A Two Dimensional Fermi Liquid. Part 2: Convergence

Using results established in other papers in our series, we prove the existence of the infinite volume, temperature zero, thermodynamic Greens functions of a two dimensional, weakly coupled fermion gas with an asymmetric Fermi curve and short range interactions. This is done by showing that our sequence of renormalization group maps converges.Research supported in part by the Natural Sciences and Engineering Research Council of Canada and the Forschunginstitut für Mathematik, ETH Zürich.     

Topologische Typen reeller kubischer Flächen

Zusammenfassung 4.11. Die topologischen Typen reeller kubischer Flächen werden durch (4.4)-(4.6) und Liste 4, die äquisingulären Isotopieklassen hierdurch und durch (4.11) vollständig klassifiziert. Für Flächen mit nur rationalen Doppelpunkten bestimmt man die Zahl der reellen Geraden nach (2.8), die Topologie aus (3.3) und (3.6).     

Asymmetric fermi surfaces for magnetic schrödinger operators

We consider Schrödinger operators with periodic magnetic field having zero flux through a fundamental cell of the period lattice. We show that, for a generic small magnetic field and a generic small Fermi energy, the corresponding Fermi surface is convex and not invariant under inversion in any point.     

Measurement of the surface excitation parameter of Kapton,polyethylene (PE), polymethyl methacrylate (PMMA), polystyrene (PS) and polytetrafluoroethylene (PTFE)

Reflection electron energy loss spectra (REELS) were measured for five insulating organic compounds: Kapton, polyethylene (PE), poly(methyl methacrylate) (PMMA), polystyrene (PS) and polytetrafluoroethylene (PTFE), as well as for Ni and Si, in the energy range between 200 and 1600 eV. The average number of surface excitations for a single surface crossing were determined from the experimental data and were found to be considerably smaller than for earlier studied materials, which mainly consisted of elemental metals [Surf. Sci. 486(2001)L461]. The surface excitation parameter, a material parameter used to quantify the relative intensity of surface losses in (photo)electron spectroscopy, was extracted from the data and compared with values found in the literature. The results indicate that surface excitations only have a minor influence on quantification of XPS spectra of polymers. On the other hand, a correction for surface excitations turns out to be essential for measurements of the electron inelastic mean free path of polymers when a metal is used as reference material.     

Proton spin-lattice relaxation time of hydrated gelatin

In this work we obtain a model to describe the relaxativity of water molecules, adsorbed on macromolecules, as a function of the concentration. Excellent agreement with experimental data was obtained. The model allows us to estimate the adsorption energy of water molecules on different sites of the macromolecules.     

Electron inelastic mean free path (IMFP) values of Kapton,polyethylene (PE), polymethylmethacrylate (PMMA), polystyrene (PS) and polytetrafluoroethylene (PTFE) measured with elastic peak electron spectroscopy (EPES)

Elastic peak electron spectroscopy (EPES) was employed to measure the inelastic mean free path (IMFP) for energies between 500 and 1600 eV for five insulating organic compounds: Kapton, polyethylene (PE), poly(methyl methacrylate) (PMMA), polystyrene (PS) and polytetrafluoroethylene (PTFE). A Ni and a Si sample were used as reference materials to avoid measurement of the elastic reflection coefficient in absolute units. Correction of experimental elastic peak intensities for surface excitations was performed which turned out to be essential. The results are compared with recent evaluations of optical constants to yield the IMFP in the literature giving satisfactory agreement, with deviations generally below 20%. Investigation of the kinematics in an electron reflection experiment shows that the dispersion coefficient used in REELS data analysis cannot be identified with the true plasmon dispersion.     

The Temporal Ultraviolet Limit for Complex Bosonic Many-body Models

We consider the partition function for a many-body model consisting of a weakly coupled gas of bosons at any temperature T > 0 and any chemical potential μ, but with both infrared and ultraviolet cutoffs imposed in both temporal and spatial directions. We take the limit as the ultraviolet cutoff in the temporal direction is removed and develop a representation for the limit that, hopefully, provides a suitable starting point for controlling the limit as the infrared cutoffs are removed.     

The Temperature Zero Limit

We prove that, for a broad class of many-fermion models, the amplitudes of renormalized Feynman diagrams converge to their temperature zero values in the limit as the temperature tends to zero.