It is claimed that the abstract analytic continuation of hypercubic lattices to noninteger dimensionalities can be implemented explicitly by certain fractal lattices of low lacunarity. These lattices are special examples of Sierpinski carpets. Their being of low lacunarity means that they are arbitrarily close to being translationally invariant. The claim is substantiated for the Ising model in $D=1+\epsilon$ dimensions, and for resistor network models with $1<D<\mathrm{}2\mathrm{}$.

A renormalizable relativistic quantum field theory of nuclear interactions is shown to possess not only Yukawa-type solutions, but also a topologically nontrivial one. It corresponds to a hadronic monopole, called a hadroid. Experimental evidence suggesting the existence of such a nuclear state is considered.

The presence and properties of x-ray evanescent waves are demonstrated detecting their absorption and their excitation in the vicinity of a target surface. The role of microscopic reversibility in relating the two cases is discussed and practical applications of the phenomena to probe interfaces are suggested.

The fully quantum mechanical treatment of superfluorescence buildup in the linearized regime of superfluorescence is presented for coherently, optically pumped three-level systems. It is shown that to order $\frac{{\tau }_p}{{\tau }_R}$, where ${\tau }_p$ is the pump time duration and ${\tau }_R$ the characteristic superfluorescence time, fluorescence buildup during the dynamical pumping process contributes significantly to quantum initiation of superfluorescence.

An on-axis solution to the nonlinear instability treatment is presented where a single "sinusoidal" spike is superimposed on a constant plane laser background. Introduction of the phenomenological depletion of the background leads to the stabilization of intensity in the spike and an accurate prediction of its diameter.

Numerical evidence is presented for period doubling and chaos at attainable laser powers in a model for optical tristability comprising two ring-cavity modes coupled via a $J=\frac{1}{2}$ to $J=\frac{1}{2}$ transition. A sequence of periodic windows found embedded in the chaos for this model has also been found in the Lorenz equations. It is suggested that it begins an infinite sequence of a new period-doubling type.

The long-time containment of pure electron-plasma columns has been found to depend strongly on the plasma length $L$, as well as on the axial magnetic field $B$. Plasma evolution times are observed to scale as ${\left(\frac{L}{B}\right)}^{-2\mathrm{}}$ over a range of more than five decades. This transport is probably caused by small azimuthal asymmetries in the applied magnetic or electric fields.

The effect of tokamak magnetic field helicity, i.e., rotational transform, on the propagation of lower hybrid resonance cones is clearly observed in the California Institute of Technology Encore tokamak. The observations are in excellent agreement with the predictions of a recent theory.

A new attenuation mechanism has been identified for third sound propagating in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films. Attenuated transmissions and phase-inverted reflections have been observed to occur for both macroscopic and microscopic surface defects in the substrate used to support superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films. The data were obtained by using sound frequencies in the 20 to 200 kHz range.

High-resolution phase diagrams of four binary liquid-crystal mixtures exhibiting nematic, smectic-$A$, smectic-$C$ multicritical points are found to be universal.

Dramatic differences in structure, elastic properties, and order-disorder temperatures are observed for stage-2 Li-graphite of different in-plane density, indicating the importance of long-range interactions in cohesive properties. Li${\mathrm{C}}_{12}$ is three-dimensionally ordered up to ∼ 500 K with $\sqrt{3}\times \sqrt{3}$ Li superlattice and $\mathrm{AA}$ graphite stacking, whereas Li${\mathrm{C}}_{18}$ is disordered at 300 K and has $\mathrm{AB}$ stacking. LO and LA ($00l$) phonon energies are 30% greater in the former, which can be understood in terms of electrostatic effects.

Measurements of transient magnetic birefringence are reported for isotropic solutions of a biological rodlike macromolecule, bacterial virus fd. A steep increase of the birefringence and a slowing down of the relaxation process are observed just below the concentration at which the liquid-crystalline phase appears. These pretransitional phenomena are considered to be due to the short-range order effects, and a Landau-de Gennestype approach based on the Onsager theory describes our results semiquantitatively.

