Specific-heat and thermal-conductivity measurements were made on a series of base-catalyzed silica aerogels at temperatures between 0.05 and 20 K. Evidence for a crossover between regimes of characteristically different excitations was observed. The data analysis indicates a ‘‘bump’’ in the density of vibrational states g(ω) at the crossover frequency from phonon to fracton behavior.

Scaling curves for the density of states and localization length of fractons near a percolation threshold are obtained for dilute and superconducting lattices in both two and three dimensions. These are used to verify the predictions of single-parameter scaling and to show that the energy dependence of the inverse localization length is consistent with known values of the spectral dimensionalities of these structures. The results demonstrate that eigenstates of an infinite, percolating, dilute structure exhibit superlocalization of the form ψ(r)∼${\mathit{e}}^{\mathrm{-}\mathrm{\beta }\mathit{r}\mathrm{\delta }}$ with values of δ=1.13±0.06 and 1.39±0.07 in two and three dimensions, respectively.

Intrinsic high-frequency oscillations (≊2.5 THz) in current and corresponding quantum-well density have been simulated for the first time for a fixed-bias voltage in the negative differential resistance (NDR) region of the current-voltage (I-V) characteristics of a resonant tunneling diode. Scattering and self-consistency are included. Hysteresis and ‘‘plateaulike’’ behavior of the time-averaged I-V curve are simulated in the NDR region. Intrinsic bistability is manifested by the phenomenon of unstable electron charge buildup and ejection from the quantum well.

Resonant tunneling through a quantum-box level is investigated in terms of nonequilibrium Green’s functions. A Hamiltonian with a Hubbard-type term, accounting for charging effects in the box, is proposed. Besides the resonance-level feature in the current-voltage characteristic, a satellite feature appears due to charging effects. A tuning between the two features is found by varying the tunneling rates through the emitter and the collector barriers; this provides a method for distinguishing charging effects from lateral-confinement effects.

We show that the magnetic dipolar energy of antiparallel dipoles in the surface layers contributes to the intrinsic perpendicular anisotropy in amorphous rare-earth–transition-metal films. The volume anisotropy energy density ${\mathit{K}}_{\mathit{u}}$ of this contribution depends inversely on the thickness of the film. For an amorphous GdCo film with a thickness of 1000 Å the calculated ${\mathit{K}}_{\mathit{u}}$ is on the order of ${10}^{3–}$${10}^4$ ergs ${\mathrm{cm}}^3$. Dependence of ${\mathit{K}}_{\mathit{u}}$ on temperature and atomic concentration is also calculated.

We study the critical behavior of fully frustrated XY and Josephson-junction systems by means of a coupled XY-Ising model. From Monte Carlo and transfer-matrix calculations, we find separate XY and Ising and first-order transitions, depending on the parameters. In addition, a line of continuous transitions is found, with simulataneous loss of XY and Ising order and novel critical behavior. This result is supported by Monte Carlo simulations of frustrated XY models on square and triangular lattices.

We predict that series arrays of point-contact Josephson junctions, shunted by a resistive load, should be unusually sensitive to noise. This behavior stems from a dynamical symmetry which prohibits the existence of in-phase attractors. Simulations verify that breaking the symmetry can radically improve the phase-locking performance of the array.

We report measurements of the a-b-plane thermopower (S) on crystalline ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ (δ≤0.16) for temperatures below 310 K. Much sharper features in the T dependence of S are observed than have been previously reported. Both the temperature and oxygen-doping dependences of S, which have caused confusion, are consistently accounted for by conventional metallic theory for the first time. Strong phonon drag and two carrier species are indicated, with holes on the planes and electrons on the chains. An anomalous, positive component to S, observed for T<160 K, is attributed to a freeze-out of carrier-phonon umklapp processes involving holes in the ${\mathrm{CuO}}_2$ planes and optical-mode phonons.

Transmission-electron-microscopy observations of silicon layers obtained by chemical vapor deposition at 540 °C onto ${\mathrm{SiO}}_2$ substrates reveal the presence of nanometer-diameter crystal seeds. Ion bombardment with 600-keV Kr ions at a temperature in the range 330–450 °C produces the growth of a fraction of these seeds that increases with the irradiation temperature. The interpretation of the results implies that phase stability is still controllled by the thermodynamic transition scheme even in the presence of the large density of defects generated during each collision cascade.

