Feynman Diagrams and Differential Equations

We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of one- and two-loop corrections to the photon propagator in QED, by computing the Vacuum Polarization tensor exactly in D. Finally, we treat two cases of less trivial differential equations, respectively associated to a two-loop three-point, and a four-loop two-point integral. These two examples are the playgrounds for showing more technical aspects about: Laurent expansion of the differential equations in D (around D=4); the choice of the boundary conditions; and the link among differential and difference equations for Feynman integrals.Comment: invited review article from Int. J. Mod. Phys.

The potassic sedimentary rocks in Gale Crater, Mars, as seen by ChemCam on board Curiosity

The Mars Science Laboratory rover Curiosity encountered potassium-rich clastic sedimentary rocks at two sites in Gale Crater, the waypoints Cooperstown and Kimberley. These rocks include several distinct meters thick sedimentary outcrops ranging from fine sandstone to conglomerate, interpreted to record an ancient fluvial or fluvio-deltaic depositional system. From ChemCam Laser-Induced Breakdown Spectroscopy (LIBS) chemical analyses, this suite of sedimentary rocks has an overall mean K2O abundance that is more than 5 times higher than that of the average Martian crust. The combined analysis of ChemCam data with stratigraphic and geographic locations reveals that the mean K2O abundance increases upward through the stratigraphic section. Chemical analyses across each unit can be represented as mixtures of several distinct chemical components, i.e., mineral phases, including K-bearing minerals, mafic silicates, Fe-oxides, and Fe-hydroxide/oxyhydroxides. Possible K-bearing minerals include alkali feldspar (including anorthoclase and sanidine) and K-bearing phyllosilicate such as illite. Mixtures of different source rocks, including a potassium-rich rock located on the rim and walls of Gale Crater, are the likely origin of observed chemical variations within each unit. Physical sorting may have also played a role in the enrichment in K in the Kimberley formation. The occurrence of these potassic sedimentary rocks provides additional evidence for the chemical diversity of the crust exposed at Gale Crater

A measurement of the differential cross section for the two-body photodisintegration of 3He at theta_LAB = 90deg using tagged photons in the energy range 14 -- 31 MeV

The two-body photodisintegration of 3He has been investigated using tagged photons with energies from 14 -- 31 MeV at MAX-lab in Lund, Sweden. The two-body breakup channel was unambiguously identified by the (nonsimultaneous) detection of both protons and deuterons. This approach was made feasible by the over-determined kinematic situation afforded by the tagged-photon technique. Proton- and deuteron-energy spectra were measured using four silicon surface-barrier detector telescopes located at a laboratory angle of 90deg with respect to the incident photon-beam direction. Average statistical and systematic uncertainties of 5.7% and 6.6% in the differential cross section were obtained for 11 photon-energy bins with an average width of 1.2 MeV. The results are compared to previous experimental data measured at comparable photon energies as well as to the results of two recent Faddeev calculations which employ realistic potential models and take into account three-nucleon forces and final-state interactions. Both the accuracy and precision of the present data are improved over the previous measurements. The data are in good agreement with most of the previous results, and favor the inclusion of three-nucleon forces in the calculations.Comment: 12 pages, 13 figures; further Referee comments addresse

Electron Spin for Classical Information Processing: A Brief Survey of Spin-Based Logic Devices, Gates and Circuits

In electronics, information has been traditionally stored, processed and communicated using an electron's charge. This paradigm is increasingly turning out to be energy-inefficient, because movement of charge within an information-processing device invariably causes current flow and an associated dissipation. Replacing charge with the "spin" of an electron to encode information may eliminate much of this dissipation and lead to more energy-efficient "green electronics". This realization has spurred significant research in spintronic devices and circuits where spin either directly acts as the physical variable for hosting information or augments the role of charge. In this review article, we discuss and elucidate some of these ideas, and highlight their strengths and weaknesses. Many of them can potentially reduce energy dissipation significantly, but unfortunately are error-prone and unreliable. Moreover, there are serious obstacles to their technological implementation that may be difficult to overcome in the near term. This review addresses three constructs: (1) single devices or binary switches that can be constituents of Boolean logic gates for digital information processing, (2) complete gates that are capable of performing specific Boolean logic operations, and (3) combinational circuits or architectures (equivalent to many gates working in unison) that are capable of performing universal computation.Comment: Topical Revie

