Abelian Landau-Pomeranchuk-Migdal effects

It is shown that the high-energy expansion of the scattering amplitude calculated from Feynman diagrams factorizes in such a way that it can be reduced to the eikonalized form up to the terms of inverse power in energy in accordance with results obtained by solving the Klein-Gordon equation. Therefore the two approaches when applied to the suppression of the emission of soft photons by fast charged particles in dense matter should give rise to the same results. A particular limit of thin targets is briefly discussed.Comment: 14 pages, LATEX, 1 Fig. ps, submitted to Mod. Phys. Lett.

Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals

We investigate the non-ergodic properties of blinking nano-crystals using a stochastic approach. We calculate the distribution functions of the time averaged intensity correlation function and show that these distributions are not delta peaked on the ensemble average correlation function values; instead they are W or U shaped. Beyond blinking nano-crystals our results describe non-ergodicity in systems stochastically modeled using the Levy walk framework for anomalous diffusion, for example certain types of chaotic dynamics, currents in ion-channel, and single spin dynamics to name a few.Comment: 5 pages, 3 figure

Fractional Quantum Mechanics

A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the L\'evy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the L\'evy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and statistical mechanics have been developed via our fractional path integral approach. A fractional generalization of the Schr\"odinger equation has been found. A relationship between the energy and the momentum of the nonrelativistic quantum-mechanical particle has been established. The equation for the fractional plane wave function has been obtained. We have derived a free particle quantum-mechanical kernel using Fox's H function. A fractional generalization of the Heisenberg uncertainty relation has been established. Fractional statistical mechanics has been developed via the path integral approach. A fractional generalization of the motion equation for the density matrix has been found. The density matrix of a free particle has been expressed in terms of the Fox's H function. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum and statistical mechanics.Comment: 27 page

Psi-Series Solution of Fractional Ginzburg-Landau Equation

One-dimensional Ginzburg-Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg-Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order $alpha$ with polynomial nonlinearity of order $s$ have the noninteger power-like behavior of order $\alpha/(1-s)$ near the singularity.Comment: LaTeX, 19 pages, 2 figure

Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches

Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived. Fractional equations of motion are obtained by fractional variation of Lagrangian and Hamiltonian that have only integer derivatives.Comment: 21 pages, LaTe

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived. All terms of order 1 microarcsecond are taken into account, parametrized, and classified in accordance with their physical origin. We calculate the instantaneous patterns of the light-ray deflections caused by the monopole, the dipole and the quadrupole moments, and derive equations describing apparent motion of the deflected position of the star in the sky plane as the impact parameter of the light ray with respect to the planet changes due to its orbital motion. The present paper gives the physical interpretation of the observed light-ray deflections and discusses the observational capabilities of the near-future optical (SIM) and radio (SKA) interferometers for detecting the Doppler modulation of the radial deflection, and the dipolar and quadrupolar light-ray bendings by the Jupiter and the Saturn.Comment: 33 pages, 10 figures, accepted to Phys. Rev.

Aerosol composition and source apportionment in the Mexico City Metropolitan Area with PIXE/PESA/STIM and multivariate analysis

International audienceAerosols play an important role in the atmosphere but are poorly characterized, particularly in urban areas like the Mexico City Metropolitan Area (MCMA). The chemical composition of urban particles must be known to assess their effects on the environment, and specific particulate emissions sources should be identified to establish effective pollution control standards. For these reasons, samples of particulate matter ?2.5 ?m (PM2.5) were collected during the MCMA-2003 Field Campaign for elemental and multivariate analyses. Proton-Induced X-ray Emission (PIXE), Proton-Elastic Scattering Analysis (PESA) and Scanning Transmission Ion Microscopy (STIM) measurements were done to determine concentrations of 19 elements from Na to Pb, hydrogen, and total mass, respectively. The most abundant elements from PIXE analysis were S, Si, K, Fe, Ca, and Al, while the major emissions sources associated with these elements were industry, wind-blown soil, and biomass burning. Wind trajectories suggest that metals associated with industrial emissions came from northern areas of the city whereas soil aerosols came from the southwest and increased in concentration during dry conditions. Elemental markers for fuel oil combustion, V and Ni, correlated with a large SO2 plume to suggest an anthropogenic, rather than volcanic, emissions source. By subtracting major components of soil and sulfates determined by PIXE analysis from STIM total mass measurements, we estimate that approximately 50% of non-volatile PM2.5 consisted of carbonaceous material

