Generic continuous spectrum for multi-dimensional quasi periodic Schr\"odinger operators with rough potentials

We study the multi-dimensional operator $(H_x u)_n=\sum_{|m-n|=1}u_{m}+f(T^n(x))u_n$, where $T$ is the shift of the torus \T^d. When $d=2$, we show the spectrum of $H_x$ is almost surely purely continuous for a.e. $\alpha$ and generic continuous potentials. When $d\geq 3$, the same result holds for frequencies under an explicit arithmetic criterion. We also show that general multi-dimensional operators with measurable potentials do not have eigenvalue for generic $\alpha$

2-Resonant fullerenes

A fullerene graph $F$ is a planar cubic graph with exactly 12 pentagonal faces and other hexagonal faces. A set $\mathcal{H}$ of disjoint hexagons of $F$ is called a resonant pattern (or sextet pattern) if $F$ has a perfect matching $M$ such that every hexagon in $\mathcal{H}$ is $M$-alternating. $F$ is said to be $k$-resonant if any $i$ ($0\leq i\leq k$) disjoint hexagons of $F$ form a resonant pattern. It was known that each fullerene graph is 1-resonant and all 3-resonant fullerenes are only the nine graphs. In this paper, we show that the fullerene graphs which do not contain the subgraph $L$ or $R$ as illustrated in Fig. 1 are 2-resonant except for the specific eleven graphs. This result implies that each IPR fullerene is 2-resonant.Comment: 34 pages, 25 figure

Detection of diffuse gamma-ray emission near the young massive cluster NGC 3603

We report the Fermi Large Area Telescope's detection of extended gamma-ray emission towards the direction of the young massive star cluster NGC 3603. The emission shows a hard spectrum with a photon index of 2.3 from 1 GeV to 250 GeV. The large size and high luminosity of this structure make it unlikely a pulsar wind nebular. On the other hand the spatial correlation with the ionised gas indicate a hadronic origin. The total cosmic ray (CR) protons energy are estimated to be of the order $10^{50} ~\rm erg$ assuming the gamma-ray are produced in the interaction of CRs with ambient gas . The environment and spectral features show significant similarity with the Cygnus cocoon. It reveals that the young star clusters may be a gamma-ray source population and they can potentially accelerate a significant fraction of the Galactic cosmic rays.Comment: 6 pages, 5 figures, submitted to A&

Interpretation of the excess of antiparticles within a modified paradigm of galactic cosmic rays

We argue that the anomalously high fluxes of positrons and antiprotons found in cosmic rays (CR) can be satisfactorily explained by introducing two additional elements to the current "standard" paradigm of Galactic CRs. First, we propose that the antiparticles are effectively produced in interactions of primary CRs with the surrounding gas not only in the interstellar medium (ISM) but also inside the accelerators. Secondly, we postulate the existence of two source populations injecting CRs into the ISM with different, (1) soft (close to $FI \propto E^{-2.3}$) and (2) hard ($FII \propto E^{-1.8}$ or harder), energy distributions. Assuming that CRs in the 2nd population of accelerators accumulate "grammage" of the order of $1 \ \rm g/cm^2$ before their leakage into ISM, we can explain the energy distributions and absolute fluxes of both positrons and antiprotons, as well as the fluxes of secondary nuclei of the (Li,Be,B) group. The superposition of contributions of two source populations also explains the reported hardening of the spectra of CR protons and nuclei above 200 GV. The 2nd source population accelerating CRs with a rate at the level below 10 percent of the power of the 1st source population, can be responsible for the highest energy protons and nuclei of Galactic CRs up to the "knee" around $10^{15} \ \rm eV$.Comment: accepted for publication in PR

On the photofragmentation of SF2+_2^+: Experimental evidence for a predissociation channel

We report on the first observation of the photofragmentation dynamics of SF$_2^+$. With the aid of state-of-the-art ab initio calculations on the low-lying excited cationic states of SF$_2^+$ performed by Lee et al. [J. Chem. Phys. 125, 104304 (2006)], a predissociation channel of SF$_2^+$ is evidenced by means of resonance-enhanced multilphoton ionization spectroscopy. This work represents a second experimental investigation on the low-lying excited cationic states of SF$_2^+$. [The first one is the He I photoelectron spectrum of SF$_2^+$ reported by de Leeuw et al. three decades ago, see Chem. Phys. 34, 287 (1978).]Comment: 7 pages, 3 figures, submitted to JCP as a Not