Extended structures of polyiodide salts of transition metal macrocyclic complexes

The structures of five polyiodide salts, [Co([9]aneS3)2]I11 (1), [Ni([9]aneS3)2]I6 (2), [Ni([9]aneS3)2]I10 (3), [Pd([12]aneS4)]I6 (4) and [Pd([14]aneS4)]I10#1;MeCN (5), containing the template cations [Co([9]aneS3)2]3+, [Ni([9]aneS3)2]2+, [Pd([12]aneS4)]2+ and [Pd([14]aneS4)]2+ ([9]aneS3 = 1,4,7-trithiacyclononane, [12]aneS4 = 1,4,7,10-tetrathiacyclododecane, [14]aneS4 = 1,4,8,11-tetrathiacyclotetradecane) exhibit a range of polyiodide and polyanionic framework structures. In (1) the charge on the CoIII cation is balanced by three I#2; 3 anions, which along with a neutral di-iodine molecule form I3#2; 11 rings in an extended structure comprising undulating chains of alternating I3#2; 11 rings and complex cations. In (2) the complex cation is linked to two tri-iodide anions by S#1; #1; #1;I interactions into well separated sheets of cations and anions, while in (3), I#2; 5 anions are linked by I#1; #1; #1;I interactions into helices which are crosslinked by S#1; #1; #1;I contacts to form sheets. Rather longer I#1; #1; #1;I contacts in (4) assemble I#2; 3 ions into 2 #3; 2 rods, which are linked into a three-dimensional network by S#1; #1; #1;I contacts. In (5) the N atom of the acetonitrile solvent molecule forms an array of four weak C—H#1; #1; #1;N hydrogen bonds to the macrocycle. The extended structure comprises corrugated zigzag chains of polyiodide rings formed by linked I#2; 5 units; the complex cations are attached to the polyiodide network by S...I contacts, which link the chains to form layers

Pervasively Altered Hematite-Rich Deposits Southeast of Home Plate, Gusev Crater, Mars

The investigation of Home Plate and its surroundings in the Inner Basin of the Columbia Hills in Gusev Crater has added substantially to the water story on Mars. Textural, morphological, and geochemical evidence from Home Plate point towards an explosive origin, probably a hydrovolcanic explosion [1]. High silica deposits in the immediate vicinity of Home Plate suggest hydrothermal alteration [e.g. 2,3]. Pervasively altered deposits rich in hematite were investigated to the southeast of Home Plate. Of these, the target Halley, the target KingGeorgeIsland on the GrahamLand outcrop, and the targets Montalva and Riquelme on the Troll outcrop were investigated in situ with the Alpha Particle X-ray spectrometer (APXS), the Microscopic Imager (MI), and the Moessbauer (MB) spectrometer (Fig. 1)

The dynamical evolution of the circumstellar gas around low-and intermediate-mass stars I: the AGB

We have investigated the dynamical interaction of low- and-intermediate mass stars (from 1 to 5 Msun) with their interstellar medium (ISM). In this first paper, we examine the structures generated by the stellar winds during the Asymptotic Giant Branch (AGB) phase, using a numerical code and the wind history predicted by stellar evolution. The influence of the external ISM is also taken into account. We find that the wind variations associated with the thermal pulses lead to the formation of transient shells with an average lifetime of 20,000 yr, and consequently do not remain recorded in the density or velocity structure of the gas. The formation of shells that survive at the end of the AGB occurs via two main processes: shocks between the shells formed by two consecutive enhancements of the mass-loss or via continuous accumulation of the material ejected by the star in the interaction region with the ISM. Our models show that the mass of the circumstellar envelope increases appreciably due to the ISM material swept up by the wind (up to 70 % for the 1 Msun stellar model). We also point out the importance of the ISM on the deceleration and compression of the external shells. According to our simulations, large regions (up to 2.5 pc) of neutral gas surrounding the molecular envelopes of AGB stars are expected. These large regions of gas are formed from the mass-loss experienced by the star during the AGB evolution.Comment: 43 pages, 15 figures. Accepted for publication in the Astrophysical Journa

