A compactness theorem for complete Ricci shrinkers

We prove precompactness in an orbifold Cheeger-Gromov sense of complete gradient Ricci shrinkers with a lower bound on their entropy and a local integral Riemann bound. We do not need any pointwise curvature assumptions, volume or diameter bounds. In dimension four, under a technical assumption, we can replace the local integral Riemann bound by an upper bound for the Euler characteristic. The proof relies on a Gauss-Bonnet with cutoff argument.Comment: 28 pages, final version, to appear in GAF

Multiphoton Coincidence Spectroscopy

We extend the analysis of photon coincidence spectroscopy beyond bichromatic excitation and two-photon coincidence detection to include multichromatic excitation and multiphoton coincidence detection. Trichromatic excitation and three-photon coincidence spectroscopy are studied in detail, and we identify an observable signature of a triple resonance in an atom-cavity system.Comment: 6 page, REVTeXs, 6 Postscript figures. The abstract appeared in the Proceedings of ACOLS9

Ehrenfest time in the weak dynamical localization

The quantum kicked rotor (QKR) is known to exhibit dynamical localization in the space of its angular momentum. The present paper is devoted to the systematic first--principal (without a regularizer) diagrammatic calculations of the weak--localization corrections for QKR. Our particular emphasis is on the Ehrenfest time regime -- the phenomena characteristic for the classical--to--quantum crossover of classically chaotic systems.Comment: 27 pages, 9 figure

Improved rain rate and drop size retrievals from airborne Doppler radar

Satellite remote sensing of rain is important for quantifying the hydrological cycle, atmospheric energy budget, and cloud and precipitation processes; however, radar retrievals of rain rate are sensitive to assumptions about the raindrop size distribution. The upcoming EarthCARE satellite will feature a 94 GHz Doppler radar alongside lidar and radiometer instruments, presenting opportunities for enhanced retrievals of the raindrop size distribution. We demonstrate the capability to retrieve rain rate as a function of drop size and drop number concentration from airborne 94 GHz Doppler radar measurements using CAPTIVATE, the variational retrieval algorithm developed for EarthCARE. For a range of rain regimes observed during the Tropical Composition, Cloud and Climate Coupling field campaign, we explore the contributions of mean Doppler velocity and path-integrated attenuation (PIA) measurements to the retrieval of rain rate, and the retrievals are evaluated against independent measurements from an independent 9.6 GHz Doppler radar. The retrieved drop number concentrations vary over 5 orders of magnitude between very light rain from melting ice and warm rain from liquid clouds. In light rain conditions mean Doppler velocity facilitates estimates of rain rate without PIA, suggesting the possibility of EarthCARE rain rate estimates over land; in moderate warm rain, drop number concentration can be retrieved without mean Doppler velocity, with possible applications to CloudSat

Effect of oxygen plasma etching on graphene studied with Raman spectroscopy and electronic transport

We report a study of graphene and graphene field effect devices after exposure to a series of short pulses of oxygen plasma. We present data from Raman spectroscopy, back-gated field-effect and magneto-transport measurements. The intensity ratio between Raman "D" and "G" peaks, I(D)/I(G) (commonly used to characterize disorder in graphene) is observed to increase approximately linearly with the number (N(e)) of plasma etching pulses initially, but then decreases at higher Ne. We also discuss implications of our data for extracting graphene crystalline domain sizes from I(D)/I(G). At the highest Ne measured, the "2D" peak is found to be nearly suppressed while the "D" peak is still prominent. Electronic transport measurements in plasma-etched graphene show an up-shifting of the Dirac point, indicating hole doping. We also characterize mobility, quantum Hall states, weak localization and various scattering lengths in a moderately etched sample. Our findings are valuable for understanding the effects of plasma etching on graphene and the physics of disordered graphene through artificially generated defects.Comment: 10 pages, 5 figure

Charged and spin-excitation gaps in half-filled strongly correlated electron systems: A rigorous result

By exploiting the particle-hole symmetries of the Hubbard model, the periodic Anderson model and the Kondo lattice model at half-filling and applying a generalized version of Lieb's spin-reflection positivity method, we show that the charged gaps of these models are always larger than their spin excitation gaps. This theorem confirms the previous results derived by either the variational approach or the density renormalization group approach.Comment: 20 pages, no figur

Worldsheet boundary conditions in Poisson-Lie T-duality

We apply canonical Poisson-Lie T-duality transformations to bosonic open string worldsheet boundary conditions, showing that the form of these conditions is invariant at the classical level, and therefore they are compatible with Poisson-Lie T-duality. In particular the conditions for conformal invariance are automatically preserved, rendering also the dual model conformal. The boundary conditions are defined in terms of a gluing matrix which encodes the properties of D-branes, and we derive the duality map for this matrix. We demonstrate explicitly the implications of this map for D-branes in two non-Abelian Drinfel'd doubles.Comment: 20 pages, Latex; v2: typos and wording corrected, references added; v3: three-dimensional example added, reference added, discussion clarified, published versio