Semiorthogonal decompositions of derived categories of equivariant coherent sheaves

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of bounded derived category of G-equivariant coherent sheaves on X into components, equivalent to derived categories of twisted representations of the group. If the group is finite or reductive over the algebraically closed field of zero characteristic, this gives a full exceptional collection in the derived equivariant category. We apply our results to particular varieties such as projective spaces, quadrics, Grassmanians and Del Pezzo surfaces.Comment: 28 pages, uses XY-pi

Photon losses depending on polarization mixedness

We introduce a quantum channel describing photon losses depending on the degree of polarization mixedness. This can be regarded as a model of quantum channel with correlated errors between discrete and continuous degrees of freedom. We consider classical information over a continuous alphabet encoded on weak coherent states as well as classical information over a discrete alphabet encoded on single photons using dual rail representation. In both cases we study the one-shot capacity of the channel and its behaviour in terms of correlation between losses and polarization mixedness

GRB Sky Distribution Puzzles

We analyze the randomness of the sky distribution of cosmic gamma-ray bursts. These events are associated with massive galaxies, spiral or elliptical, and therefore their positions should trace the large-scale structure, which, in turn, could show up in the sky distribution of fluctuations of the cosmic microwave background (CMB). We test this hypothesis by mosaic correlation mapping of the distributions of CMB peaks and burst positions, find the distribution of these two signals to be correlated, and interpret this correlation as a possible systematic effect.Comment: 12 pages, 16 figures, 1 tabl

Future of superheavy element research: Which nuclei could be synthesized within the next few years?

Low values of the fusion cross sections and very short half-lives of nuclei with Z$>$120 put obstacles in synthesis of new elements. Different nuclear reactions (fusion of stable and radioactive nuclei, multi-nucleon transfers and neutron capture), which could be used for the production of new isotopes of superheavy (SH) elements, are discussed in the paper. The gap of unknown SH nuclei, located between the isotopes which were produced earlier in the cold and hot fusion reactions, can be filled in fusion reactions of $^{48}$Ca with available lighter isotopes of Pu, Am, and Cm. Cross sections for the production of these nuclei are predicted to be rather large, and the corresponding experiments can be easily performed at existing facilities. For the first time, a narrow pathway is found to the middle of the island of stability owing to possible $\beta^+$-decay of SH isotopes which can be formed in ordinary fusion reactions of stable nuclei. Multi-nucleon transfer processes at near barrier collisions of heavy (and very heavy, U-like) ions are shown to be quite realistic reaction mechanism allowing us to produce new neutron enriched heavy nuclei located in the unexplored upper part of the nuclear map. Neutron capture reactions can be also used for the production of the long-living neutron rich SH nuclei. Strong neutron fluxes might be provided by pulsed nuclear reactors and by nuclear explosions in laboratory conditions and by supernova explosions in nature. All these possibilities are discussed in the paper.Comment: An Invited Plenary Talk given by Valeriy I. Zagrebaev at the 11th International Conference on Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1, 2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference Series (JPCS

Laser-stimulated Synthesis of Large Nanostructured Fractal Silver Aggregates

A Laser-stimulated synthesis of large silver nanoaggregates consisting of hundreds to thousands of nanoparticles is investigated. It is shown that the morphology of the synthesized nanostructures can be controlled with light and monitored via the evolution of the colloid absorption spectra. A solution method is demonstrated that enables production of a bulk amount of metal nanoaggregates, which are of paramount importance for subwavelength concentration and dramatic enhancement of the electromagnetically-induced processes at the nanoscale.Comment: 10 pages, 8 figures, 13 reference

Gyroscope deviation from geodesic motion: quasiresonant oscillations on a circular orbit

General relativistic spin-orbit interaction leads to the quasiresonant oscillation of the gyroscope mass center along the orbital normal. The beating amplitude does not include the speed of light and equals the ratio of the intrinsic momentum of the gyroscope to its orbital momentum. The modulation frequency equals the angular velocity of the geodetic precession that prevents the oscillation from resonance. The oscillation represents the precession of the gyroscope orbital momentum. Within an acceptable time the oscillation amplitude reaches the values that are amenable to being analyzed experimentally. Taking into account the source oblateness decreases the beating amplitude and increases the modulation frequency by the factor that is equal to the ratio of the quadrupole precession velocity to the geodetic precession velocity. The period of the quadrupole precession turns out to be a quite sufficient time to form a measurable amplitude of the oscillation.Comment: 5 pages, LaTeX2e, 1 eps figure, to appear in J. Exp. Theor. Phy

Observation of the onset of strong scattering on high frequency acoustic phonons in densified silica glass

The linewidth of longitudinal acoustic waves in densified silica glass is obtained by inelastic x-ray scattering. It increases with a high power alpha of the frequency up to a crossover where the waves experience strong scattering. We find that \alpha is at least 4, and probably larger. Resonance and hybridization of acoustic waves with the boson-peak modes seems to be a more likely explanation for these findings than Rayleigh scattering from disorder.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Letter

Detection of an intergalactic meteor particle with the 6-m telescope

On July 28, 2006 the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences recorded the spectrum of a faint meteor. We confidently identify the lines of FeI and MgI, OI, NI and molecular-nitrogen N_2 bands. The entry velocity of the meteor body into the Earth's atmosphere estimated from radial velocity is equal to 300 km/s. The body was several tens of a millimeter in size, like chondrules in carbon chondrites. The radiant of the meteor trajectory coincides with the sky position of the apex of the motion of the Solar system toward the centroid of the Local Group of galaxies. Observations of faint sporadic meteors with FAVOR TV CCD camera confirmed the radiant at a higher than 96% confidence level. We conclude that this meteor particle is likely to be of extragalactic origin. The following important questions remain open: (1) How metal-rich dust particles came to be in the extragalactic space? (2) Why are the sizes of extragalactic particles larger by two orders of magnitude (and their masses greater by six orders of magnitude) than common interstellar dust grains in our Galaxy? (3) If extragalactic dust surrounds galaxies in the form of dust (or gas-and-dust) aureoles, can such formations now be observed using other observational techniques (IR observations aboard Spitzer satellite, etc.)? (4) If inhomogeneous extragalactic dust medium with the parameters mentioned above actually exists, does it show up in the form of irregularities on the cosmic microwave background (WMAP etc.)?Comment: 9 pages, 6 EPS figure