the mobility edge results in a strong renormalization of the zero-temperature coherence length. This implies the breakdown of the Ginzburg criterion close to the metal-insulator transition and thus the importance of fluctuations in this regime. The upper critical field is calculated and possible experiments are also discussed.

The temperature dependence of the upper critical magnetic field $H_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$ of the heavy-fermion superconductor U${\mathrm{Be}}_{13}$ was determined resistively. The magnitude of the initial slope of $H_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$, ∼420 kOe/K, is the largest value ever reported for a bulk superconductor. The curve of $H_{c2\mathrm{}}$ vs $T$ has an extremely unusual shape with a linear region that persists to very low temperatures. The anomalous shape of $H_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$ cannot be accounted for by current theories of either conventional or $p$-wave superconductivity.

Specific heat, thermal expansion, and electrical resistivity show that YbPd undergoes four phase transitions at 0.5, 1.9, 105, and 125 K. From magnetic-susceptibility measurements the transition at 0.5 K is found to be magnetic. The quasielastic magnetic linewidth is large as usual for mixed valence, but decreases with temperature and is smaller than $k_{\mathrm{B}}T$ everywhere. The magnetic order of YbPd occurs at a fractional Yb valence of $v=2.8\mathrm{}$ (measured by $L_{\mathrm{III}}$ absorption), i.e., near configurational crossover of $4f^{13}$ and $4f^{14}$.

It is been shown previoulsy that the existence of a tiny abundance of nuclei which have an additional embedded hadronic particle, $Q$-nuclei, can solve the solar-neutrino problem. We present here detailed predictions of solar-neutrino detection rates for detectors of ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$, and ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$. It is found that, while $Q$-nuclei could reduce the ${}_{}{}^{37}{}_{}{}^{}\mathrm{Cl}$ detection rate from that of the standard model to the experimental value, they would also produce a dramatic increase in the rates for the ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$ and ${}_{}{}^{115}{}_{}{}^{}\mathrm{In}$ detectors.

The relativistic Doppler shift is measured by the counting of the frequency difference between two cw dye lasers. One laser is locked to a two-photon transition in a fast beam of neon, and the other is locked to the same two-photon transition in thermal neon. The experimental result is compared to the prediction of special relativity. The result is in excellent agreement with this theory. An accuracy of 4×${10}^{-5\mathrm{}}$ is obtained, which provides the most accurate direct verification of time dilatation to date.

We describe a precise mathematical theory of the Laughlin argument for the quantization of the Hall conductance for general multiparticle Schrödinger operators with general background potentials. The quantization is a consequence of the geometric content of the conductance, namely, that it can be identified with an integral over the first Chern class. This generalizes ideas of Thouless et al., for noninteracting Bloch Hamiltonians to general (interacting and nonperiodic) ones.

The phase diagram of a Hamiltonian which describes a particle moving in a periodic potential and coupled to an external heat bath has been analyzed in detail. By renormalization-group methods, it is proved that this system exhibits an unusual transition between diffusive behavior and a self-trapped phase. The dynamics along the transition line is shown to be integrable and the order parameter, the mobility, is computed exactly.

We introduce a new random walk with the property that it is strictly self-avoiding and grows forever. It belongs to a different universality class from the usual self-avoiding walk. By definition the critical exponent $\gamma$ is equal to 1. To calculate the exponent $\nu$ of the mean square end-to-end distance we have performed exact enumerations on the square lattice up to 22 steps. This gives the value $\nu =0.57\mathrm{}\pm 0.01$.

The distribution of particles in three-jet events is compared with the predictions of three fragmentation models currently in use: the Lund string model, the Webber cluster model, and an independent fragmentation model. The Lund model and, to a certain extent, the Webber model provide reasonable descriptions of the data. The independent fragmentation model does not describe the distribution of particles at large angles with respect to the jet axes. The results provide evidence that the sources of hadrons are Lorentz boosted with respect to the overall c.m.

The inclusive production cross section of $\Lambda$, $\overline{\Lambda }$ in $e^{+}{e}^{-}$ annihilation at a c.m. energy of 29 GeV has been measured with the time-projection-chamber detector at PEP. The average $\Lambda$, $\overline{\Lambda }$ multiplicity has been measured to be 0.197 ± 0.012(stat.) ±0.017(syst.). $\Lambda -\overline{\Lambda }$ pairs have been observed in jets for the first time, and the average number of $\Lambda -\overline{\Lambda }$ pairs per event has been measured to be 0.042 ± 0.017 ± 0.014.

We compute one-loop radiative corrections, including contributions from virtual gravitons and gravitinos, to the scalar potential in $N=1\mathrm{}$ supergravity with an arbitrary superpotential. We show that, in a large class of locally supersymmetric grand unified theories, these corrections do not upset the tree-level gauge hierarchy.

A lower limit of 5×${10}^{22}$ yr (68% confidence level) has been obtained for the half-life of the neutrinoless double beta decay of ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}$. This process would require lepton-number nonconservation and that the electron neutrino have a mass and/or the weak interaction have right-handed currents. Ge detectors of 178 and 158 ${\mathrm{cm}}^3$ were used inside a NaI active shield for 1618 h. The radioactivity background was kept so low that, despite operating above ground, there was only 2×${10}^{-3\mathrm{}}$ count/keV·h total at the expected 2.041-MeV peak.

The precise ${}_{}{}^3{}_{}{}^{}\mathrm{H}$-${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atomic mass difference has been measured by high-resolution (${10}^{-8\mathrm{}}$) ion cyclotron resonance in a 4.7-T magnetic field. The result of 18 599 ± 2 eV favors a nonzero electron antineutrino mass.

Nuclear collisions from 0.3 to 2 GeV/nucleon are studied in a microscopic theory based on Vlasov's self-consistent mean field and Uehling-Uhlenbeck's two-body collision term which respects the Pauli principle. The theory explains simultaneously the observed collective flow and the pion multiplicity and gives their dependence on the nuclear equation of state.

The relative weight of proton and neutron spin-flip contributions to the $M1\mathrm{}$ excitation of the recently discovered $J^{\pi }=1^{+}$ state at $E_x=5.846\mathrm{}$ MeV has been determined by comparison of the momentum-transfer dependence of the measured electron-scattering form factor ($q_{\mathrm{eff}}=0.44-1.59\mathrm{}$ ${\mathrm{fm}}^{-1\mathrm{}}$) to results from a simple two-state model and from random-phase-approximation calculations using a spin- and spin-isospin-dependent effective separable interaction. The $M1\mathrm{}$ transition is shown to be predominantly of isoscalar nature.