By analytically studying random walk generating functions on a wide class of disordered branched structures we obtain the exact values of their spectral dimensions, which turn out to depend only on the branching degree of these structures. The results show that the spectral dimension is a universal quantity largely disorder independent provided that some boundedness conditions are satisfied; its values are also always less than 2, so that these branched structures are all recursive graphs.

We consider the weakly first-order phase transition between the isotropic and ordered phases of nematics in terms of the behavior of topological line defects. Specifically, we present analytical and Monte Carlo results for a new coarse-grained theory of nematics which incorporates the inversion symmetry of nematics as a local gauge invariance. Increasing the disclination core energy makes the nematic-isotorpic transition more weakly first order, and eventually splits it into two continuous transitions which involve the unbinding and condensation of defects, respectively. We find a novel isotropic phase with toplogical order.

We derive a general expression for the defect chemical potential of amphoteric silicon dangling bond states in amorphous silicon. We show that a single expression is valid, irrespective of the charge state of the dangling bond. We apply this result in a defect pool model for the formation of dangling bonds by the breaking of weak silicon-silicon bonds, with and without hydrogen motion. We calculate the resulting energy dependent density of states.

A novel transition has been investigated within the stripe phase of a monomolecular organic (‘‘Langmuir’’) film. This transition mediates the transformation of an isotropic stripe liquid into an anisotropic state exhibiting twofold rotation symmetry. Stripe undulation and thickness fluctuations persist in the ordered state which also displays a high density of quenched topological defects. Stripe ‘‘melting’’ appears to coincide with the occurrence of thermal fluctuations which mediate the spontaneous breaking and rejoining of stripes, thereby altering the pattern connectivity.

The smoothing kinetics of a rough surface have been studied using time-resolved high resolution low energy electron diffraction. By depositing ∼100 monolayers of Cu on Cu(100) near room temperature, a rough surface results with an initial morphology of multilevel, roughly circular terraces separated by monatomic steps. Upon annealing at elevated temperatures, two growth regimes are distinguished for the average terrace width L(t) versus time t: The earlier one varies as ${\mathit{t}}^{1/3}$, consistent with kinetics driven by the line tension of curved step edges, and the later one follows ${\mathit{t}}^{1/5}$. Also, in the ${\mathit{t}}^{1/3}$ growth regime, scaling is observed.

Using a combination of perturbation theory and quantum Monte Carlo, we elucidate the behavior of the single-particle Green’s function and the local spin-spin correlation function near the Mott transition in the infinite dimensional Hubbard model at half filling. The model has three fixed points: the Fermi liquid phase qualitatively described by the Brinkman-Rice picture, the insulating phase resembling Hubbard’s solution, and an unstable Mott point which connects the two.

The symmetric periodic Anderson model is studied in the limit of infinite spatial dimensions within an essentially exact quantum Monte Carlo method. The single-particle spectral function develops a gap Δ, and the neutron structure factor also develops a gap ≊2Δ. Depending upon the ratio of Δ to other energy scales, there is a transition to an antiferromagnetic state. In the paramagnetic state, both the f-orbital specific heat and ferromagnetic susceptibility display rough scaling with T/Δ; for T>Δ they are heavy-fermion-like while for T<Δ they are insulatorlike.

The motion of the classical polaron in a dc electric field is investigated numerically. In a limited range of parameters (field and coupling constant) a stable stationary asymptotic drift of the electron with a constant velocity is shown to exist. Outside this range of parameters the electron is asymptotically accelerated by the field, like a free charge. This model is an illustration of the dissipative behavior of a classical mechanical subsystem coupled to a mechanical system with an infinite number of degrees of freedom (here the classical LO- phonon field).

Spin-orbit interaction produces persistent spin and mass currents in a ring via the Aharonov-Casher effect. An experiment in the ${}_{}{}^3{}_{}{}^{}\mathit{A}_1^{}{}_{}{}^{}$ phase in which this effect leads to the excitation of mass and spin supercurrent is proposed.

A nonthermal, quasimonoenergetic exciton distribution is observed in time-resolved photoluminescence measurements up to 150 ps after excitation if a quantum wire is excited resonantly and with low excitation density of ${10}^2$ ${\mathrm{cm}}^{\mathrm{-}1}$. The scattering rate increases only slowly with increasing exciton density. This is the first evidence in optical experiments for strongly reduced exciton-exciton scattering rates in one-dimensional systems.

We calculate the quasiparticle electronic structure of a Al/GaAs(110) Schottky barrier as a function of distance from the interface, using the GW self-energy operator. The GaAs band gap is significantly narrowed near the metal, although the classical picture of image-potential narrowing is subject to large quantum corrections. The nature of these corrections is explored further using model calculations.

U${\mathrm{Pt}}_3$ appears to have a tetracritical point in the $H-T$ plane for all orientations $\hat{\mathrm{H}}$ of H. Such a point can exist only if the Ginzburg-Landau (GL) "Hamiltonian" has a conserved quantity $Q$. It is shown that the model of a two-component vector order parameter admits a $Q$ for H∥c, but has no tetracritical point. Hence, accidentally nearly degenerate order parameters are examined, particularly the model where one behaves as an $A$ and the other as a $B$ representation of $D_{6h}$. This model can yield a tetracritical point for all $\hat{\mathrm{H}}$. Its physical properties are calculated and GL parameters are fitted to experiment.