On distributions of functionals of anomalous diffusion paths

Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger equation in imaginary time. In recent years there is a growing interest in particular functionals of non-Brownian motion, or anomalous diffusion, but no equation existed for their PDF. Here, we derive a fractional generalization of the Feynman-Kac equation for functionals of anomalous paths based on sub-diffusive continuous-time random walk. We also derive a backward equation and a generalization to Levy flights. Solutions are presented for a wide number of applications including the occupation time in half space and in an interval, the first passage time, the maximal displacement, and the hitting probability. We briefly discuss other fractional Schrodinger equations that recently appeared in the literature.Comment: 25 pages, 4 figure

Taking the Measure of the Universe: Precision Astrometry with SIM PlanetQuest

Precision astrometry at microarcsecond accuracy has application to a wide range of astrophysical problems. This paper is a study of the science questions that can be addressed using an instrument that delivers parallaxes at about 4 microarcsec on targets as faint as V = 20, differential accuracy of 0.6 microarcsec on bright targets, and with flexible scheduling. The science topics are drawn primarily from the Team Key Projects, selected in 2000, for the Space Interferometry Mission PlanetQuest (SIM PlanetQuest). We use the capabilities of this mission to illustrate the importance of the next level of astrometric precision in modern astrophysics. SIM PlanetQuest is currently in the detailed design phase, having completed all of the enabling technologies needed for the flight instrument in 2005. It will be the first space-based long baseline Michelson interferometer designed for precision astrometry. SIM will contribute strongly to many astronomical fields including stellar and galactic astrophysics, planetary systems around nearby stars, and the study of quasar and AGN nuclei. SIM will search for planets with masses as small as an Earth orbiting in the `habitable zone' around the nearest stars using differential astrometry, and could discover many dozen if Earth-like planets are common. It will be the most capable instrument for detecting planets around young stars, thereby providing insights into how planetary systems are born and how they evolve with time. SIM will observe significant numbers of very high- and low-mass stars, providing stellar masses to 1%, the accuracy needed to challenge physical models. Using precision proper motion measurements, SIM will probe the galactic mass distribution and the formation and evolution of the Galactic halo. (abridged)Comment: 54 pages, 28 figures, uses emulateapj. Submitted to PAS

Characterization of ambient aerosols in Mexico City during the MCMA-2003 campaign with Aerosol Mass Spectrometry: results from the CENICA Supersite

International audienceAn Aerodyne Aerosol Mass Spectrometer (AMS) was deployed at the CENICA Supersite, during the Mexico City Metropolitan Area field study (MCMA-2003) from 31 March-4 May 2003 to investigate particle concentrations, sources, and processes. The AMS provides real time information on mass concentration and composition of the non-refractory species in particulate matter less than 1 µm (NR-PM1) with high time and size-resolution. In order to account for the refractory material in the aerosol, we also present estimates of Black Carbon (BC) using an aethalometer and an estimate of the aerosol soil component obtained from Proton-Induced X-ray Emission Spectrometry (PIXE) analysis of impactor substrates. Comparisons of AMS + BC + soil mass concentration with other collocated particle instruments (a LASAIR Optical Particle Counter, a PM2.5 Tapered Element Oscillating Microbalance (TEOM), and a PM2.5 DustTrak Aerosol Monitor) show that the AMS + BC + soil mass concentration is consistent with the total PM2.5 mass concentration during MCMA-2003 within the combined uncertainties. In Mexico City, the organic fraction of the estimated PM2.5 at CENICA represents, on average, 54.6% (standard deviation ?=10%) of the mass, with the rest consisting of inorganic compounds (mainly ammonium nitrate and sulfate/ammonium salts), BC, and soil. Inorganic compounds represent 27.5% of PM2.5 (?=10%); BC mass concentration is about 11% (?=4%); while soil represents about 6.9% (?=4%). Size distributions are presented for the AMS species; they show an accumulation mode that contains mainly oxygenated organic and secondary inorganic compounds. The organic size distributions also contain a small organic particle mode that is likely indicative of fresh traffic emissions; small particle modes exist for the inorganic species as well. Evidence suggests that the organic and inorganic species are not always internally mixed, especially in the small modes. The aerosol seems to be neutralized most of the time; however, there were some periods when there was not enough ammonium to completely neutralize the nitrate, chloride and sulfate present. The diurnal cycle and size distributions of nitrate suggest local photochemical production. On the other hand, sulfate appears to be produced on a regional scale. There are indications of new particle formation and growth events when concentrations of SO2 were high. Although the sources of chloride are not clear, this species seems to condense as ammonium chloride early in the morning and to evaporate as the temperature increases and RH decreases. The total and speciated mass concentrations and diurnal cycles measured during MCMA-2003 are similar to measurements during a previous field campaign at a nearby location