Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.Comment: 4 pages no figur

Neutrino emission from a GRB afterglow shock during an inner supernova shock breakout

The observations of a nearby low-luminosity gamma-ray burst (GRB) 060218 associated with supernova SN 2006aj may imply an interesting astronomical picture where a supernova shock breakout locates behind a relativistic GRB jet. Based on this picture, we study neutrino emission for early afterglows of GRB 060218-like GRBs, where neutrinos are expected to be produced from photopion interactions in a GRB blast wave that propagates into a dense wind. Relativistic protons for the interactions are accelerated by an external shock, while target photons are basically provided by the incoming thermal emission from the shock breakout and its inverse-Compton scattered component. Because of a high estimated event rate of low-luminosity GRBs, we would have more opportunities to detect afterglow neutrinos from a single nearby GRB event of this type by IceCube. Such a possible detection could provide evidence for the picture described above.Comment: 6 pages, 2 figures, accepted for publication in MNRA

Diffusion of a liquid nanoparticle on a disordered substrate

We perform molecular dynamic simulations of liquid nanoparticles deposited on a disordered substrate. The motion of the nanoparticle is characterised by a 'stick and roll' diffusive process. Long simulation times ($\simeq \mu s$), analysis of mean square displacements and stacking time distribution functions demonstrate that the nanoparticle undergoes a normal diffusion in spite of long sticking times. We propose a phenomenological model for the size and temperature dependence of the diffusion coefficient in which the activation energy scales as $N^{1/3}$.Comment: Accepted for publication in Phys. Rev.

Strongly Correlated Two-Photon Transport in One-Dimensional Waveguide Coupled to A Two-Level System

We show that two-photon transport is strongly correlated in one-dimensional waveguide coupled to a two-level system. The exact S-matrix is constructed using a generalized Bethe-Ansatz technique. We show that the scattering eigenstates of this system include a two-photon bound state that passes through the two-level system as a composite single particle. Also, the two-level system can induce effective attractive or repulsive interactions in space for photons. This general procedure can be applied to the Anderson model as well.Comment: 12 pages. 3 figures. Accepted by Physical Review Letter

Air-snow exchange of HNO3 and NOy at Summit, Greenland

Ice core records of NO3− deposition to polar glaciers could provide unrivaled information on past photochemical status and N cycling dynamics of the troposphere, if the ice core records could be inverted to yield concentrations of reactive N oxides in the atmosphere at past times. Limited previous investigations at Summit, Greenland, have suggested that this inversion may be difficult, since the levels of HNO3 and aerosol-associated NO3− over the snow are very low in comparison with those of NO3− in the snow. In addition, it appears that some fraction of the NO3− in snow may be reemitted to the atmosphere after deposition. Here we report on extensive measurements of HNO3, including vertical gradients between 1.5 and 7 m above the snow, made during the summers of 1994 and 1995 at Summit. These HNO3 data are compared with NO3− concentrations in surface snow and the first measurements of the concentrations and fluxes of total reactive nitrogen oxides (Ny) on a polar glacier. Our results confirm that HNO3 concentrations are quite low (mean 0.5 nmol m−3) during the summer, while NO3− is the dominant ion in snow. Daytime peaks in HNO3− appear to be due at least partly to emissions from the snow, an assertion supported by gradients indicating a surface source for HNO3− on many days. Observed short-term increases in NO3− inventory in the snow can be too large to be readily attributed to deposition of HNO3− suggesting that deposition of one or more other N oxides must be considered. We found that the apparent fluxes of HNO3 and NOy were in opposite directions during about half the intervals when both were measured, with more cases of HNO3 leaving the snow, against an NOy flux into the snow, than the reverse. The concentrations of NOy are generally about 2 orders of magnitude greater than those of HNO3; hence deposition of only a small, non-HNO3, fraction of this pool could dominate NO3− in snow, if the depositing species converted to NO3−, either in the snowpack or upon melting for analysis

Concentrations and snow-atmosphere fluxes of reactive nitrogen at Summit, Greenland

Concentrations and fluxes of NOy (total reactive nitrogen), ozone concentrations and fluxes of sensible heat, water vapor, and momentum were measured from May 1 to July 20, 1995 at Summit, Greenland. Median NOy concentrations declined from 947 ppt in May to 444 ppt by July. NOy fluxes were observed into and out of the snow, but the magnitudes were usually below 1 μmol m−2 h−1 because of the low HNO3 concentration and weak turbulence over the snow surface. Some of the highest observed fluxes may be due to temporary storage by equilibrium sorption of peroxyacetylnitrate (PAN) or other organic nitrogen species on ice surfaces in the upper snowpack. Sublimation of snow at the surface or during blowing snow events is associated with efflux of NOy from the snowpack. Because the NOy fluxes during summer at Summit are bidirectional and small in magnitude, the net result of turbulent NOyexchange is insignificant compared to the 2 μmol m−2 d−1 mean input from fresh snow during the summer months. If the arctic NOy reservoir is predominantly PAN (or compounds with similar properties), thermal dissociation of this NOy is sufficient to support the observed flux of nitrate in fresh snow. Very low HNO3 concentrations in the surface layer (1% of total NOy) reflect the poor ventilation of the surface layer over the snowpack combined with the relatively rapid uptake of HNO3 by fog, falling snow, and direct deposition to the snowpack