The driving force for surface reconstruction is shown to be given by the (usually nonzero) difference between the surface energy and stress, leading to a ground state characterized by an isotropic stress tensor with vanishing shear components. The analytic results, illustrated by atomistic simulations of the missing row reconstruction of the Au(110) surface, permit likely reconstructions to be identified based on the stress and energy in the unreconstructed surface.

The stabilities of GaAs(001) As-rich surfaces have been determined for the first time by state-of-the-art total-energy calculations. The As-rich surface is found to be inherently rough; it cannot exist thermodynamically in a complete As monolayer structure, but in a missing-As-dimer or a two-As-layered structure. The steepening relaxation of the As-dimer block is essential to the stability of the As-rich surface. The peculiar interaction between As dimers as obtained, which may play an important role in the growth mechanism. The validity of the electron counting model is discussed.

A previously unnoticed group structure for the transfer matrices of mesoscopic systems is identified. From the invariant measure for this group and a maximum entropy ansatz we derive the Laguerre ensemble of random matrices. A comparison with the Hofstadter model shows that the Laguerre ensemble provides a quantitative description of scattering in mesoscopic systems under applied magnetic fields.

We study the effect of correlations on the Aharonov-Bohm effect in small one-dimensional rings. We use the Luttinger and Hubbard models to describe electrons in the ring with two contacts on opposite sites and a magnetic field passing through the hole of the circuit. We show that correlations change the fundamental periodicity of the transmittance as a function of the magnetic flux. We interpret this new effect as a consequence of the charge and spin separation in the one-dimensional conductors.

Motivated by the observation of fractional quantum Hall effect (FQHE) at filling factor ν=2+1/2 by Willett et al., we investigate the nature of the spin-singlet FQHE at ν=1/2. We show that a simple trial wave function for the ν=1/2 state, proposed earlier by one of us, is the exact nondegenerate ground state of a hard-core interaction model, and provide numerical evidence that it is adiabatically connected to the true Coulomb ground state.

We report Hall effect measurements of the localized two-dimensional electron system at low Landau level filling factors ν, including the same regime previously identified as a pinned Wigner crystal. We find that the Hall resistivity is universally given by the classical, free-electron gas value of h/ν${\mathit{e}}^2$ to within 5% even when the diverging diagonal resistivity reaches ∼100h/ν${\mathit{e}}^2$. This implies that both Hall and diagonal conductivities approach zero in the localized regime.

Subwavelength focusing of far-infrared light (λ=392 μm) is introduced to resolve spatially the photoconductivity of a two-dimensional electron gas. An increased cyclotron resonance amplitude is observed at one of the sample edges which proves that it is at the edge where states with nonequilibrium population can exist.

Two-photon photoemission spectroscopy was employed for an investigation of the image states on Pd(111) with various coverages of Ag. Image state, from areas with different thicknesses of the Ag layer can be observed simultaneously. This proves the applicability of the concept of a local work function. The decay length of the wave function of the image state on Ag(111) into the metal was determined experimentally to be 7.6±1.2 Å, and the probability to find the electron in the metal is estimated as 10%.

I present a new method of determining the anisotropy of the gap function in layered high-${\mathit{T}}_{\mathit{c}}$ superconductors. Careful inelastic neutron scattering measurements at low temperature of the phonon dispersion curves in the (100) and (210) directions in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ would determine whether the gap is predominantly s wave or d wave. I also propose an experiment to determine the gap at each point on a quasi-two-dimensional Fermi surface.

We have studied numerically the dynamics of a directed elastic string in a two-dimensional array of quenched random impurities. The string is driven by a constant transverse force and thermal fluctuations are neglected. There is a transition from pinned to unpinned behavior at a critical value ${\mathit{F}}_{\mathit{T}}$ of the driving force. At the transition the average string velocity scales with the driving force. The scaling is equally well described by a power law ${\mathit{v}}_{\mathit{d}}$∼(F-${\mathit{F}}_{\mathit{T}}$${)}^{\mathrm{\zeta }}$, with ζ=0.24±0.1, or by a logarithm, ${\mathit{v}}_{\mathit{d}}$∼1/ln(F-${\mathit{F}}_{\mathit{T}}$). The divergence of the velocity-velocity correlation length at threshold is characterized by an exponent ν=1.05±0.1.

