A Symplectic Slice Theorem

We provide a model for an open invariant neighborhood of any orbit in a symplectic manifold endowed with a canonical proper symmetry. Our results generalize the constructions of Marle and Guillemin and Sternberg for canonical symmetries that have an associated momentum map. In these papers the momentum map played a crucial role in the construction of the tubular model. The present work shows that in the construction of the tubular model, the so-called Chu map, can be used instead, which exists for any canonical action, unlike the momentum map. Hamilton's equations for any invariant Hamiltonian function take on a particularly simple form in these tubular variables. As an application we will find situations, that we will call tubewise Hamiltonian, in which the existence of a standard momentum map in invariant neighborhoods is guaranteed.     

Confining surface state electrons in less than two dimensions: A spectroscopic study

We observe the partial confinement of the twodimensional electron gas of ans-p-like surface state by the regular step distribution of several vicinal Cu(111) surfaces. The spatial distribution of the surface state is visualized by scanning tunneling microscopy. Local tunneling spectroscopy reveals a shift of the maximum of the density of states of the surface state towards the Fermi level, which correlates with the size of the terraces. The average shift is also measured by angle-resolved photoemission and found to be consistent with a one-dimensional Kronig-Penney model.     

Constraints on the time scale of nuclear breakup from thermal hard-photon emission

Measured hard-photon multiplicities from second-chance nucleon-nucleon collisions are used in combination with a kinetic thermal model to estimate the breakup times of excited nuclear systems produced in nucleus-nucleus reactions at intermediate energies. The obtained nuclear breakup time for the ¹²⁹Xe + ^natSn reaction at 50 A MeV is Δτ ≈ 100-300 fm/c for all reaction centralities. The lifetime of the radiating sources produced in seven other different heavy-ion reactions studied by the TAPS experiment is consistent with Δτ ≈ 100 fm/c, such relatively long thermal photon emission times do not seemingly support the interpretation of nuclear breakup as due to a fast spinodal process for the heavy nuclear systems studied.     

Schottky barrier formation in the low metal coverage limit

A theoretical discussion of the state of the art in the field of Schottky barrier formation is presented. The thin metal layer limit is analyzed for Al and In on GaAs(110), and the adsorption sites are determined as a function of the metal coverage. Intrinsic and extrinsic charge neutrality levels are also discussed for the In-case.     

Congruence classes of Frenet curves in complex quadrics

Congruent classes of Frenet curves of order 2 in the complex quadric are studied, obtaining that each congruence class is a level set of a family of certain smooth functions, that are generalizations of isoparametric functions on the unit sphere in the tangent space of the complex quadric.     

Effect of substrate’s nature on the growth of HgBCCO thin films

The synthesis of HgBCCO films by spray pyrolysis on single crystals is investigated. It is shown that in conditions where the precursor is expected to give Hg-1223, Hg-1212 grows on LaAlO₃ (0 0 1) while Hg-1223 grows on MgO (0 0 1). The samples are analysed by X-ray pole figures, SEM and critical current measurements. Both samples were superconducting but the sample on MgO had a negligible I_c while 17 A was measured on LAO at 77 K (sf). These differences are analysed in terms of texture and microstructure and some conclusions concerning the growth are drawn. On LAO, the nucleation is probably epitaxial and the anisotropy of the growth inhibits the transformation into Hg-1223 while some interfacial contribution expected to occur on MgO makes this transformation easier.     

Determination of the second order susceptibility tensor in banana-shaped liquid crystals

Optical second harmonic generation (SHG) measurements have been carried out on the B2 phases of three liquid crystal materials composed of conventional banana-shaped molecules (P-10-O-PIMB, P-8-O-PIMB and P-8-PIMB). Quantitative values of the second order susceptibilities d_ij have been deduced from SHG measurements at oblique incidences on polydomain racemic samples under an electric field. The d_ij coefficients are in the range 1-10 pm V^-1.     

Singular Reduction of Poisson Manifolds

The conditions under which it is possible to reduce a Poisson manifold via a regular foliation have been completely characterized by Marsden and Ratiu. In this Letter we show that this characterization can be generalized in a natural way to the singular case and, as a corollary, we obtain that when the singular distribution is given by the tangent spaces to the orbits created by a Hamiltonian Lie group action, one reproduces the Universal Reduction Procedure of Arms, Cushman, and Gotay.     

Resonance and non-resonance in a problem of boundedness

This paper studies the existence of bounded solutions of a forced non-linear differential equation of arbitrary order. Necessary and sufficient conditions for the existence of such solutions are obtained. These results are inspired by classical results on the periodic problem, both in the resonant and non-resonant cases.

     

Real Hypersurfaces in Quaternionic Space Forms Satyisfying Axioms of Planes

A Riemannian manifold satisfies the axiom of 2-planes if at each point, there are suficiently many totally geodesic surfaces passing through that point. Real hypersurfaces in quaternionic space forms admit nice families of tangent planes, namely, totally real, half-quaternionic and quaternionic. Several definitions of axiom of planes arise naturally when we consider such families of tangent planes. We are able to classify real hypersurfaces in quaternionic space forms satisfying these definitions.