A density-functional theory of freezing into an aperiodic lattice is presented. With use of freeenergy functionals for inhomogeneous hard-sphere fluids, the stability of a density wave with the structure of Bernal random packing is evaluated. Although the properties of the transition are sensitive to the form of the direct correlation function, the present calculations indicate a limit of metastability at a density $\rho =1.03\mathrm{}$. The frozen lattice becomes more stable than the liquid at a density $\rho =1.14\mathrm{}$.

Many results of the mean-field theory of spin-glasses violate simple scaling laws, including the magnetic field dependence of the transition lines, crossover effects of random anisotropy, and critical behavior in the ordered phase. These violations arise from two dangerously irrelevant variables. Below eight dimensions some mean-field exponents change and at $d=6\mathrm{}$ scaling is restored. Below $d=6\mathrm{}$ all scaling laws should be valid implying that the critical properties of real spin-glasses should be simpler than in mean-field theory. Experimental consequences are discussed.

The Eu $L_{\mathrm{III}}$-edge x-ray-absorption spectrum of Eu${\mathrm{Pd}}_2$${\mathrm{P}}_2$ exhibits a double-peaked white-line structure typical for mixed-valent materials, while Mössbauer isomer-shift and other magnetic measurements prove the divalent ground state of this compound. This discrepancy clearly shows the possible presence of final-state configuration-interaction effects in the $L_{\mathrm{III}}$-edge spectra of heavy-rare-earth systems, as well as a significant $4f$ covalent bonding, contrary to previous assumptions.

By means of a simple experimental heat-treatment procedure, the anomalous far-infrared absorption of superconducting Sn particle composites is shown to be associated with clustering. The structural insights thus obtained lead to a new theory in which the composite electric dipole absorption is dominated by poorly conducting clusters and is much larger than that of isolated metal particles. For superconducting particles, the theory predicts the absorption at frequencies above the gap frequency to be larger than in the normal state, in agreement with experiment.

Composite energy bands are subdivided into two classes. Class-I bands are shown to decompose into a set of simple bands. This is achieved by replacement of the Bloch functions (labeled by the energy) by basis functions that are labeled by the symmetry centers of the band. Because of their decomposition into simple bands, class-I bands have uniquely defined Wannier functions with an exponential falloff. Symmetry arguments are used to prove that Bloch functions of any composite band are necessarily discontinuous.

The density dependence of the mobility of Si(100) inversion layers is calculated within a multiple-scattering theory. Two scattering mechanisms are included. Because of surface-roughness scattering and charged-impurity scattering, a peak mobility ${\mu }_m$ is found at a characteristic electron density $n_m$. The inclusion of a mobility edge for low electron densities sharpens the peak structure drastically in comparison with the linear scattering theory. The comparison of calculated mobilities with experimental results gives good agreement in the full measured density range.

A new kinetic percolation model which exhibits diffusion-limited growth is studied. The model is a modification of the (site-) percolation model of Alexandrowicz in the sense that sites connected to the growing polymer are not incorporated at random but according to their probability of being reached by a monomer diffusing from far away. The critical exponents differ from those for random percolation, diffusion-limited aggregation, and Bethe lattice percolation.

The two-dimensional theory of gravity proposed by Jackiw is exactly quantized in the open case. The Wheeler-DeWitt equation is solved in closed form with and without cosmological constant. The theory has no degree of freedom and the unique wave functional reflects the classical aspects of the solution.

The renormalized trajectory for the O(3) Heisenberg model is found by use of a recently proposed microcanonical Monte Carlo method. On this trajectory, a remarkable improvement in the approach to the continuum limit is observed by evaluation of the mass gap.

A class of $\mathrm{SU}\mathrm{}\left(n\right)\mathrm{}$ antiferromagnetic quantum "spin" chains is solved in the large-$n$ limit. While the low-lying spectrum of the normal spin chain ($n=2\mathrm{}$) consists of massless solitons, in the large-$n$ limit the soliton is massive. Furthermore, the models exhibit many features of the $C{P}^n$ field theories at nonzero topological charge, which, it was recently argued, they become in the limit of a large representation.

