Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory

The classical Kepler problem, as well as its quantum mechanical version, the Hydrogen atom, enjoy a well-known hidden symmetry, the conservation of the Laplace-Runge-Lenz vector, which makes these problems superintegrable. Is there a relativistic quantum field theory extension that preserves this symmetry? In this Letter we show that the answer is positive: in the non-relativistic limit, we identify the dual conformal symmetry of planar $\mathcal{N}=4$ super Yang-Mills with the well-known symmetries of the Hydrogen atom. We point out that the dual conformal symmetry offers a novel way to compute the spectrum of bound states of massive $W$ bosons in the theory. We perform nontrivial tests of this setup at weak and strong coupling, and comment on the possible extension to arbitrary values of the coupling.Comment: 4 pages, 3 figures. Clarifications added; published versio

Heavy Quark Thermalization in Classical Lattice Gauge Theory: Lessons for Strongly-Coupled QCD

Thermalization of a heavy quark near rest is controlled by the correlator of two electric fields along a temporal Wilson line. We address this correlator within real-time, classical lattice Yang-Mills theory, and elaborate on the analogies that exist with the dynamics of hot QCD. In the weak-coupling limit, it can be shown analytically that the dynamics on the two sides are closely related to each other. For intermediate couplings, we carry out non-perturbative simulations within the classical theory, showing that the leading term in the weak-coupling expansion significantly underestimates the heavy quark thermalization rate. Our analytic and numerical results also yield a general understanding concerning the overall shape of the spectral function corresponding to the electric field correlator, which may be helpful in subsequent efforts to reconstruct it from Euclidean lattice Monte Carlo simulations.Comment: 22 pages. v2: a reference and clarifications added; published versio

Subleading Regge limit from a soft anomalous dimension

Wilson lines capture important features of scattering amplitudes, for example soft effects relevant for infrared divergences, and the Regge limit. Beyond the leading power approximation, corrections to the eikonal picture have to be taken into account. In this paper, we study such corrections in a model of massive scattering amplitudes in N = 4 super Yang-Mills, in the planar limit, where the mass is generated through a Higgs mechanism. Using known three-loop analytic expressions for the scattering amplitude, we find that the first power suppressed term has a very simple form, equal to a single power law. We propose that its exponent is governed by the anomalous dimension of a Wilson loop with a scalar inserted at the cusp, and we provide perturbative evidence for this proposal. We also analyze other limits of the amplitude and conjecture an exact formula for a total cross-section at high energies.Comment: 19 pages, several appendices, many figure

Fluctuation, dissipation, and thermalization in non-equilibrium AdS_5 black hole geometries

We give a simple recipe for computing dissipation and fluctuations (commutator and anti-commutator correlation functions) for non-equilibrium black hole geometries. The recipe formulates Hawking radiation as an initial value problem, and is suitable for numerical work. We show how to package the fluctuation and dissipation near the event horizon into correlators on the stretched horizon. These horizon correlators determine the bulk and boundary field theory correlation functions. In addition, the horizon correlators are the components of a horizon effective action which provides a quantum generalization of the membrane paradigm. In equilibrium, the analysis reproduces previous results on the Brownian motion of a heavy quark. Out of equilibrium, Wigner transforms of commutator and anti-commutator correlation functions obey a fluctuation-dissipation relation at high frequency.Comment: 28 pages, 6 figure

Testing Luminescence Dating Methods for Small Samples from Very Young Fluvial Deposits

The impetus behind this study is to understand the sedimentological dynamics of very young fluvial systems in the Amazon River catchment and relate these to land use change and modern analogue studies of tidal rhythmites in the geologic record. Initial quartz optically stimulated luminescence (OSL) dating feasibility studies have concentrated on spit and bar deposits in the Rio Tapajós. Many of these features have an appearance of freshly deposited pristine sand, and these observations and information from anecdotal evidence and LandSat imagery suggest an apparent decadal stability. The characteristics of OSL from small (~5 cm) sub-samples from ~65 cm by ~2 cm diameter vertical cores are quite remarkable. Signals from medium-sized aliquots (5 mm diameter) exhibit very high specific luminescence sensitivity, have excellent dose recovery and recycling, essentially independent of preheat, and show minimal heat transfer even at the highest preheats. These characteristics enable measurement of very small signals with reasonable precision and, using modified single-aliquot regenerative-dose (SAR) approaches, equivalent doses as low as ~4 mGy can be obtained. Significant recuperation is observed for samples from two of the study sites and, in these instances, either the acceptance threshold was increased or growth curves were forced through the origin; recuperation is considered most likely to be a measurement artefact given the very small size of natural signals. Dose rates calculated from combined inductively coupled plasma mass spectrometry/inductively coupled plasma optical emission spectrometry (ICP-MS/ICP-OES) and high-resolution gamma spectrometry range from ~0.3 to 0.5 mGya−1 , and OSL ages for features so far investigated range from 13 to 34 years to several 100 years. Sampled sands are rich in quartz and yields of 212–250 µm or 250–310 µm grains indicate high-resolution sampling at 1–2 cm intervals is possible. Despite the use of medium-sized aliquots to ensure the recovery of very dim natural OSL signals, these results demonstrate the potential of OSL for studying very young active fluvial processes in these settings

