A vanishing theorem for operators in Fock space

We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that rotation invariance implies the absence of terms which either create or annihilate only a single particle. We outline an application of this result in an operator theoretic renormalization analysis of Hamilton operators, which occur in non-relativistic qed.Comment: 14 page

On the Smooth Feshbach-Schur Map

A new variant of the Feshbach map, called smooth Feshbach map, has been introduced recently by Bach et al., in connection with the renormalization analysis of non-relativistic quantum electrodynamics. We analyze and clarify its algebraic and analytic properties, and we generalize it to non-selfadjoint partition operators $\chi$ and \chib.Comment: 8 page

The heat kernel expansion for the electromagnetic field in a cavity

We derive the first six coefficients of the heat kernel expansion for the electromagnetic field in a cavity by relating it to the expansion for the Laplace operator acting on forms. As an application we verify that the electromagnetic Casimir energy is finite.Comment: 12 page

Four dimensional observations of clouds from geosynchronous orbit using stereo display and measurement techniques on an interactive information processing system

Simultaneous Geosynchronous Operational Environmental Satellite (GOES) 1 km resolution visible image pairs can provide quantitative three dimensional measurements of clouds. These data have great potential for severe storms research and as a basic parameter measurement source for other areas of meteorology (e.g. climate). These stereo cloud height measurements are not subject to the errors and ambiguities caused by unknown cloud emissivity and temperature profiles that are associated with infrared techniques. This effort describes the display and measurement of stereo data using digital processing techniques

Uniqueness of the ground state in the Feshbach renormalization analysis

In the operator theoretic renormalization analysis introduced by Bach, Froehlich, and Sigal we prove uniqueness of the ground state.Comment: 10 page

Measurements of a Quantum Dot with an Impedance-Matching On-Chip LC Resonator at GHz Frequencies

We report the realization of a bonded-bridge on-chip superconducting coil and its use in impedance-matching a highly ohmic quantum dot (QD) to a $\rm{3~GHz}$ measurement setup. The coil, modeled as a lumped-element $LC$ resonator, is more compact and has a wider bandwidth than resonators based on coplanar transmission lines (e.g. $\lambda/4$ impedance transformers and stub tuners) at potentially better signal-to-noise ratios. In particular for measurements of radiation emitted by the device, such as shot noise, the 50$\times$ larger bandwidth reduces the time to acquire the spectral density. The resonance frequency, close to 3.25 GHz, is three times higher than that of the one previously reported wire-bonded coil. As a proof of principle, we fabricated an $LC$ circuit that achieves impedance-matching to a $\rm{\sim 15~k\Omega}$ load and validate it with a load defined by a carbon nanotube QD of which we measure the shot noise in the Coulomb blockade regime.Comment: 7 pages, 6 figure

Absolutely continuous spectrum for a random potential on a tree with strong transverse correlations and large weighted loops

We consider random Schr\"odinger operators on tree graphs and prove absolutely continuous spectrum at small disorder for two models. The first model is the usual binary tree with certain strongly correlated random potentials. These potentials are of interest since for complete correlation they exhibit localization at all disorders. In the second model we change the tree graph by adding all possible edges to the graph inside each sphere, with weights proportional to the number of points in the sphere.Comment: 25 pages, 4 figure

Shot noise of a quantum dot measured with GHz stub impedance matching

The demand for a fast high-frequency read-out of high impedance devices, such as quantum dots, necessitates impedance matching. Here we use a resonant impedance matching circuit (a stub tuner) realized by on-chip superconducting transmission lines to measure the electronic shot noise of a carbon nanotube quantum dot at a frequency close to 3 GHz in an efficient way. As compared to wide-band detection without impedance matching, the signal to noise ratio can be enhanced by as much as a factor of 800 for a device with an impedance of 100 k$\Omega$. The advantage of the stub resonator concept is the ease with which the response of the circuit can be predicted, designed and fabricated. We further demonstrate that all relevant matching circuit parameters can reliably be deduced from power reflectance measurements and then used to predict the power transmission function from the device through the circuit. The shot noise of the carbon nanotube quantum dot in the Coulomb blockade regime shows an oscillating suppression below the Schottky value of $2eI$, as well an enhancement in specific regions.Comment: 6 pages, 4 figures, supplementar