We have measured the energy dissipation and pinning of the flux line lattice (FLL) of vibrating high-${\mathit{T}}_{\mathit{c}}$ superconducting crystals as a function of temperature, magnetic field, and angle θ between field and ${\mathrm{CuO}}_2$ planes. For ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ and oxygen-deficient (${\mathrm{Y}}_{0.94}$${\mathrm{Gd}}_{0.06}$)${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.83}$ superconductors and for θ∼0° we observed an anomalous depinning of the FLL at ∼30 K. This anomaly cannot be explained by a thermally activated depinning mechanism and suggests the existence of a phase transition of the FLL.

We report linear and nonlinear electrical transport in perpendicular magnetic fields of very thin amorphous ${\mathrm{Mo}}_{79}$${\mathrm{Ge}}_{21}$ superconducting films. At low fields, we demonstrate the existence of a barrier to vortex motion away from the sample edges. In regimes where the vortex motion is not substantially affected by the sample edges, we observe manifestly collective activated behavior. We relate the field dependence of the observed activation energies to possible mobile configurations of vortices.

We present results obtained (by exact diagonalization) for the problem of two t-J planes with an interlayer coupling ${\mathit{t}}_{\mathrm{\perp }}$. Our results for small hole concentrations show that in-plane superconducting correlations are enhanced by ${\mathit{t}}_{\mathrm{\perp }}$. When the constraint on double occupancy in the t-J model is relaxed, the enhancement disappears. These results illustrate the interlayer tunneling mechanism for superconductivity.

Transmission electorn microscopy and electron diffraction studies reveal the presence of a macroscopic incommensurate structural modulation in the heavy fermion superconductor ${\mathrm{UPt}}_3$. Two sharp superconducting transitions in the heat capacity are found to exist only in homogeneous samples with a well-developed modulation. There is evidence for a strong coupling between the structural modulation and superconductivity; this may determine the structure of the rich H-T-p phase diagram.

Supercomputing correlations in the two dimensional t-J model at zero temperature are evaluated using numerical techniques. At the fermionic density 〈n〉∼1/2, strong signals of ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ superconductivity were observed in the ground state. These conclusions are based on a study of static pairing correlations, the Meissner effect, and flux quantization as indicators of superconductivity. A tentative phase diagram of the two dimensional t-j model is presented.

The non-Fermi-liquid fixed point of the overscreened Kondo problem is studied in the limit of a large number of conduction electron channels, k≫1, using perturbation theory in 1/k. By expanding the beta function and self-energy to sub-leading-order in 1/k, we examine the scaling, thermodynamics, and dynamic response functions in detail. Our results compliment and extend previous work based on conformal field theory. We present the dynamical spin susceptibility for the first time and show that the impurity spin is marginally quenched, with an inelastic linewidth of order T.

We studied the very slow nuclear spin-lattice relaxation of solid ${}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}$ as a function of temperature and magnetic field using laser-polarized nuclei. Relaxation times in excess of 500 h were measured. We present evidence for a new relaxation mechanism which results from a Raman spin-phonon scattering process involving the spin-rotation interaction. We also establish the existence of cross relaxation between ${}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}$ and the other magnetic isotope ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$ and demonstrate that laser-polarized ${}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}$ can be used to cross polarize other nuclei that are present in the lattice.

Sum rules are derived for the circular dichroic response of a core line (CMXD). They relate the intensity of the CMXD signal to the ground-state expectation value of the magnetic field operators (orbital, spin, and magnetic dipole) of the valence electrons. The results obtained are discussed and tested for transition metals and rare earths.

The possible amount of information transfer between any source and any user via a quantum system is bounded through the quantum entropy function. In contrast to the classical case, this shows that infinite information transfer implies infinite entropy. The entropy bound is also applied to obtain the ultimate quantum information transmission capacity of the free electromagnetic field under a power and a bandwidth constraint.

Some new symmetry algebras are found for the vacuum Einstein equations. Among them there exists an infinite-dimensional algebra representing the symmetries analogous to the generalized symmetries of the integrable nonlinear partial differential equations.