We study the effect of fluctuations in the vicinity of an Eckhaus instability. Fluctuations smear out the stability limit into a region in which fluctuations and nonlinearities dominate the decay of unstable states. We also find an effective stability boundary that depends on the intensity of fluctuations. A numerical solution of the stochastic Swift-Hohenberg equation in one dimension is used to test these predictions and to study pattern selection when the initial unstable state lies within the fluctuation dominated region. The nonlinear relaxation is shown to exhibit a scaling form.

The hydrodynamic Maxwell equations of continuous media, valid for large amplitudes and small frequencies, are derived. As any hydrodynamic theory, these equations are universal, nonlinear, and irreversible. Consequences for dielectric liquids, ferrofluids, superconductors, and nematic liquid crystals are briefly outlined.

We have measured the autocorrelation of the fluorescence of single aromatic molecules in polyethylene at T≊2 K. Assuming intensity fluctuations to be caused by frequency jumps when two-level systems (TLS’s) change states, we show that individual TLS’s can be probed, allowing direct measurement of some of their properties, with minimal recourse to theory and no assumptions about the distribution of TLS parameters. Besides providing a simple confirmation of the tunneling theory of TLS’s, this new method, by eliminating statistical uncertainties, proves that while some TLS’s may be stable for several hours others are modified by transitions of their neighbors. Tunneling times of individual TLS’s are measured directly, as are their temperature dependences, revealing three types of TLS-phonon coupling, of which one is new.

The kinetics of photoinduced defect formation in high-purity silicas has been studied by femtosecond transient absorption spectroscopy in the visible and ultraviolet. Band edge two-photon excitation produces singlet excitons which decay in 0.25 ps into defects with the absorption spectra of nonbridging oxygen hole centers (≡Si-O⋅) and silicon E’ centers (≡Si⋅). We identify these defect pairs with the self-trapped triplet exciton and the 0.25 ps decay with the motion of the photoexcited oxygen atom. Similar results were obtained with both crystalline and amorphous silica samples.

A two-dimensional model of steady-state crack propagation, in which the stress acting on the fracture surface includes a dissipative term, exhibits a dissipation-dependent effective threshold for fracture. The crack creeps very slowly at external stresses just above the Griffith threshold, and makes an abrupt transition to propagation at roughly the Rayleigh wave speed at higher stresses. When heating due to dissipation is taken into account, the model may exhibit a maximum in the crack propagation speed as a function of applied stress.

We relate a cycle model for the collapse of branched polymers without holes (in d=2) to the problem of self-avoiding rings with an area fugacity, studied in the context of vesicles. This relation together with arguments which show that the collapse transition of branched polymers (with holes) is described by the tricritical-zero-state Potts model allows a determination of all critical exponents at this collapse point; ν=1/2, φ=2/3, τ=2, in agreement with numerical results. We also comment on the universality of this result.

The ordering processes in a binary liquid mixture confined in a Vycor type of pore and at temperatures near the transition temperature of the pure system ${\mathit{T}}_{\mathit{c}}$ are studied using a kinetic Ising model and the method of Monte Carlo simulations. The results for dynamics show quite clear signatures of the pore width but no notable difference between T>${\mathit{T}}_{\mathit{c}}$ and T<${\mathit{T}}_{\mathit{c}}$. In the results for statics, the small angle part of the structure factor increases rapidly as T approaches ${\mathit{T}}_{\mathit{c}}$ in the one-phase region. This suggests the onset of ordering but the fluctuation of energy shows no sign of criticality.

The sticking coefficient of atomic hydrogen at ${\mathit{T}}_{\mathit{G}}$=1815 K on a Cu(110) surface has been determined to be 18%. In addition to the buildup of a chemisorption layer the absorption of atomic H into subsurface sites is observed. The subsurface sites are thermally less stable than the chemisorption sites. Model calculations for the phononic energy transfer and estimates for the parallel momentum transfer as well as for electron-hole pair excitation indicate that the first two mechanisms dominate the accommodation process.

The analogy between temporally periodic phases of noisy extended driven systems and smooth interfaces in growth models is used to derive results for both problems, viz., stable, temporally quasiperiodic phases with long-range spatial order can in fact occur for noisy, short-range, isotropic rules in dimensions d>2. For d=2, temporally quasiperiodic phases have algebraic, rather than long-range order, and occur only in anisotropic systems. Anisotropic rules can also produce smooth, commensurately growing interfaces with d≥2 dimensions for generic parameter values.