The densities of vortex lines in He II due to rotation and axial counterflow do not simply add. With slow rotation, the critical counterflow velocity is greatly reduced. At high counterflow velocities, rotation adds fewer lines than expected, suggesting that the vortex tangle is polarized by rotation. Two critical velocities are found, the smaller of which agrees quantitatively with an explanation by Glaberson, Johnson, and Ostermeier of an instability found by Cheng, Cromar, and Donnelly.

Helium desorption is treated in a model where the film is assumed to have the thermodynamic properties of bulk liquid and the vapor is described by kinetic theory. Equations for energy and mass conservation determine the dynamics of the system. The model resolves some puzzling features of a number of experiments, and predicts a thermally activated desorption time constant in reasonable agreement with experiment, without adjustable parameters.

The spin-diffusion coefficient $D$ of a polarized two-dimensional degenerate Fermi fluid is evaluated as a model of adsorbed ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. Because in two dimensions, for zero or weak polarization, the only allowed scattering angles are 0 and $\pi$, the transport coefficients become expressible in terms of Landau parameters without approximation. For unpolarized and weakly polarized systems it is shown that $D^{-1\mathrm{}}\sim T^2\ln T$ and $T^2\ln \left(\mathrm{polarization}\right)$, respectively. The two-dimensional kinetic equation is found to be exactly solvable.

A lattice rescaling method is applied to the equations of motion of the dilute Heisenberg chain and leads via a probabilistic integral equation to an iterative map for the characteristic frequency $\beta$ and concentration $p$. Dilution induces a crossover in the $\beta$ scaling from "chaotic" (ergodic and mixing) behavior, corresponding to the sampling of the pure band, to periodic orbits corresponding to isolated cluster response. A dynamic scaling form is obtained for the critical dynamics by fixed-point analysis.

Absorption and emission measurements of the ${}_{}{}^4{}_{}{}^{}A_2^{}{}_{}{}^{}-{}_{}{}^2{}_{}{}^{}E$ transitions of ${\mathrm{Cr}}^{3+}$ in GdAl${\mathrm{O}}_3$ at $T<~4.2$ K, in magnetic fields up to 6 T parallel to the easy axis, are consistent with a magnetic Franck-Condon principle for which the energy difference between the absorption and emission lines arises mainly from the spin relaxation, rather than the neighboring ion space coordinates around the impurity. The Cr-Gd exchange-coupling constant changes with the applied magnetic field from $J=2.1\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ at $H=0\mathrm{}$ to $J_{\mathrm{sat}}=1.46\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ at high field.

A resolution to the controversy over the magnitude of the effective short-range Coulomb interaction in molecular conductors is proposed by showing that it depends very strongly on band filling because of intermolecular correlations.

The polarizability function of a two-dimensional electron layer submerged in a threedimensional dielectric material and interacting with a random distribution of static charged impurity centers is calculated. Scattering and screening are treated self-consistently and each affects the other. The resultant scattering time is found to depend on the impurity density $N_i$ through the ${(a{N}_i+b{N_i}^2)}^{-1\mathrm{}}$ law which has been observed experimentally in silicon inversion layers. The theory is in good agreement with the experimental findings on the parameters $a$ and $b$.

The first self-consistent $X\alpha$ study of trans-polyacetylene, ${\left(\mathrm{CH}\right)}_x$, is reported. This study is carried out by application of a new linear-combination-of-atomic-orbitals method which determines both the electronic structure and geometry of periodic chain polymers variationally from the $X\alpha$ total-energy functional. The present trans-${\left(\mathrm{CH}\right)}_x$ results compare favorably with experiment and indicate that the present method will be useful in the study of both the electronic and geometric properties of other quasi one-dimensional systems.