The c-axis resistivity of ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{\mathit{x}}$ single crystals shows a magnetic-field-dependent peak below the zero-field ${\mathit{T}}_{\mathit{c}}$. We find good agreement with the temperature and field dependence of the peak, by modeling the c-axis conduction as a series stack of Josephson tunnel junctions. For intermediate values of the Josephson coupling, we predict such a peak and verify it by measurements on discreet, thin-film Josephson junctions. The exaggerated effects in ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{\mathit{x}}$ result from its unusually large energy gap and fluctuations.

A critical analysis of experimental data reveals a universal relationship between ${\mathit{T}}_{\mathit{c}}$/${\mathit{T}}_{\mathit{c},\mathrm{m}\mathrm{a}\mathrm{x}}$ and hole content among the p-type high-${\mathit{T}}_{\mathit{c}}$ cuprate superconductors. Each individual compound is characterized by the value of its maximum ${\mathit{T}}_{\mathit{c}}$, ${\mathit{T}}_{\mathit{c},\mathrm{m}\mathrm{a}\mathrm{x}}$ while the variation of ${\mathit{T}}_{\mathit{c}}$/${\mathit{T}}_{\mathit{c},\mathrm{m}\mathrm{a}\mathrm{x}}$ with the hole content is independent of the compound considered. The universal curve is characterized by a plateau, rather than a parabold, with sharp bends at both sides. The ${\mathit{T}}_{\mathit{c}}$ versus hole content curve has a close relation to hole contents determined by ordered arrangements of holes in the two-dimensional ${\mathrm{CuO}}_2$ layer.

Normal transport properties and their size effect of ${\mathrm{PrBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ are studied using planar-type junction specimens. The transport properties of ${\mathrm{PrBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ are in accordance with a variable-range-hopping mechanism. The localized wave function for this conduction has a decay length of 8.5 nm, and the hopping distance is 96 nm at 2 K. The conductance properties of junctions with a length of a few times the hopping distance show a size effect. A Coulomb correlation gap is observed at temperatures lower than 4 K, and the minimum conductance at the Coulomb gap depends weakly on temperature and magnetic field.

We consider the isotropic XY model in a transverse magnetic field in one dimension. One can alternatively call this model the Heisenberg XXO antiferromagnet. We solve the problem of the evaluation of asymptotics of temperature correlations and explain the physical meaning of our result. To do this we represent the quantum correlation function as a tau function of a completely integrable differential equation. This is the well-known Ablowitz-Ladik lattice nonlinear Schrödinger differential equation.

Dark solitons of magnetostatic surface waves in magnetic films have been observed for the first time. The experiments were conducted at 5.19 GHz on 7.2 μm single-crystal yttrium iron garnet films. The dark solitons were excited by 15 ns wide ‘‘off’’ pulses in a high power cw microwave signal applied to the film. The characteristic soliton narrowing effect in the output pulses was observed as the input power was increased above the 0.5–1 W threshold levels. The shape of the ‘‘dark’’ pulse agrees with the ‖tanh‖ functional dependence predicted from theory. Direct measurements of the carrier signal showed a phase shift of close to 180° at the center of the dark soliton, also in agreement with theory.

A significant change in the oscillatory exchange coupling corresponding to the contraction of the Fermi surface in spacer layers is found in the Co/${\mathrm{Cu}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ni}}_{\mathit{x}}$(110) system. The oscillation period becomes longer with increasing Ni concentration: from 12 Å (0% Ni) to 23 Å (35% Ni). This change manifests that the long-period oscillation across Cu-Ni(110) arises from the singularity at the neck orbit of the spacer Fermi surface. The neck diameters estimated from the measured periods are in good agreement with those of bulk Cu-Ni Fermi surfaces.

We present Raman spectra of natural Ge, ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}$, and ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}_{0.5}^{}{}_{}{}^{}$ ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}_{0.5}^{}{}_{}{}^{}$ in the TO phonon region. The spectrum of the isotopically pure ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}$ shows only the Raman-active phonon with k→=0 (Γ), as required by k→ conservation. The two isotopically disordered crystals, however, show spectra at the low energy side of the Γ phonon which correspond to isotopic disorder-induced scattering by TO phonons with k→≠0 (band modes). The line shape and the strength of the observed spectra agree with calculations based on the coherent potential approximation and an ansatz for the Raman polarizability. The novel ${}_{}{}^{70}{}_{}{}^{}\mathrm{Ge}_{0.5}^{}{}_{}{}^{}$ ${}_{}{}^{76}{}_{}{}^{}\mathrm{Ge}_{0.5}^{}{}_{}{}^{}$ thus proves to be an ideal crystal to investigate mass disorder effects.

Using inverse photoemission with variable photon energy (17≤hν≤25 eV), the existence of a surface shift of the unoccupied 4f state in La metal, analogous to the well-known surface core-level shift in photoemission from occupied levels, is demonstrated. In the outermost surface layer, the 4${\mathit{f}}^1$ electron-addition state shifts by ${\mathrm{\delta }}_{\mathit{s}}$=-0.65±0.10 eV relative to the bulk, i.e., towards the Fermi level, in quantitative agreement with the prediction of a thermochemical model. This observation opens new opportunities in the study of surface phenomena in rare-earth materials by inverse photoemission.