A new method is described for recording the motion of a single adsorbed atom or molecule in real time, with an ultimate achievable resolution of ${10}^{\mathrm{-}14}$ s. The time dependence of electron field emission through an atom adsorbed on a metal tip is measured by focusing the electrons into a beam, which is swept across a detector screen. Similtaneous temporal and one-dimensional spatial resolution of the dynamics is possible. The motion of single Cs atoms between sites on atomically characterized W(111) tips is observed at 2 ps resolution.

We report real space views of the homoepitaxial growth of Fe on Fe(001) whiskers observed by scanning tunneling microscopy. A measure of the surface diffusion of the Fe atoms is obtained over the temperature range of 20–250 °C. The effect of the diffusion kinetics is observed in the surface morphology as a decrease in the interface width with temperature. Measurements of reflection-high-energy-electron diffraction during growth allow a comparison of real and reciprocal space techniques.

We present evidence for a new class of magnetic materials, namely two-dimensional, ordered surface alloys. Structure and composition of the prototype Cu(100)c(2×2)Mn were determined by a quantitative low energy electron diffraction analysis, which shows an unusually large buckling in the surface alloy layer. By comparing our results with ab initio total energy calculations we identified the magnetism of Mn as the driving force for the buckling and moreover for the stability of the alloy. Possible additional members of this new class of materials are suggested.

We have detected a reentrant phase transition within well-separated bimolecular layers of diacylphosphates. The disorder-order-disorder transitions of the hydrocarbon chains can be accounted for on the basis of the electrostatic energy between bilayers and the elastic compressibility energy within bilayers.

The stick-slip process in a spring-block model is considered in terms of cellular automaton. The probability of the slip size is exactly calculated. It is shown analytically that there is a scaling relation D(Δ)∝${\mathrm{\Delta }}^{\xi }$ exp(-Δ/${\mathrm{\Delta }}_0$) between the slip size Δ and its probability D(Δ) with a universal exponent ξ=-3/2, while the value of ${\mathrm{\Delta }}_0$ depends on the details of the system.

We present a method for obtaining the band-structure energy and density of states for large, sparse Hamiltonian matrices as occur in electronic structure problems. The computation scales linearly with the dimension of the matrix. We use a statistical approach using random vectors along with the principle of maximum entropy to obtain highly accurate estimates for integrals over the density of states. We offer several tests of the approach using tight-binding Hamiltonians and apply the scheme to large icosahedral fullerenes with 720 and 2160 atoms.

The problem of nonlinear resonant tunneling through an Anderson impurity is investigated in this Letter using a combined approach of Keldysh formalism and 1/N expansion at zero temperature. We find that to order 1/N, the Kondo resonance is not destroyed by any finite potential difference between external probes. The resulting one-electron Green’s functions and differential conductance are presented. The effect of finite temperature is discussed.

We study the effects of electron-electron interactions on the ground state of integral quantum Hall edge states in the Hartree-Fock approximation. We find that, in the absence of Zeeman splitting, the outermost edge state undergoes a spontaneous transition between spin-unpolarized and spin-polarized ground states at a sample-dependent critical value of the bulk filling ${\nu }_{\mathrm{bulk}}^{\mathit{c}}$∼4. The abrupt appearance, in the spin-polarized state, of a sizable (about a magnetic length) separation between edge states of opposite spin should make the transition accessible to a range of magnetotransport experiments.

A microscopic picture of electron-electron pair scattering in single mode quantum wires is introduced which includes electron spin. A new source of excess noise for hot carriers is presented. We show that zero magnetic field spin splitting in quantum wires can lead to a dramatic spin-subband dependence of electron-electron scattering, including the possibility of strong suppression. As a consequence extremely long electron coherence lengths and new spin-related phenomena are predicted. Since electron bands in III-V semiconductor quantum wires are in general spin split in zero applied magnetic field, these new transport effects are of general importance.

We investigate the supercurrent drag effect due to the Coulomb interaction between two spatially separated superconductors. The supercurrent for a given wire/layer is shown to depend on the superfluid velocity in the other wire/layer. The magnitude of this effect is calculated. This supercurrent drag effect should be observable in experiments.

The magnetic susceptibility of single-crystal ${\mathrm{CuGeO}}_3$, a linear ${\mathrm{Cu}}^{2+}$ (spin-1/2) chain compound, was measured. The susceptibilities in all the directions rapidly drop to small constant values with decreasing temperature below a phase transition temperature near 14 K. The magnetic-field dependence of the transition temperature quantitatively agrees with both theoretical predictions and experimental results for organic spin-Peierls systems. This Letter is the first report of an unambiguous determination of the existence of the spin-Peierls transition in an inorganic compound.