Using an ultrasensitive, cryogenic, current-comparator bridge the quantized Hall resistance ${\mathit{R}}_{\mathit{H}}$(2) in a GaAs/AlGaAs heterostructure has been compared directly with ${\mathit{R}}_{\mathit{H}}$(4) in a silicon MOSFET. The measurements show that ${\mathit{R}}_{\mathit{H}}$(2;GaAs)/${\mathit{R}}_{\mathit{H}}$(4;Si)=2[1-0.22(3.5)×${10}^{\mathrm{-}10}$]. Within the 1σ combined uncertainty of ±3.5×${10}^{\mathrm{-}10}$ the result suggests that the quantized Hall resistance is a universal quantity, independent of the host lattice and Landau-level index, and is probably equivalent to h/${\mathit{e}}^2$, the relationship predicted theoretically.

A general analytic method for calculating finite-size corrections, central charges, and scaling dimensions of solvable lattice models is presented. The approach is to solve the special functional equations or inversion identities satisfied by the commuting row transfer matrices of these lattice models at criticality. For purposes of illustration, the method is applied to calculate the central charge c=4/5 and leading magnetic scaling dimension x=2/15 of hard hexagons. These numbers are rational due to special values of Rogers dilogarithms.

In chaotic scattering there is a Cantor set of input-variable values of zero Lebesgue measure (i.e., zero total length) on which the scattering function is singular. For cases where the dynamics leading to chaotic scattering is nonhyperbolic (e.g., there are Kolmogorov-Arnol’d-Moser tori), the nature of this singular set is fundamentally different from that in the hyperbolic case. In particular, for the nonhyperbolic case, although the singular set has zero total length, we present strong evidence that its fractal dimension is 1.

The deformation of the energy-level spectra of quantum systems as a function of a control parameter governing the strength of a nonintegrable perturbation can be determined by standard molecular-dynamics techniques. The integration of Newton’s equations of motion provides detailed information on the spectral deformation when the classical system undergoes a transition from mostly regular to mostly chaotic motion. This method is used to study the changes in the energy-level statistics and allows the direct determination of the Brody parameter in the predominantly chaotic regime.

A novel random-matrix ensemble is introduced which mimics the global structure inherent in the Hamiltonian matrices of autonomous, ergodic systems. Changes in its parameters induce a transition between a Poisson and a Wigner distribution for the level spacings, P(s). The intermediate distributions are uniquely determined by a single scaling variable. Semiclassical constraints force the ensemble to be in a regime with Wigner P(s) for systems with more than two freedoms.

By constructing action variables that are very nearly invariant in a region Ω of phase space, and by examining their residual variation, we set long-term bounds on any orbit starting in an open subregion of Ω. A new and generally applicable method for constructing the required high-precision invariants is applied. The technique is illustrated for transverse oscillations in a circular accelerator, a case with 21/2 degrees of freedom and strong nonlinearity.

We use a new numerical code to evolve collisionless gas spheroids in full general relativity. In all cases the spheroids collapse to singularities. When the spheroids are sufficiently compact, the singularities are hidden inside black holes. However, when the spheriods are sufficiently large, there are no apparent horizons. These results lend support to the hoop conjecture and appear to demonstrate that naked singularities can form in asymptotically flat spacetimes.

For an SU(N) gauge theory without dynamical fermions, at temperatures above the deconfining transition there are Z(N) degenerate vacua. The interface tension between distinct Z(N) vacua is computed in weak coupling by semiclassical techniques.

It is shown that a phenomenon analogous to Berry’s phase and Hannay’s angle occurs in dissipative systems. Adiabatic transport of a dissipative oscillatory system about a closed path in parameter space produces a geometric shift in the variable parametrizing the limit cycle. This quantity is written as the integral of a two-form over a surface bounded by the parameter-space loop.

Equivalence-principle experiments with ordinary matter probe the gravivector acceleration of antimatter in the same way as do direct measurements of antimatter in free fall and set stringent upper limits on the gravivector acceleration of antimatter predicted by certain quantum-gravity models.

Tests of the weak equivalence principle for antiprotons and positrons are inferred from the results of particle-antiparticle cyclotron-frequency comparisons. The potential improvements from future, higher-precision experiments are discussed.