Dimer decimation and intricately nested localized-ballistic phases of a kicked Harper model

A new decimation scheme is introduced to study localization transitions in tight binding models with long range interaction. Within this scheme, the lattice models are mapped to a vectorized dimer where an asymptotic dissociation of the dimer is shown to correspond to the vanishing of the transmission coefficient through the system. When applied to the kicked Harper model, the method unveils an intricately nested extended and localized phases in two-dimensional parameter space. In addition to computing transport characteristics with extremely high precision, the renormalization tools also provide a new method to compute quasienergy spectrum.     

Quantized orbits and resonant transport

A tight-binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of "quantized" bands of orbits. New bands appear when renormalized Harper parameters exceed integer multiples of pi/2. Orbits with frequencies commensurate with the kicking frequency are shown to correlate with classical accelerator modes in the original kicked problem. Signatures of this superdiffusive and, in our view, resonant transport are seen in both classical and quantum behavior. An important feature of our analysis is the emergence of a natural scaling relating classical and quantum couplings which is necessary for establishing correspondence.     

On the origins of sudden adhesion loss at a critical relative humidity: examination of bulk and interfacial contributions

The origins for abrupt adhesion loss at a critical relative humidity (RH) for polymeric adhesives bonded to inorganic surfaces have been explored using a model poly(methyl methacrylate) (PMMA) film on glass. The interfacial and bulk water concentrations within the polymer film as a function of D 2O partial pressure were quantified using neutron reflectivity. Adhesion strength of these PMMA/SiO 2 interfaces under the same conditions was quantified using a shaft loaded blister test. A drop in adhesion strength was observed at a critical RH, and at this same RH, a discontinuity in the bulk moisture concentration occurred. The moisture concentration near the interface was higher than that in the bulk PMMA, and at the critical RH, the breadth of the interfacial water concentration distribution as a function of distance from the SiO 2/PMMA interface increased dramatically. We propose a mechanism for loss of adhesion at a critical RH based upon the interplay between bulk swelling induced stress and weakening of the interfacial bond by moisture accumulation at the PMMA/SiO 2 interface.     

Influence of the electric field on a bio-mimetic film supported on a gold electrode

A model biological membrane was formed by fusion of mixed cholesterol and DMPC (dimyristoylphosphatidylcholine) phospholipid vesicles onto a gold-coated quartz support. The gold surface was charged and the influence of the charge at the solid support on the structure and integrity of the phospholipid bilayer was investigated using the specular reflection of neutrons and electrochemical measurements. When the surface charge density is close to zero, the lipid vesicles fuse directly on the surface to form a bilayer with a small number of defects and hence low water content. When the support's surface is negatively charged the film swells and incorporates water due to the field driven poration of the membrane. When the charge density is more negative then -8 microC cm(-2) the bilayer is detached from the metal surface. However, it remains in close proximity to the metal electrode, suspended on a thin cushion of water. The film thicknesses, calculated from neutron reflectivity, have allowed us to determine the tilt angle of the lipid molecules as a function of the support's charge density. The lipid molecules are tilted 55 degrees from the surface normal at zero charge density but become significantly more perpendicular (30 degrees tilt angle) at charge densities more negative than -8 microC cm(-2). The tilt angle measurements are in very good agreement with previous IR studies. This paper describes the highlights of a more in-depth study which is fully described in [1].     

Direct measurement of the counterion distribution within swollen polyelectrolyte films

The depth profile of the counterion concentration within thin polyelectrolyte films was measured in situ using contrast variant specular neutron reflectivity to characterize the initial swelling stage of the film dissolution. We find substantial counterion depletion near the substrate and enrichment near the periphery of the film extending into the solution. These observations challenge our understanding of the charge distribution in polyelectrolyte films and are important for understanding film dissolution in medical and technological applications.     

Molecular view of the isothermal transformation of a stable glass to a liquid

We have used neutron reflectivity to measure translational motion on the nanometer length scale in exceptionally stable glasses of tris(naphthylbenzene). These glasses are prepared by vapor deposition onto a substrate held somewhat below the glass transition temperature (T(g) = 342 K). When the most stable samples are annealed at 345 K, no translational motion is observed on the 12 nm length scale for over 10,000 s and full mixing requires more than 60,000 s. For comparison, the equilibrium supercooled liquid mixes in 1000 s at this temperature and on this length scale. These measurements provide insight into the mechanism by which a stable glass transforms into a liquid. "Melting" of the stable glass appears to occur by the growth of liquid regions into the surrounding glassy matrix, perhaps by a surface-initiated growth process. At 345 K, translational motion in the stable glass is at least 100 times slower than motion in the supercooled liquid.     

Enrichment of deuterium oxide at hydrophilic interfaces in aqueous solutions

The structure of water at aqueous interfaces is of the utmost importance in biology, chemistry, and geology. We use neutron reflectivity and quartz crystal microbalance to probe an interface between hydrophilic quartz and bulk liquid solutions of H2O/D2O mixtures. We find that near the interface the neutron scattering length density is larger than in the bulk solution and there is an excess adsorbed mass. We interpret this as showing that there is a region adjacent to the quartz that is enriched in D2O and extends 5-10 nm into the solution. This suggests caution when interpreting results where D2O is substituted for H2O in aqueous interfacial chemistry.     

Fractal characteristics of critical and localized states in incommensurate quantum systems

Incommensurate quantum systems with two competing periodicities exhibit metallic (with Bloch-type extended wave functions), insulating (with exponentially localized wave functions) as well ascritical (with fractal wave functions) phases. An exact renormalization method, which takes into account the inherent incommensurability, is used to obtain the phase diagram of various quantum models for the two-dimensional electron gas and for quantum spin chains in a magnetic field. In this approach, the scaling properties of the fractal eigenstates are characterized by a fixed point or a strange invariant set of the renormalization flow. One of our novel results is the existence of self-similar fluctuations in the localized states once the exponentially decaying envelope is factorized out. In almost all cases under investigation here, the universality classes can be broadly classified as those of the nearest-neighbor square or triangular lattices.     

Chaos in a damped and driven toda system

We describe our numerical studies of chaos for a damped and driven single Toda particle and in a Toda lattice. Comparisons are made with chaos in other classes of nonlinear potentials.