Pair distribution function in a two-dimensional electron gas

We calculate the pair distribution function, $g(r)$, in a two-dimensional electron gas and derive a simple analytical expression for its value at the origin as a function of $r_s$. Our approach is based on solving the Schr\"{o}dinger equation for the two-electron wave function in an appropriate effective potential, leading to results that are in good agreement with Quantum Monte Carlo data and with the most recent numerical calculations of $g(0)$. [C. Bulutay and B. Tanatar, Phys. Rev. B {\bf 65}, 195116 (2002)] We also show that the spin-up spin-down correlation function at the origin, $g_{\uparrow \downarrow}(0)$, is mainly independent of the degree of spin polarization of the electronic system.Comment: 5 figures, pair distribution dependence with distance is calculate

Dijet production as a centrality trigger for p-p collisions at CERN LHC

We demonstrate that a trigger on hard dijet production at small rapidities allows to establish a quantitative distinction between central and peripheral collisions in pbar-p and p-p collisions at Tevatron and LHC energies. Such a trigger strongly reduces the effective impact parameters as compared to minimum bias events. This happens because the transverse spatial distribution of hard partons (x >~ 10^{-2}) in the proton is considerably narrower than that of soft partons, whose collisions dominate the total cross section. In the central collisions selected by the trigger, most of the partons with x >~ 10^{-2} interact with a gluon field whose strength rapidly increases with energy. At LHC (and to some extent already at Tevatron) energies the strength of this interaction approaches the unitarity ('black-body') limit. This leads to specific modifications of the final state, such as a higher probability of multijet events at small rapidities, a strong increase of the transverse momenta and depletion of the longitudinal momenta at large rapidities, and the appearance of long-range correlations in rapidity between the forward/backward fragmentation regions. The same pattern is expected for events with production of new heavy particles (Higgs, SUSY). Studies of these phenomena would be feasible with the CMS-TOTEM detector setup, and would have considerable impact on the exploration of the physics of strong gluon fields in QCD, as well as the search for new particles at LHC.Comment: 17 pages, Revtex 4, 14 EPS figures. Expanded discussion of some points, added 3 new figures and new references. Included comment on connection with cosmic ray physics near the GZK cutoff. To appear in Phys Rev

Analytical expressions for the charge-charge local-field factor and the exchange-correlation kernel of a two-dimensional electron gas

We present an analytical expression for the static many-body local field factor $G_{+}(q)$ of a homogeneous two-dimensional electron gas, which reproduces Diffusion Monte Carlo data and embodies the exact asymptotic behaviors at both small and large wave number $q$. This allows us to also provide a closed-form expression for the exchange and correlation kernel $K_{xc}(r)$, which represents a key input for density functional studies of inhomogeneous systems.Comment: 5 pages, 3 figure

Temperature and Humidity Dependence of Air Fluorescence Yield measured by AIRFLY

The fluorescence detection of ultra high energy cosmic rays requires a detailed knowledge of the fluorescence light emission from nitrogen molecules over a wide range of atmospheric parameters, corresponding to altitudes typical of the cosmic ray shower development in the atmosphere. We have studied the temperature and humidity dependence of the fluorescence light spectrum excited by MeV electrons in air. Results for the 313.6 nm, 337.1 nm, 353.7 nm and 391.4 nm bands are reported in this paper. We found that the temperature and humidity dependence of the quenching process changes the fluorescence yield by a sizeable amount (up to 20%) and its effect must be included for a precise estimation of the energy of ultra high energy cosmic rays.Comment: presented at the 5th Fluorescence Workshop, El Escorial - Madrid, Spain, 16 - 20 September 2007, to appear in Nuclear Instruments and Methods

On local linearization of control systems

We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control (static feedback transformations) that are topological but not necessarily differentiable. We prove that local topological linearization implies local smooth linearization, at generic points. At arbitrary points, it implies local conjugation to a linear system via a homeomorphism that induces a smooth diffeomorphism on the state variables, and, except at "strongly" singular points, this homeomorphism can be chosen to be a smooth mapping (the inverse map needs not be smooth). Deciding whether the same is true at "strongly" singular points is tantamount to solve an intriguing open question in differential topology