The $\mathrm{CP}$-nonconserving portion of the gauge-field effective action for an even number of left-handed SU(2) fermion doublets, with nonzero chemical potentials ${\mu }^i$, is calculated to leading order in the inverse temperature, $T^{-1\mathrm{}}$. It is shown to be ${}_{}{}^i{}_{}{}^{}\Sigma _i^{}{}_{}{}^{}\left(\frac{{\mu }^i}{T}\right)W\left[A\right]\mathrm{}$, where $W\left[A\right]\mathrm{}$ is the Chern-Simons topological mass term. This result is also shown to be a consequence of the $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_L$ anomaly at zero temperature, but with $\mu \ne 0$. Because of the $i$ in front of the Chern-Simons term, this produces magnetic screening only if $\mu$ is complex.

Quarks and antiquarks within colliding protons and antiprotons are assumed to be composites which can factorize into spin-½ and spin-0 constituents. If the spin-0 constituents can form by their recombination the standard $W^{\pm }$ or $Z^0$, the possibility arises that the spin-½ constituents can recombine into new, nonstandard bosons. Along the lines of Abbott and Farhi a simple model is constructed predicting processes which may be releveant for CERN collider experiments in progress.

High-spin states in the transitional nucleus ${}_{}{}^{158}{}_{}{}^{}\mathrm{Yb}$ were populated via several (HI, $4n$) reactions. Two yrast bands were established up to $I^{\pi }=\left({40}^{+}\right) \mathrm{and} \left({31}^{-}\right)$. In contrast to the negative-parity band up to $I=31\mathrm{}$ and the positive-parity states up to $I=24\mathrm{}$ which show collective rotational patterns, states with $I^{\pi }={26}^{+}-{36}^{+}$ exhibit a nearly vibrational excitation mode. Such a quasivibrational pattern suggests a gradual transition toward oblate shapes and is the first evidence for a "band termination" in a heavy nucleus.

The unusual yrast spectrum of ${}_{}{}^{158}{}_{}{}^{}\mathrm{Yb}$ at very high spins is interpreted in terms of a band termination at $I^{\pi }={36}^{+}$. A similar spectrum with band terminations is obtained in microscopic cranking calculations for this nucleus. A basic element of the theory is that the finiteness of rotational bands is connected with a gradual shape change until the rotation takes place around a symmetry axis.

Detailed examination of the $\gamma$-ray spectrum due to the reaction ${}_{}{}^9{}_{}{}^{}\mathrm{Be}(n, \gamma ){}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$ reveals the presence of a spin-spin interaction of magnitude $V_{I\sigma }=1.65\mathrm{}\pm 0.15$ MeV. In addition, the spectroscopic factor of the second $0^{+}$ state at 6190 keV is determined to be $S_{\mathrm{dp}}=0.032\mathrm{}\pm 0.005$ which suggests that this state is an intruder state.

The propagator for relativistic quasiclassical multiple-scattering theories used in models of heavy-ion collisions is derived by use of the covariant Wigner representation. The results show how, in a classical theory, particles can propagate offshell and yet be found only onshell asymptotically and, in some detail, how multiple scattering vanishes with increasing incident energy.

We have produced a sample of free sodium atoms at rest in the laboratory by decelerating atoms in an atomic beam using momentum transfer from a counterpropagating, resonant laser beam. These atoms have a density of about ${10}^5$ ${\mathrm{cm}}^{-3\mathrm{}}$ and a velocity spread of about 15 m/s full width at half maximum corresponding to a kinetic temperature less than 100 mK.

Atomic-beam sodium atoms were slowed to zero or negative velocities by counterpropagating laser radiation which was frequency chirped with precise electro-optic modulation techniques. The resulting "gas cloud" had a temperature below 50 mK and a density above ${10}^6$ atoms/${\mathrm{cm}}^3$. We mention future possibilities in atom slowing, deflection, and storage.

It is shown that, in the context of an idealized ‘‘macroscopic quantum coherence’’ experiment, the predictions of quantum mechanics are incompatible with the conjunction of two general assumptions which are designated ‘‘macroscopic realism’’ and ‘‘noninvasive measurability at the macroscopic level.’’ The conditions under which quantum mechanics can be tested against these assumptions in a realistic experiment are discussed.

The quantum spectrum is studied in a corresponding classically nonintegrable triangular three-spin system with antiferromagnetic exchange coupling. A critical energy ${\mathrm{E}}_{\mathrm{c}}$ is identified numerically. Irregularly distributed (bandlike) levels and well-separated clusters of (localized) levels appear below and above ${\mathrm{E}}_{\mathrm{c}}$, respectively. The statistical average of second-order differences of eigenvalues shows a scaling behavior when the spin magnitude is increased towards +∞.