Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED

We consider a class of translation invariant models of non-relativistic QED with net charge. Under certain natural assumptions we prove that ground states do not exist in the Fock space.     

Qualitative und quantitative Spektralanalyse

Ohne Zusammenfassung     

Convergent expansions in non-relativistic qed: Analyticity of the ground state

We consider the ground state of an atom in the framework of non-relativistic qed. We show that the ground state as well as the ground state energy are analytic functions of the coupling constant which couples to the vector potential, under the assumption that the atomic Hamiltonian has a non-degenerate ground state. Moreover, we show that the corresponding expansion coefficients are precisely the coefficients of the associated Raleigh-Schrödinger series. As a corollary we obtain that in a scaling limit where the ultraviolet cutoff is of the order of the Rydberg energy the ground state and the ground state energy have convergent power series expansions in the fine structure constant α, with α dependent coefficients which are finite for α?0.     

Organosoluble copper clusters as precatalysts for carbon-heteroelement bond-forming reactions: microwave and conventional heating

The coupling of aryl iodides with alcohols under mild conditions has been explored using self-assembled octanuclear copper clusters as catalysts. Reactions involving tetrahydrofurfuryl alcohol were typically complete in 4-8 h at 110 degrees C using an oil bath or 1-3 h with microwave heating. High yields of alkyl aryl ethers were obtained with catalyst loadings as low as 0.4 mol % cluster.     

Subpicosecond electro-optic measurement of relativistic electron pulses

Time-resolved measurements of the transverse electric field associated with relativistic electron bunches are presented. Using an ultrafast electro-optic sensor close to the electron beam, the longitudinal profile of the electric field was measured with subpicosecond time resolution and without time-reversal ambiguity. Results are shown for two cases: inside the vacuum beam line in the presence of wake fields, and in air behind a beryllium window, effectively probing the near-field transition radiation. Especially in the latter case, reconstruction of the longitudinal electron bunch shape is straightforward.     

Anderson Localization at Band Edges for Random Magnetic Fields

We consider a magnetic Schrödinger operator in two dimensions. The magnetic field is given as the sum of a large and constant magnetic field and a random magnetic field. Moreover, we allow for an additional deterministic potential as well as a magnetic field which are both periodic. We show that the spectrum of this operator is contained in broadened bands around the Landau levels and that the edges of these bands consist of pure point spectrum with exponentially decaying eigenfunctions. The proof is based on a recent Wegner estimate obtained in Erd?s and Hasler (Commun. Math. Phys., preprint, arXiv:1012.5185) and a multiscale analysis.