A hypercyclic finite rank perturbation of a unitary operator

A unitary operator $V$ and a rank $2$ operator $R$ acting on a Hilbert space \H are constructed such that $V+R$ is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic.Comment: published in Mathematische Annale

Status of neutrino oscillations 2018: first hint for normal mass ordering and improved CP sensitivity

We present a new global fit of neutrino oscillation parameters within the simplest three-neutrino picture, including new data which appeared since our previous analysis~\cite{Forero:2014bxa}. In this update we include new long-baseline neutrino data involving the antineutrino channel in T2K, as well as new data in the neutrino channel, data from NO$\nu$A, as well as new reactor data, such as the Daya Bay 1230 days electron antineutrino disappearance spectrum data and the 1500 live days prompt spectrum from RENO, as well as new Double Chooz data. We also include atmospheric neutrino data from the IceCube DeepCore and ANTARES neutrino telescopes and from Super-Kamiokande. Finally, we also update our solar oscillation analysis by including the 2055-day day/night spectrum from the fourth phase of the Super-Kamiokande experiment. With the new data we find a preference for the atmospheric angle in the upper octant for both neutrino mass orderings, with maximal mixing allowed at $\Delta\chi^2 = 1.6 \, (3.2)$ for normal (inverted) ordering. We also obtain a strong preference for values of the CP phase $\delta$ in the range $[\pi,2\pi]$, excluding values close to $\pi/2$ at more than 4$\sigma$. More remarkably, our global analysis shows for the first time hints in favour of the normal mass ordering over the inverted one at more than 3$\sigma$. We discuss in detail the origin of the mass ordering, CP violation and octant sensitivities, analyzing the interplay among the different neutrino data samples.Comment: Updated neutrino oscillation analysis using the most recent results from T2K, NO$\nu$A, RENO and Super-Kamiokande. 17 pages, 8 figures, 1 tabl

Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics

The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain requirements of the theory. The discussion of such limitations arising from the so-called superselection rules is the main purpose of this paper. Some of their principal consequences are also discussed. The univalence, mass and particle number superselection rules of non-relativistic quantum mechanics are also derived using rather simple methods.Comment: 22 pages, no figure

Diffeomorphisms, Noether Charges and Canonical Formalism in 2D Dilaton Gravity

We carry out a parallel study of the covariant phase space and the conservation laws of local symmetries in two-dimensional dilaton gravity. Our analysis is based on the fact that the Lagrangian can be brought to a form that vanishes on-shell giving rise to a well-defined covariant potential for the symplectic current. We explicitly compute the symplectic structure and its potential and show that the requirement to be finite and independent of the Cauchy surface restricts the asymptotic symmetries.Comment: 14 pages, latex with psfig macro, one figur

A Post-AGB Star in the Small Magellanic Cloud Observed with the Spitzer Infrared Spectrograph

We have observed an evolved star with a rare combination of spectral features, MSX SMC 029, in the Small Magellanic Cloud (SMC) using the low-resolution modules of the Infrared Spectrograph on the Spitzer Space Telescope. A cool dust continuum dominates the spectrum of MSX SMC 029. The spectrum also shows both emission from polycyclic aromatic hydrocarbons (PAHs) and absorption at 13.7 micron from C2H2, a juxtaposition seen in only two other sources, AFGL 2688 and IRAS 13416-6243, both post-asymptotic giant branch (AGB) objects. As in these sources, the PAH spectrum has the unusual trait that the peak emission in the 7-9 micron complex lies beyond 8.0 micron. In addition, the 8.6 micron feature has an intensity as strong as the C-C modes which normally peak between 7.7 and 7.9 micron. The relative flux of the feature at 11.3 micron to that at 8 micron suggests that the PAHs in MSX SMC 029 either have a low ionization fraction or are largely unprocessed. The 13-16 micron wavelength region shows strong absorption features similar to those observed in the post-AGB objects AFGL 618 and SMP LMC 11. This broad absorption may arise from the same molecules which have been identified in those sources: C2H2, C4H2, HC3N, and C6H6. The similarities between MSX SMC 029, AFGL 2688, and AFGL 618 lead us to conclude that MSX SMC 029 has evolved off the AGB in only the past few hundred years, making it the third post-AGB object identified in the SMC.Comment: 4 figures, Fig. 4 color; to appear in the 20 November 2006 Astrophysical Journal Letter