We have measured the magnetization of the ferromagnetic second layer of pure ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ films adsorbed on Grafoil down to 0.075 mK. The zero-temperature magnetization is linear in second layer density (${\mathrm{\rho }}_2$) and rises by a factor of ∼7 with a 6% increase in ${\mathrm{\rho }}_2$ and less than a factor of 2 increase in the apparent exchange energy, indicating that the ferromagnetic phase coexists with a lower density phase. This is the first experiment to measure the low-temperature limiting magnetization of a 2D Heisenberg ferromagnet. Our data may also support Elser’s model of a registered antiferromagnetic phase at lower ${\mathrm{\rho }}_2$.

We report measurements of the nuclear magnetic susceptibility of the monolayer two-dimensional solid formed by ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ adsorbed on graphite plated with two atomic layers of HD. A low-density solid is observed, consistent with a √7 × √7 registered structure, which exhibits large antiferromagnetic exchange. A distinct cusp in the susceptibility is observed near 1 mK, suggestive of a magnetic phase transition. The evolution of this and other features with surface density is discussed.

It is shown that during the growth of ${\ln }_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As on GaAs, the strain-induced lattice distortion oscillates as a function of monolayer completion in both purely 2D and quasi-2D layer-by-layer growth regimes. This is explained by considering that nontetragonal elastic distortion occurs at the free edges of 2D monolayer islands. Numerical relaxation using a simplified model of interatomic forces gives the correct order of magnitude of the strain relaxation by this process.

Local-density-approximation calculations are used to show that the metal-metal distance along the chains controls the charge-density wave (CDW) in halogen-bridged transition-metal linear-chain compounds. The strength of the CDW can be understood in terms of a two-band Su-Schrieffer-Heeger model if a hard-core ion-ion repulsion potential is also added. We predict a second-order phase transition from an insulating to a semimetallic ground state and explain trends in dimerization, bond-length ratios, band gaps, and Raman breathing modes in terms of the metal-metal distance.

We report the observation of a strong temperature dependence of the Kondo resonance in the valence-band photoemission spectrum and of the 3d→4f white line in the x-ray absorption spectrum of ${\mathrm{YbAl}}_3$. The asymmetric Kondo resonance has a binding energy of ∼35 meV with a ∼50 meV width. The temperature dependence of the Yb 4f spectral features and valence are well reproduced by Anderson impurity model calculations with a Kondo temperature of ${\mathit{T}}_{\mathit{K}}$≊400 K, demonstrating that both spectroscopic and near ground state properties can be described within a unified theoretical framework.

The geometrical structures of linear chain systems are shown to be sensitively reflected on the optical spectrum of Frenkel and Wannier excitons. The effects of shape of the chain on Frenkel exciton absorption spectrum are represented by the geometrical factor describing the global chain structure and the line broadening due to the structure fluctuations. The corner with the stronger curvature induces the stronger attractive potential on the Wannier exciton so that the bound states are formed.

A new variational principle for the energy eigenvalues of a confined quantum system is presented. Whereas the exact wave function Ψ must vanish on the bounding surface of the region, the trial function ψ in this principle need not obey any specific boundary condition. Calculationally, the method is similar to the conventional variational method except that kinetic energy turns out to be a weighted average of -Fψ${\mathrm{\nabla }}^2$ψ dτ and F(∇ψ)⋅(∇ψ)dτ in the ratio 2:-1. Although the principle is not a definite (minimum) one, good results are obtained in several examples.

Transmission and absorption spectra of CuCl epitaxial films are studied. Many structures are observed over the ${\mathit{Z}}_3$ exciton region, corresponding to the quantization condition ${\mathit{K}}_{\mathit{n}}$=nπ/L with odd n (${\mathit{K}}_{\mathit{n}}$: wave number). The absence of the states with even n is interpreted in terms of the parity selection rule in the confined exciton system. The value of the oscillator strength for the nth exciton is found to be proportional to L/${\mathit{n}}^2$ for odd n and zero for even n, in accordance with theoretical expectation. As a polariton system, this belongs to a simple regime of long wavelength approximation.

We calculate the tunnel current between two parallel two-dimensional electron systems in a strong perpendicular magnetic field. We model the strongly correlated electron systems by Wigner crystals, and describe their low-energy dynamics in terms of magnetophonons. A tunneling electron shakes up magnetophonons, which results in a conductance peak that is displaced away from zero voltage and broadened compared with the case of no magnetic field. Our results are in very good quantitative agreement with recent experiments.

We report the first experimental observation of a magnetic-field-induced transition from an Anderson insulator to a quantum Hall conductor in a two-dimensional electron gas (2DEG) system. With sufficiently strong disorder, the 2DEG is an Anderson insulator with a divergent resistance at B=0. The 2DEG is transformed into a quantum Hall conductor with a vanishing resistance as T→0 and a quantized Hall resistance when the lowest Landau level is filled. The observations demonstrate the magnetic-field-induced delocalization and are consistent with a recently proposed global phase diagram.

