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

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.

Applications of Lagrangian dispersion modeling to the analysis of changes in the specific absorption of elemental carbon

International audienceWe use a Lagrangian dispersion model driven by a mesoscale model with four-dimensional data assimilation to simulate the dispersion of elemental carbon (EC) over a region encompassing Mexico City and its surroundings, the study domain for the 2006 MAX-MEX experiment, which was a component of the MILAGRO campaign. The results are used to identify periods when biomass burning was likely to have had a significant impact on the concentrations of elemental carbon at two sites, T1 and T2, downwind of the city, and when emissions from the Mexico City Metropolitan Area (MCMA) were likely to have been more important. They are also used to estimate the median ages of EC affecting the specific absorption of light, ?ABS, at 870 nm as well as to identify periods when the urban plume from the MCMA was likely to have been advected over T1 and T2. Median EC ages at T1 and T2 are substantially larger during the day than at night. Values of ?ABS at T1, the nearer of the two sites to Mexico City, were smaller at night and increased rapidly after mid-morning, peaking in the mid-afternoon. The behavior is attributed to the coating of aerosols with substances such as sulfate or organic carbon during daylight hours, but such coating appears to be limited or absent at night. Evidence for this is provided by scanning electron microscopy images of aerosols collected at the sampling sites. During daylight hours the values of ?ABS did not increase with aerosol age for median ages in the range of 1?4 h. There is some evidence for absorption increasing as aerosols were advected from T1 to T2 but the statistical significance of that result is not strong

Path Integral Approach to the Non-Relativistic Electron Charge Transfer

A path integral approach has been generalized for the non-relativistic electron charge transfer processes. The charge transfer - the capture of an electron by an ion passing another atom or more generally the problem of rearrangement collisions is formulated in terms of influence functionals. It has been shown that the electron charge transfer process can be treated either as electron transition problem or as elastic scattering of ion and atom in the some effective potential field. The first-order Born approximation for the electron charge transfer cross section has been reproduced to prove the adequacy of the path integral approach for this problem.Comment: 19 pages, 1 figure, to appear in Journal of Physics B: Atomic, Molecular & Optical, vol.34, 200

Spectro-microscopic measurements of carbonaceous aerosol aging in Central California

Carbonaceous aerosols are responsible for large uncertainties in climate models, degraded visibility, and adverse health effects. The Carbonaceous Aerosols and Radiative Effects Study (CARES) was designed to study carbonaceous aerosols in the natural environment of the Central Valley, California, and learn more about their atmospheric formation and aging. This paper presents results from spectro-microscopic measurements of carbonaceous particles collected during CARES at the time of a pollution accumulation event (27–29 June 2010), when in situ measurements indicated an increase in the organic carbon content of aerosols as the Sacramento urban plume aged. Computer-controlled scanning electron microscopy coupled with an energy dispersive X-ray detector (CCSEM/EDX) and scanning transmission X-ray microscopy coupled with near-edge X-ray absorption spectroscopy (STXM/NEXAFS) were used to probe the chemical composition and morphology of individual particles. It was found that the mass of organic carbon on individual particles increased through condensation of secondary organic aerosol. STXM/NEXAFS indicated that the number fraction of homogenous organic particles lacking inorganic inclusions (greater than ~50 nm equivalent circular diameter) increased with plume age, as did the organic mass per particle. Comparison of the CARES spectro-microscopic dataset with a similar dataset obtained in Mexico City during the MILAGRO campaign showed that fresh particles in Mexico City contained three times as much carbon as those sampled during CARES. The number fraction of soot particles at the Mexico City urban site (ranging from 16.6 to 47.3%) was larger than at the CARES urban site (13.4–15.7%), and the most aged samples from CARES contained fewer carbon–carbon double bonds. Differences between carbonaceous particles in Mexico City and California result from different sources, photochemical conditions, gas phase reactants, and secondary organic aerosol precursors. The detailed results provided by these spectro-microscopic measurements will allow for a comprehensive evaluation of aerosol process models used in climate research

Influence of crustal dust and sea spray supermicron particle concentrations and acidity on inorganic NO_3^- aerosol during the 2013 Southern Oxidant and Aerosol Study

Inorganic aerosol composition was measured in the southeastern United States, a region that exhibits high aerosol mass loading during the summer, as part of the 2013 Southern Oxidant and Aerosol Study (SOAS) campaign. Measurements using a Monitor for AeRosols and GAses (MARGA) revealed two periods of high aerosol nitrate (NO_^3−) concentrations during the campaign. These periods of high nitrate were correlated with increased concentrations of supermicron crustal and sea spray aerosol species, particularly Na^+ and Ca^(2+), and with a shift towards aerosol with larger (1 to 2.5 μm) diameters. We suggest this nitrate aerosol forms by multiphase reactions of HNO_3 and particles, reactions that are facilitated by transport of crustal dust and sea spray aerosol from a source within the United States. The observed high aerosol acidity prevents the formation of NH_4NO_3, the inorganic nitrogen species often dominant in fine-mode aerosol at higher pH. Calculation of the rate of the heterogeneous uptake of HNO_3 on mineral aerosol supports the conclusion that aerosol NO_3^− is produced primarily by this process, and is likely limited by the availability of mineral cation-containing aerosol surface area. Modeling of NO_3^− and HNO_3 by thermodynamic equilibrium models (ISORROPIA II and E-AIM) reveals the importance of including mineral cations in the southeastern United States to accurately balance ion species and predict gas–aerosol phase partitioning

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.

Numerical simulation of the thermal fragmentation process in fullerene C60

The processes of defect formation and annealing in fullerene C60 at T=(4000-6000)K are studied by the molecular dynamics technique with a tight-binding potential. The cluster lifetime until fragmentation due to the loss of a C2 dimer has been calculated as a function of temperature. The activation energy and the frequency factor in the Arrhenius equation for the fragmentation rate have been found to be Ea = (9.2 +- 0.4) eV and A = (8 +- 1)10^{19} 1/s. It is shown that fragmentation can occur after the C60 cluster loses its spherical shape. This fact must be taken into account in theoretical calculations of Ea.Comment: 12 pages, 3 figure

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