Ultra-High Energy Cosmic Rays in a Structured and Magnetized Universe

We simulate propagation of cosmic ray nucleons above 10^{19} eV in scenarios where both the source distribution and magnetic fields within about 50 Mpc from us are obtained from an unconstrained large scale structure simulation. We find that consistency of predicted sky distributions with current data above 4 x 10^{19} eV requires magnetic fields of ~0.1 microGauss in our immediate environment, and a nearby source density of ~10^{-4}-10^{-3} Mpc^{-3}. Radio galaxies could provide the required sources, but only if both high and low-luminosity radio galaxies are very efficient cosmic ray accelerators. Moreover, at ~10^{19} eV an additional isotropic flux component, presumably of cosmological origin, should dominate over the local flux component by about a factor three in order to explain the observed isotropy. This argues against the scenario in which local astrophysical sources of cosmic rays above ~10^{19} eV reside in strongly magnetized (B~0.1 microGauss) and structured intergalactic medium. Finally we discuss how future large scale full-sky detectors such as the Pierre Auger project will allow to put much more stringent constraints on source and magnetic field distributions.Comment: 11 revtex pages, 10 postscript figures included, final version to appear in PR

Super-GZK Photons from Photon-Axion Mixing

We show that photons with energies above the GZK cutoff can reach us from very distant sources if they mix with light axions in extragalactic magnetic fields. The effect which enables this is the conversion of photons into axions, which are sufficiently weakly coupled to travel large distances unimpeded. These axions then convert back into high energy photons close to the Earth. We show that photon-axion mixing facilitates the survival of super-GZK photons most efficiently with a photon-axion coupling scale of order 10^11 GeV, which is in the same range as the scale for the photon-axion mixing explanation for the dimming of supernovae without cosmic acceleration. We discuss possible observational consequences of this effect.Comment: 17 pages, 5 figures. Published versio

Ultra-High Energy Cosmic Ray Nuclei from Individual Magnetized Sources

We investigate the dependence of composition, spectrum and angular distributions of ultra-high energy cosmic rays above 10^19 eV from individual sources on their magnetization. We find that, especially for sources within a few megaparsecs from the observer, observable spectra and composition are severely modified if the source is surrounded by fields of ~ 10^-7 Gauss on scales of a few megaparsecs. Low energy particles diffuse over larger distances during their energy loss time. This leads to considerable hardening of the spectrum up to the energy where the loss distance becomes comparable to the source distance. Magnetized sources thus have very important consequences for observations, even if cosmic rays arrive within a few degrees from the source direction. At the same time, details in spectra and chemical composition may be intrinsically unpredictable because they depend on the unknown magnetic field structure. If primaries are predominantly nuclei of atomic mass A accelerated up to a maximum energy E_max with spectra not much softer than E^-2, secondary protons from photo-disintegration can produce a conspicuous peak in the spectrum at energy ~ E_max/A. A related feature appears in the average mass dependence on energy.Comment: 15 pages, 16 ps figures, published version with minor changes, see http://stacks.iop.org/1475-7516/2004/i=08/a=01

Maximum Likelihood Analysis of Clusters of Ultra-High Energy Cosmic Rays

We present a numerical code designed to conduct a likelihood analysis for clusters of nucleons above 10**19 eV originating from discrete astrophysical sources such as powerful radio galaxies, gamma-ray bursts or topological defects. The code simulates the propagation of nucleons in a large-scale magnetic field and constructs the likelihood of a given observed event cluster as a function of the average time delay due to deflection in the magnetic field, the source activity time scale, the total fluence of the source, and the power law index of the particle injection spectrum. Other parameters such as the coherence length and the power spectrum of the magnetic field are also considered. We apply it to the three pairs of events above 4X10**19 eV recently reported by the Akeno Giant Air Shower Array (AGASA) experiment, assuming that these pairs were caused by nucleon primaries which originated from a common source. Although current data are too sparse to fully constrain each of the parameters considered, and/or to discriminate models of the origin of ultra-high energy cosmic rays, several tendencies are indicated. If the clustering suggested by AGASA is real, next generation experiments with their increased exposure should detect more than 10 particles per source over a few years and our method will put strong constraints on both the large-scale magnetic field parameters and the nature of these sources.Comment: 11 latex pages, 8 postscript figures included, uses revtex.sty in two-column format and epsf.sty. Submitted to Physical Review