We report an analytical solution for the vibrations of a Bethe lattice having a random and uncorrelated set of dihedral angles $\left\{{\phi }_i\right\}$. The resultant $\phi$-averaged Bethe lattice provides a very good fit to the Raman spectra of vitreous Si${\mathrm{O}}^2$, and is a powerful tool for the treatment of network and defect vibrations in this and other amorphous solids.

From sound-velocity measurements we found that the presence of helium in the pores of Vycor increased the relaxation rates of two-level systems in the glass. Superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ caused a much larger increase than either solid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ or liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. The results are interpreted in terms of additional thermal phonons in the helium, with fourth-sound modes possibly causing the faster relaxation for superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.

The structure change of incommensurate potassium monolayers on low-dislocation-density copper (001) has been observed at 330 K by low-energy electron diffraction. The orientation angle was found to increase uniformly from 3.3° to 6.0° when the potassium interatomic spacing was varied from 4.72 to 4.57 Å. The existence of rotational epitaxy, observed previously for physisorbed rare-gas monolayers, has been demonstrated for an alkalimetal monolayer on a metal surface.

A Monte Carlo calculation for light intensities scattered from a random Gaussian-correlated surface is presented for the first time. It is shown that small randomness on a grating surface can considerably change the intensities and, in particular, the surface polariton resonances. These results should be used to check perturbation-theory calculations.

New NMR measurements are reported on continuous ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$ vortices in tilted magnetic fields. We introduce a symmetry classification of the continuous vortices with broken axial symmetry. It is found that the discrete internal symmetry may in addition be broken in two inequivalent ways, producing two different continuous vortices. Although NMR may not distinguish between these two vortices, the observed vortex satellite peak is well accounted for by spin waves localized in the soft core of such vortices.

By use of a Pd-Si${\mathrm{O}}_2$-Si structure as a hydrogen sensor, very small changes in the hydrogen pressure can be detected. Furthermore, such a structure can be used to detect hydrogen with perfect discrimination during a catalytic surface reaction. By using this technique, together with work-function and desorption measurements, in the study of the water-forming reaction on Pd, we conclude that hydrogen has an activated lateral mobility on Pd.

Quantum exchange effects, predicted to occur in the spin diffusion of polarized nondegenerate gases, have been observed in a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixture by spin-echo techniques. Measurements of the spin rotation parameter ${\left(\mu M_0\right)}^2$ and diffusion constant $D$ are in reasonable agreement with theoretical predictions until the degeneracy temperature is approached.

We report self-consistent Green's-function total-energy calculations which provide, for the first time, a firm theoretical framework for understanding the microscopic mechanisms of atomic diffusion in Si. We find that the self-interstitial has negative-$U$ properties, roughly the same formation energy at several sites, small migration barriers, and charge-state instabilities that allow athermal migration along several paths. We also find that both vacancies and interstitials mediate self-diffusion and reconcile contrasting low- and high-temperature data.

Cholesterics, uniaxial and biaxial nematics, and the dipole-free $A$ phase of superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are characterized by order parameters which are left invariant by suitable "symmetry" groups $H$. We show that in the presence of defects, the full group $H$ may not be implementable on the states because of topological obstructions. Thus $H$ is topologically broken in the presence of suitable defects.

Using a "spatial correlation" model with a Gaussian correlation function we have for the first time quantitatively explained the broadening and asymmetry of the first-order longitudinal-optic phonon Raman spectrum induced by alloy potential fluctuations. The systems studied were the representative alloy semiconductors ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}/\mathrm{GaAs}$ and ${\mathrm{Ga}}_{0.47}$${\mathrm{In}}_{0.53}$As/InP. This analysis provides important insights into the microscopic nature of the alloy potential fluctuations.

By use of the new technique of $k$-resolved inverse photoemission spectroscopy, an unoccupied $s$-like surface state on Ag(110) has been detected, which lies within the projected $L_{2^{\prime }}\to L_1$ gap of the bulk. At the $\overline{X}$ point of the surface Brillouin zone, the energy of the surface state is 1.65 eV above the Fermi level $E_{\mathrm{F}}$, and exhibits a band dispersion $E\left(k_{\parallel }\right)$ towards higher energies. The surface-state emission is immediately quenched when the surface is exposed to very small amounts of oxygen or hydrogen.

We argue that the widely held view that MnO, FeO, CoO, and NiO are Mott insulators is incorrect. Intra-atomic potential energies do not dominate interatomic kinetic energies, to the extent commonly believed; both are 1-2 eV in magnitude. A measure of the importance of interatomic effects is our finding that both the crystal structure and the magnetic structure of these materials are crucial to their insulating behavior.

X-ray and high-resolution uv photoemission spectroscopy of the conduction band of Am metal directly reveal that the $5f$ electrons in Am are localized, in contrast to the $5f$ electrons in the lighter actinide metals. The observed $5f$ final-state multiplet structure arises from a trivalent $5f^6$ Am ground state. The withdrawal of the $5f$ electrons from the Fermi level is also manifested in the core-hole screening mechanism: The $4f$ core-level spectrum shows the poorly screened peak ($s$,$d$ electrons) to be the most intense one.

A nonlinear stochastic process is presented that, for each realization and for large times, reproduces Lüder's projection postulate. The corresponding density operator undergoes a linear evolution reproducing von Neumann's projection postulate. The violation of the Bell inequality, for instance, is described with the two apparatus acting independently on the composed system.

The Hausdorff dimension $D_0$ of a strange attractor is argued to be the fixed point of a recursive relation, defined in terms of a suitable average of the smallest distances ${\delta }_i$ between points on the attractor. A fast numerical algorithm is developed to compute $D_0$. The spread $\lambda$ in the convergence rates towards zero of the distances ${\delta }_i$ (uniformity factor) as well as the stability of the fixed point are discussed in terms of the entropy of the ${\delta }_i$ distribution.

For a model quantum system the distributions of the spacings between adjacent levels in specified intervals of the energy spectrum are fitted by the Brody distribution. This analysis displays for the first time the expected transition from regularity to irregularity, in terms of a smooth increase of the parameter of the Brody distribution from 0 to 1.

The model of cluster growth by diffusion-limited aggregation of clusters is studied in two dimensions and the cluster size distribution $n_s\mathrm{}\left(t\right)\mathrm{}$ is determined as a function of the cluster size $s$ and the time $t$. A dynamic scaling function of the form $n_s\mathrm{}\left(t\right)\mathrm{}\sim t^{-w}{s}^{-\tau }f\left(\frac{s}{t^z}\right)$ is proposed and is shown to lead to the scaling relation $w=(2-\tau )z$ among the critical exponents. The simulation results support this scaling law.

The phase shift introduced by rotational motion of a two-crystal neutron interferometer has been measured and found to agree with prediction within 0.4%. This agreement is obtained without making the in-crystal phase corrections employed in a recent study of a linearly accelerated three-crystal interferometer.

A weakly coupled four-dimensional model is presented which exhibits dimensional transmutation and spontaneous breaking of gauge, chiral, and super symmetries by instanton effects.

The ${\mathrm{Na}}_2$ Rydberg states have been observed for $15<~n<~90$ and $4<~J<~45$. The evolution of the spectra is studied as a function of the relative values of ${\omega }_{\mathrm{el}}$, the electronic rotational frequency, and ${\omega }_N$, the nuclear rotational frequency. The molecular eigenfunction is found to be pure Hund's case $a$ when $k{\omega }_{\mathrm{el}}=2\mathrm{}{\omega }_N$ ($k$ being an integer). This may be explained in terms of stroboscopic effects arising from the movement of the Rydberg electron relative to the ionic core.