A correct long-wavelength theory for convection near onset with free-slip boundary conditions requires two fields and reversible couplings. The wavelengths for which stable rolls exist are dramatically modified when the generation of vertical vorticity is taken into consideration. For small Prandtl numbers and rigid boundaries, the skewedvaricose instability of Busse and Clever is recovered by a plausible but nonrigorous modification of our free-slip equations.

The presence of unitary group generators in the time evolution of $N$-level quantum systems is shown to suggest a class of new nonlinear constants of motion, and to permit the description of the evolution in terms of the rotations of a real coherence vector.

Nonresonant parametric decay of lower-hybrid waves, observed in a number of high-power tokamak rf-heating experiments, is positively identified as a decay into ion-cyclotron quasimodes. The decay-wave spectrum, wavelength, and amplitude profile are measured inside a toroidal plasma with pump frequency $f_0\sim 3.5f_{\mathrm{pi}}\sim 25f_{\mathrm{ci}}$.

A large birefringence $\delta n$ has been discovered in the critical binary fluids nitrobenzene—$n$-hexane and isobutyric-acid-water submitted to a shear flow (rate $S$). In agreement with the Onuki and Kawasaki theory, two typical regions are in evidence: (i) strong shear, where $\delta n\sim S^{\frac{1}{3}}$ and is temperature independent; (ii) weak shear, where $\delta n\sim S$ and varies strongly with temperature. Moreover, this effect confirms the contribution of fluctuations to the critical anomaly of the refractive index in fluids at equilibrium, and could become a new tool for studying critical phenomena.

Deformations of the charged surface of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ are studied by optical means. Near the dimple-crystal-formation point we observe saturation effects and a stripe structure exhibiting hysteresis. We discuss imperfect lattices and dimple glasses and compare data with existing theories of nonlinear equilibrium.

Magnetic resonance at 1420 MHz in zero magnetic field and for $0.06<T<\mathrm{}0.5\mathrm{}$ K has been used to determine the binding energy of H on liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, the rate constant for recombination and the frequency shift for H on ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and the sticking probability for H on ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The binding energy for H on liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is found to be 0.42±0.05 K, and the sticking probabilities are 0.035 for H on ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and 0.016 for H on ${}_{}{}^3{}_{}{}^{}\mathrm{He}$.

Anharmonic corrections to the familiar harmonic description of "one-dimensional solids" (i.e., liquids which develop a one-dimensional mass-density wave) are calculated by analytic renormalization-group methods in three dimensions. The elastic constants describing the compressional and undulational modes respectively vanish and diverge logarithmically at small wave vectors. Density correlations decay as ${\mathcal{r}}^{-x}$ with $x=\eta \mathrm{}\left(T\right)\mathrm{}{\left(\ln \mathcal{r}\right)}^{\tilde{\eta }}$, where the exponent $\tilde{\eta }$ assumes the universal value $\frac{1}{5}$.

The renormalization-group method has been applied to investigate vibrational properties of a diatomic mixed crystal. It has been found that there exists a fixed point which separates the one-mode behavior from the two-mode behavior. This transition depends on concentration, force constants, and mass ratios.

Luminescence and Raman measurements on a new type of superlattice consisting of $n$- and $p$-type doped GaAs layers grown by molecular-beam epitaxy confirm crucial predictions of theory. A strongly tunable energy gap is found in luminescence. Raman experiments provide the first observation of electronic subbands in purely space-charge-induced quantum wells. A combined analysis of the luminescence and Raman data yields excellent agreement with self-consistent subband calculations based only on the design parameters of the sample.

Light-Scattering measurements of energy fluctuations coupled to order-parameter fluctuations by an applied electric field are presented. A firm experimental demonstration of the static and dynamic properties of the central-peak equation is obtained. Immediately above the transition both the specific heat and the thermal diffusivity extrapolated to zero field are found to be temperature independent. The specific heat agrees with the lattice value, whereas the diffusivity appears anomalously small.

The static and dynamic magnetic response of isolated Ce ions in Th metal is microscopically observed by the time-differential perturbed $\gamma$-ray distribution method. The single—Ce-ion behavior reflects intermediate valence and a temperature-driven transition from nonmagnetic to magnetic in the range 18 to 800 K.

