On strongly stable normal operators in Krein spaces

For bounded normal operators in Krein spaces we give a necessary and sufficient condition for strong stability. The same result for unitary operators was obtained by M.G.Krein [1] (see also [2]). For selfadjoint operators we refer to the papers of P.Jonas, H.Langer [3] and H.Langer [4].     

Direct evidence for an intrinsic square vortex lattice in the overdoped high- T(c) superconductor La(1.83)Sr(0.17)CuO(4+delta)

We report here the first direct observations of a well ordered vortex lattice in the bulk of a La(2-x)Sr(x)CuO(4+delta) single crystal (slightly overdoped, x = 0.17). Our small angle neutron scattering investigation of the mixed phase reveals a crossover from triangular to square coordination with increasing magnetic field. The existence of an intrinsic square vortex lattice has never been observed in high-temperature superconductors and is indicative of the coupling of the vortex lattice to a source of anisotropy, such as those provided by a d-wave order parameter or the presence of stripes.     

Evaluating the influence of deposition conditions on solvation of reactive conducting polymers with neutron reflectivity

We describe in situ neutron reflectivity (NR) and RAIRS studies of the chemical modification of films of a polypyrrole-based conducting polymer derived from the pentafluorophenyl ester of poly(pyrrole-N-propanoic acid) (PFP) electrodeposited on electrode surfaces. We explore the role of the solvent in controlling the rate of reaction with solution-based nucleophiles (amines, which react with the ester to form amides). By varying the identity of the solvent (water vs acetonitrile) and the neutron contrast (deuteration), we find that both the identity of the solvent and its population within the film are paramount in determining chemical reactivity and electroactivity. IR signatures allow monitoring of the reaction of solution-based amine-tagged species such as amino-terminated poly(propylene glycol), ferrocene ethylamine, and lysine with film-based ester functionalities: the carbonyl bands show ester/amide interconversion and some hydrolysis to acid. Time-dependent spectral analysis shows marked variations in reaction rate with (i) (co-)polymer composition (replacement of some fluorinated ester-functionalized pyrrole with unfunctionalized pyrrole), (ii) the solvent to which the polymer film is exposed, and (iii) the rate of polymer deposition. NR data provide solvent profiles as a function of distance perpendicular to the interface, the variations of which provide an explanation for film reactivity patterns. Homopolymer films are relatively hydrophobic, thus hindering reaction with species present in water solutions. Incorporating pyrrole groups raises the solvent population-dramatically for water-thereby facilitating entry and reaction of aqueous-based lysine. Changing film deposition rate yields films with different absolute levels of solvent and reactivity patterns that are dependent on the size of the reactant molecules: more rapid deposition of polymer gives films with a more open structure leading to a higher solvent content and thence increased reactivity. These results, supported by XPS and AFM data, allow assembly of composition-structure-reactivity correlations, in which the controlling feature is film solvation.     

Flux-line lattice distortion in PrOs4Sb12

We report that the flux-line lattice in the cubic superconductor Pr(Os4Sb12 is strongly distorted from an ideal hexagonal lattice at very low temperatures in a small applied field. We attribute this to the presence of gap nodes in the superconducting state on at least some Fermi-surface sheets.     

Counterexamples to Additivity of Minimum Output p-Rényi Entropy for p Close to 0

Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Rényi entropies of channels are not generally additive for p > 1, we demonstrate here by a careful random selection argument that also at p = 0, and consequently for sufficiently small p, there exist counterexamples. An explicit construction of two channels from 4 to 3 dimensions is given, which have non-multiplicative minimum output rank; for this pair of channels, numerics strongly suggest that the p-Rényi entropy is non-additive for all p ≲ 0.11. We conjecture however that violations of additivity exist for all p < 1.     

μSR studies of the vortex lattice in high‐Tc and other superconductors

We review some of the assumptions made in the use of muon spin rotation in superconductors: i.e. that the muons are implanted at random positions in the flux lattice, remain static after implantation and do not appreciably affect the properties of the surrounding superconductor; also that the flux lines are straight and static, and that the observed muon rotation frequency spectrum reflects the microscopic distribution of field values. We shall show how evidence for and against the truth of these assumptions in particular cases may be obtained from the μSR results themselves or by comparison with other measurements, and how this in turn may lead to deeper understanding of flux line structure and motion in superconductors. This revised version was published online in August 2006 with corrections to the Cover Date.     

Probing the in-plane composition of thin polymer films with grazing-incidence small-angle neutron scattering and atomic force microscopy

The surface morphologies of confined, dewetted polymer films were investigated with atomic force microscopy (AFM) and grazing-incidence small-angle neutron scattering (GISANS). On examining homopolymer films of deuterated polystyrene (dPS) both techniques reveal the resulting droplet structure which is described by one most prominent in-plane length. Due to the contrast resulting from deuteration in the case of polymer blend films of dPS and poly(p-methyl styrene) GISANS is able to probe the in-plane composition of the dewetting structure. An additional phase separation process at different length scales gives rise to a sub- and superstructure which is not detectable by AFM. In addition, the influence of the wavelength used in the GISANS experiments on the structures observed is discussed. Received: 13 April 1999 Accepted in revised form: 29 June 1999     

Surface structure analysis of thin dewetted polymer blend films

The surface structure of thin polymer blend films of deuterated polystyrene (dPS) and polyparamethylstyrene (PpMS) after annealing above the glass transition temperature was investigated. With scanning force microscopy (SFM) the surface topography originated by a dewetting process is detected. The sample surface is covered with small droplets consisting of several polymer molecules. Utilizing grazing incidence small angle neutron scattering (GISANS) the topographical information as well as the in‐plane composition is probed. For thin confined blend films a substructure of the droplets resulting from an additional phase separation process at different length scales is detected.