Casimir forces and non-Newtonian gravitation

The search for non-relativistic deviations from Newtonian gravitation can lead to new phenomena signalling the unification of gravity with the other fundamental interactions. Various recent theoretical frameworks indicate a possible window for non-Newtonian forces with gravitational coupling strength in the micrometre range. The major expected background in the same range is attributable to the Casimir force or variants of it if dielectric materials, rather than conducting ones, are considered. Here we review the measurements of the Casimir force performed so far in the micrometre range and how they determine constraints on non-Newtonian gravitation, also discussing the dominant sources of false signals. We also propose a geometry-independent parameterization of all data in terms of the measurement of the constant c. Any Casimir force measurement should lead, once all corrections are taken into account, to a determination of the constant c which, in order to assess the accuracy of the measurement, can be compared with its more precise value known through microscopic measurements. Although the last decade of experiments has resulted in solid demonstrations of the Casimir force, the situation is not conclusive with respect to being able to discover new physics. Future experiments and novel phenomenological analysis will be necessary to discover non-Newtonian forces or to push the window for their possible existence into regions of the parameter space which theoretically appear unnatural.Comment: Also available at http://www.iop.org/EJ/abstract/1367-2630/8/10/23

Multiwavelength observations of Mkn 501 during the 1997 high state

During the observation period 1997, the nearby Blazar Mkn 501 showed extremely strong emission and high variability. We examine multiwavelength aspects of this event using radio, optical, soft and hard X-ray and TeV data. We concentrate on the medium-timescale variability of the broadband spectra, averaged over weekly intervals. We confirm the previously found correlation between soft and hard X-ray emission and the emission at TeV energies, while the source shows only minor variability at radio and optical wavelengths. The non-linear correlation between hard X-ray and TeV fluxes is consistent with a simple analytic estimate based on an SSC model in which Klein-Nishina effects are important for the highest-energy electrons in the jet, and flux variations are caused by variations of the electron density and/or the spectral index of the electron injection spectrum. The time-averaged spectra are fitted with a Synchrotron Self-Compton (SSC) dominated leptonic jet model, using the full Klein-Nishina cross section and following the self-consistent evolution of relativistic particles along the jet, accounting for gamma-gamma absorption and pair production within the source as well as due to the intergalactic infrared background radiation. The contribution from external inverse-Compton scattering is tightly constrained by the low maximum EGRET flux and found to be negligible at TeV energies. We find that high levels of the X-ray and TeV fluxes can be explained by a hardening of the energy spectra of electrons injected at the base of the jet, in remarkable contrast to the trend found for gamma-ray flares of the flat-spectrum radio quasar PKS 0528+134.Comment: accepted for publication in ApJ, 31 pages, 11 figure

Simultaneous X-Ray and TeV Gamma-Ray Observations of the TeV Blazar Markarian 421 during February and May 2000

In this paper we present the results of simultaneous observations of the TeV blazar Markarian 421 (Mrk 421) at X-ray and TeV Gamma-ray energies with the Rossi X-Ray Timing Explorer (RXTE) and the stereoscopic Cherenkov Telescope system of the HEGRA (High Energy Gamma Ray Astronomy) experiment, respectively. The source was monitored from February 2nd to February 16th and from May 3rd to May 8th, 2000. We discuss in detail the temporal and spectral properties of the source. Remarkably, the TeV observations of February 7th/8th showed statistically significant evidence for substantial TeV flux variability on 30 min time scale. We show the results of modeling the data with a time dependent homogeneous Synchrotron Self-Compton (SSC) model. The X-ray and TeV gamma-ray emission strengths and energy spectra together with the rapid flux variability strongly suggest that the emission volume is approaching the observer with a Doppler factor of 50 or higher. The different flux variability time scales observed at X-rays and TeV Gamma-rays indicate that a more detailed analysis will require inhomogeneous models with several emission zones.Comment: Accepted for Publication in ApJ, 21 Pages, 5 Figure