Al surfaces grown epitaxially on GaAs(100) substrates exhibit a nearly atomically smooth surface morphology which permits the formation of various clean and impurity-induced surface reconstructions. The Al(100)-$c(2\mathrm{}\times 2)$ reconstruction can be ascribed to a two-dimensional Fermi-surface instability. Arguments are given that suggest a charge-density-wave mechanism.

A new theory of the electronic properties of heterostructures is proposed. Linear combinations of Bloch waves, both propagating and evanescent, are matched across the interface. This leads to simple continuity conditions on the envelope functions, which can be used to solve any heterostructure problem. Calculated optical transitions in GaAs-AlGaAs and InAs-GaSb heterostructures show good agreement with experiment.

The conductance for a two-dimensional tight-binding model with on-site disorder is calculated numerically with use of the Kubo formula. For weak disorder logarithmic localization is observed, in agreement with the scaling theory. The magnetoresistance is found to be negative in both the logarithmic and exponential localization regimes. Results for a model with random complex hopping matrix elements are also presented.

A neutron interferometer experiment testing the existence of an Aharonov-Bohm effect has been performed and no measurable phase shift has been found upon reversal of the enclosed magnetic flux. A positive result would have provided evidence for a breakdown in the standard minimal-coupling scheme for the electromagnetic interaction of a neutron. The sensitivity of the experiment sets the ratio of the Aharonov-Bohm effect for a neutron to that of a particle of charge $e$ to be less than 5×${10}^{-12\mathrm{}}$.

The correlation length in the two-dimensional nonlinear O(3) $\sigma$ model is calculated with contributions of instantons included. It is given by $\xi =0.0125a$ $\frac{\exp \left[\frac{2\pi }{f\left(a\right)\mathrm{}}\right]f\left(a\right)\mathrm{}}{2\pi }$ where $f\left(a\right)\mathrm{}$ is the coupling constant defined in lattice regularization scheme and $a$ is the lattice spacing. This number remarkably coincides with the result of Monte Carlo simulations by Shenker and Tobochnik.

The breaking of supersymmetry can be implemented by the $D$ term. This term can be quadratically divergent, ruining the possibility of naturally large hierarchies. According to Witten this does not occur if the U(1) gauge group is unified in a semisimple group. We show that sufficient conditions for the $D$ counterterm to vanish are less restrictive than grand unification and only require a vanishing trace of the U(1) charge. No cancellation between high-energy and low-energy scales is involved.

We have measured the inclusive cross section for $\eta$ production in $e^{+}{e}^{-}$ interactions near charm threshold using the Crystal Ball detector. No pronounced structure in the energy dependence is observed. By comparing cross sections above and below charm threshold we obtain the limits (90% confidence limit): $R(e^{+}{e}^{-}\to F\overline{F}X)R_B(F\to \eta x)<\mathrm{}0.15-0.32\mathrm{}$ (for $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}$ from 4.0 to 4.5 GeV), $R_B(D\to \eta x)<\mathrm{}0.13\mathrm{}$. Our results are inconsistent with a previous report of a large energy dependence of the $\eta$ cross section ascribed to the crossing of the $F{F}^{*}$ and $F^{*}{F}^{*}$ production thresholds.

"Topological supersymmetry," a newly recognized feature of the zero-entropy $S$-matrix bootstrap, leads to a zero-entropy coupling constant $g_0$ whose order of magnitude is controlled by the relation $8N_g(8\mathrm{}{N}_g-1)\frac{{g_0}^2}{16{\pi }^2}\sim 1$, where $N_g=4\mathrm{}$ is the number of quark generations. A unification principle, suggested by electromagnetic extension of topological theory and encouraged by this relation, is $g_0=e$. The posture of this unifying $S$-matrix condition with respect to field-theoretical grand unification is discussed.

Topological particle theory is applied to the computation of elementary-hadron coupling constants. All are determined through topological supersymmetry by a single dimensionless "zero-entropy" constnat $g_0$. The predicted coupling-constant ratios encompass and justify those of Mandelstam. The universality conjecture, $g_0=e$, is supported (to 6%) by the accurately measured value of the pion-nucleon coupling constant. An explanation emerges for the experimental failure to find baryonium.