The critical current ${\mathit{I}}_{\mathit{c}}$ for the breakdown of the quantum Hall effect is found to scale logarithmically with the channel width for all Landau levels. We interpret this experimental result as a manifestation of a logarithmic distribution of the Hall potential, and hence current, across the channel. A new perspective on the breakdown mechanism is obtained. In particular, inter-Landau-level transitions, previously thought to predict values of ${\mathit{I}}_{\mathit{c}}$ much too high, are actually shown to be in quantitative agreement with experiments interpreted in this manner.

We present an approach to steady-state mesoscopic transport based on the masimum entropy principle formulation of nonequilibrium statistical mechanics. Our approach is not limited to the linear response regime. This approach yields the quantization observed in the integer quantum Hall effect at large currents, which until now has been unexplained. We also predict new behaviors of nonlocal resistances at large currents in the presence of dirty contacts.

The self-energy and Gibbs free energy of rigid vortex lines are calculated for a uniaxially anisotropic London superconductor with a magnetic field applied at an angle φ from the c^ axis. When the correct elliptical core cutoff is used, the Gibbs free energy may have degenerate double minima as a function of vortex orientation. This indicates the coexistence of flux lines with different orientations at fields just above ${\mathit{H}}_{\mathit{c}1}$, applied at an angle φ≠0 from the c^ axis. The regime of parameters H, φ, ${\mathit{M}}_{\mathit{z}}$/M, and κ where this occurs is mapped out.

The Hall resistivity of vortices that lie parallel to the ${\mathrm{CuO}}_2$ layers in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ is shown to be negative, in contrast with the Hall effect observed with field perpendicular to the layers (H∥c). The Magnus force component along the current is opposite in sign for vortices that lie parallel and perpendicular to the layers. In an oblique field, the opposing forces strongly influence vortex motion. This finding provides new insights into negative Hall anomaly (observed with H∥c). We show that the anomaly arises from the negative sign of the interlayer segments produced by strong fluctuations about the direction of H.

An example of a breakdown of Hund’s third rule for a system with less than a half filled electronic shell is presented. By means of spin polarized electronic structure calculations including the relativistic effects and a Zeeman term, we demonstrate that in the field induced magnetic state of uranium 3 the spin and orbital moments are coupled parallel rather than antiparallel as stipulated by Hund’s third rule. This provides an explanation for the measured field induced magnetic form factor of uranium metal.

We have determined the magnetic phase diagram of Dy as a function of epitaxial strain ɛ, applied field H, and temperature T. $roman Y sub x roman Lu sub 1-x— alloys were employed as templates to clamp the films at selected strains. The separate roles of epitaxial clamping and strain are identified for the first time. There is a clearly defined transition as the strain is changed at low temperature from the clamped helical phase to the ferromagnetic phase. The transition is modeled by a linear coupling treatment of the magnetoelastic strains.

We report muon spin rotation-relaxation measurements of the heavy fermion superconductor ${\mathrm{UPt}}_3$. The broadening of the transverse field muon precession signal sets in approximately 60 mK below ${\mathit{T}}_{\mathit{c}}$, a temperature which corresponds to the lower superconducting transition. In zero applied magnetic field, we observe an increase in the internal magnetic field within the superconducting state which can be explained if the ‘‘lower superconducting phase’’ in the H-T phase diagram of ${\mathrm{UPt}}_3$ is characterized by broken time-reversal symmetry.

We have developed a model, which includes the effects of erosion both from precipitation and from avalanching of soil on steep slopes, to simulate the formation and evolution of river networks. The avalanches provide a mechanism for competition in growth between neighboring river basins. The changing morphology follows many of the characteristics of evolution set forth by Glock. We find that during evolution the model maintains the statistical characteristics measured in natural river systems.

An approximate wave number formula is derived for one-dimensional wave transmission in linear systems that are uniform on a large scale. It is a low-frequency approximation that coincides at zero frequency with equivalent medium theory. The formula is evaluated for various lattice media models for which exact calculations can also be made.

One of the crucial aspects of density perturbations that are produced by the standard inflation scenario is that they are Gaussian where seeds produced by topological defects tend to be non-Gaussian. The three-point correlation function of the temperature anisotropy of the cosmic microwave background radiation (CBR) provides a sensitive test of this aspect of the primordial density field. In this paper, this function is calculated in the general context of various allowed non-Gaussian models. It is shown that the Cosmic Background Explorer and the forthcoming South Pole and balloon CBR anisotropy data may be able to provide a crucial test of the Gaussian nature of the perturbations.