Passivity and Microlocal Spectrum Condition

In the setting of vector-valued quantum fields obeying a linear wave-equation in a globally hyperbolic, stationary spacetime, it is shown that the two-point functions of passive quantum states (mixtures of ground- or KMS-states) fulfill the microlocal spectrum condition (which in the case of the canonically quantized scalar field is equivalent to saying that the two-pnt function is of Hadamard form). The fields can be of bosonic or fermionic character. We also give an abstract version of this result by showing that passive states of a topological *-dynamical system have an asymptotic pair correlation spectrum of a specific type. Received: 9 February 2000 / Accepted: 7 June 2000     

VUV emission of Xe III levels excited by electron impact viaN 4,5 00 Auger transitions

Optical excitation functions were measured for Xenon emission lines. The Xe III 5s 5p ⁵ levels are excited in two different processes, by a direct two electron ejection and by a 4d ionization followed by an Auger decay. An emission line found at 1089.0 Å is excited by 4d ionization. This line is assigned to the Xe III transition 5s5p ^{5 1} P ⁰ —5s ⁰ 5p ^{6 1} S. The¹ S energy level amounts to 26.14 eV.     

Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras

Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic kinematical observables and represents it through operators on a suitable Hilbert space. In a second step, one implements the constraints. The main result of the paper concerns the representation theory of the kinematical algebra: We show that there is only one cyclic representation invariant under spatial diffeomorphisms.While this result is particularly important for loop quantum gravity, we are rather general: The precise definition of the abstract *-algebra of the basic kinematical observables we give could be used for any theory in which the configuration variable is a connection with a compact structure group. The variables are constructed from the holonomy map and from the fluxes of the momentum conjugate to the connection. The uniqueness result is relevant for any such theory invariant under spatial diffeomorphisms or being a part of a diffeomorphism invariant theory.     

Electrodynamics of Perfect Conductors

The most general electrodynamic equations of a perfect conducting state are obtained using a variational principle in a classical framework, following an approach by Pierre-Gilles de Gennes. London equations are derived as the time-independent case of these equations, corresponding to the magnetostatic minimal energy state of the perfect conducting system. For further confirmation, the same equations are also derived in the classical limit of the Coleman-Weinberg model, the most successful quantum macroscopic theory of superconductivity. The magnetic field expulsion is, therefore, a direct consequence of zero resistivity and not an exclusive property of superconductors.     

On Heilbronn’s Problem in Higher Dimension

Heilbronn conjectured that given arbitrary n points in the 2-dimensional unit square [0, 1]², there must be three points which form a triangle of area at most O(1/n²). This conjecture was disproved by a nonconstructive argument of Komlós, Pintz and Szemerédi [10] who showed that for every n there is a configuration of n points in the unit square [0, 1]² where all triangles have area at least (log n/n²). Considering a generalization of this problem to dimensions d3, Barequet [3] showed for every n the existence of n points in the d-dimensional unit cube [0, 1]^d such that the minimum volume of every simplex spanned by any (d+1) of these n points is at least (1/n^d). We improve on this lower bound by a logarithmic factor (log n).     

Similarity between condensed phase and gas phase chemistry: Fragmentation of peptides containing oxidized cysteine residues and its implications for proteomics

Amino acid residues containing thioethers are easily oxidized during protein purification, derivatization, and/or digestion. For instance, oxidation of methionine residues in proteins during SDS-PAGE is commonly observed. Under low energy collision induced dissociation this gives rise to a second series of fragment ion of lower abundance that are shifted by -64 Da when compared to the oxidized methionine-containing fragments. We report here that alkylated cysteine residues can be found in their oxidized form too, indicating that the oxidation of thioethers can occur during and following protein digestion and not only during SDS-PAGE or reduction and alkylation. Collision induced dissociation experiments on the singly- and multiply-charged species reveals that these peptides preferentially undergo elimination reactions that forms a dehydroalanine from the oxidized, alkylated cysteine residue. This contrasts to the less abundant elimination reaction of peptides containing oxidized methionines which cannot form an alpha,beta-unsaturated compound, but parallels the condensed phased chemistry of sulfoxides. The masses of both precursor and product ions are shifted such that these peptides cannot be identified in database searches with current algorithms. Incorporation of this fragmentation pattern is important for the isotope-coded affinity tag approach since this method is based on peptides containing cysteine residues.     

Coloring arcs of convex sets

In this note we consider Ramsey-type problems on graphs whose vertices are represented by the vertices of a convex polygon in the Euclidean plane. The edges of the graph are represented by the segments between the points of the polygon. The edges are arbitrarily colored by a fixed number of colors and the problem is to decide whether there exist monochromatic subgraphs of certain types satisfying some geometric conditions. We will give lower and upper bounds for these geometric Ramsey numbers for certain paths and cycles and also some exact values. It turns out that the particular type of the embedding is crucial for the growth rate of the corresponding geometric Ramsey numbers. In particular, the Ramsey numbers for crossing 4-cycles and t colors grow quadratically in t, while for convex 4-cycles they grow at least exponentially.