A way to estimate the heavy quark thermalization rate from the lattice

The thermalization rate of a heavy quark is related to its momentum diffusion coefficient. Starting from a Kubo relation and using the framework of the heavy quark effective theory, we argue that in the large-mass limit the momentum diffusion coefficient can be defined through a certain Euclidean correlation function, involving color-electric fields along a Polyakov loop. Furthermore, carrying out a perturbative computation, we demonstrate that the spectral function corresponding to this correlator is relatively flat at small frequencies. Therefore, unlike in the case of several other transport coefficients, for which the narrowness of the transport peak makes analytic continuation from Euclidean lattice data susceptible to severe systematic uncertainties, it appears that the determination of the heavy quark thermalization rate could be relatively well under control.Comment: 17 pages. v2: clarifications and references added, published versio

Iterative structure of finite loop integrals

In this paper we develop further and refine the method of differential equations for computing Feynman integrals. In particular, we show that an additional iterative structure emerges for finite loop integrals. As a concrete non-trivial example we study planar master integrals of light-by-light scattering to three loops, and derive analytic results for all values of the Mandelstam variables $s$ and $t$ and the mass $m$. We start with a recent proposal for defining a basis of loop integrals having uniform transcendental weight properties and use this approach to compute all planar two-loop master integrals in dimensional regularization. We then show how this approach can be further simplified when computing finite loop integrals. This allows us to discuss precisely the subset of integrals that are relevant to the problem. We find that this leads to a block triangular structure of the differential equations, where the blocks correspond to integrals of different weight. We explain how this block triangular form is found in an algorithmic way. Another advantage of working in four dimensions is that integrals of different loop orders are interconnected and can be seamlessly discussed within the same formalism. We use this method to compute all finite master integrals needed up to three loops. Finally, we remark that all integrals have simple Mandelstam representations.Comment: 26 pages plus appendices, 5 figure

Colour-electric spectral function at next-to-leading order

The spectral function related to the correlator of two colour-electric fields along a Polyakov loop determines the momentum diffusion coefficient of a heavy quark near rest with respect to a heat bath. We compute this spectral function at next-to-leading order, O(alpha_s^2), in the weak-coupling expansion. The high-frequency part of our result (omega >> T), which is shown to be temperature-independent, is accurately determined thanks to asymptotic freedom; the low-frequency part of our result (omega << T), in which Hard Thermal Loop resummation is needed in order to cure infrared divergences, agrees with a previously determined expression. Our result may help to calibrate the overall normalization of a lattice-extracted spectral function in a perturbative frequency domain T << omega << 1/a, paving the way for a non-perturbative estimate of the momentum diffusion coefficient at omega -> 0. We also evaluate the colour-electric Euclidean correlator, which could be directly compared with lattice simulations. As an aside we determine the Euclidean correlator in the lattice strong-coupling expansion, showing that through a limiting procedure it can in principle be defined also in the confined phase of pure Yang-Mills theory, even if a practical measurement could be very noisy there.Comment: 38 page

The Mars Climate Database

The Mars Climate Database (MCD) [1] is a database of statistics describing the climate and environment of the Martian atmosphere. It was constructed directly on the basis of output from mulitannual integrations of two general circulation models (GCMs)developed by Laboratoire de Météorologie Dynamique du CNRS, France, the University of Oxford, UK, and Instituto de Astrofisica de Andalucia, Spain, with support from the European Space Agency (ESA) and Centre National d–Etudes Spatiales (CNES). A description of the MCD is given along with a comparison between spacecraft observations of Mars and results predicted at similar locations and times in the MCD. The MCD can be used as a tool for mission planning and has been applied to prepare for several missions in Europe and the USA. It also provides information for mission design specialists on the mean state and variability of the Martian environment from the surface to above 120km. The GCMs on which the database is founded, include a set of physical parameterizations (radiative transfer in the visible and thermal infrared ranges, turbulent mixing, condensation-sublimation of CO2, thermal conduction in the soil and representation of gravity waves) and two different codes for the representation of large scale dynamics: a spectral code for the AOPP version and a grid-point code for the LMD version. The GCMs correctly reproduce the main meteorological features of Mars, as observed by the Mariner 9 and Viking orbiters, the Viking landers, and Mars Global Surveyor (MGS). As well as the standard statistical measures for mission design studies, the MCD includes a novel representation of large-scale variability, using empirical eigenfunctions derived from an analysis of the full simulations, and small-scale variability based on parameterizations of processes such as gravity wave propagation. The database allows the user to choose from 5 dust storm scenarios including a best guess, default scenario, deduced from recent MGS observations, an upper boundary for an atmosphere without dust storms, as observed by Viking the landers, and a clear, cold, lower boundary scenario, as observed by Phobos 2 and from Earth. The full version of the MCD is available on CDROM (for UNIX systems and PCs) and is also accessible through an interactive WWW interface at http://www-mars.lmd.jussieu.fr/

Optical backscattering properties of the "clearest" natural waters

International audienceDuring the BIOSOPE field campaign October–December 2004, measurements of inherent optical properties from the surface to 500 m depth were made with a ship profiler at stations covering over ~8000 km through the Southeast Pacific Ocean. Data from a ~3000 km section containing the very clearest waters in the central gyre are reported here. The total volume scattering function at 117°, ßt(117°), was measured with a WET Labs ECO-BB3 sensor at 462, 532, and 650 nm with estimated uncertainties of 2×10-5, 5×10-6, and 2×10-6 m-1 sr-1, respectively. These values were approximately 6%, 3%, and 3% of the scattering by pure seawater at their respective wavelengths. From a methodological perspective, there were several results: – bbp distributions were resolvable even though some of the values from the central gyre were an order of magnitude lower than the lowest previous measurements in the literature; – Direct in-situ measurements of instrument dark offsets were necessary to accurately resolve backscattering at these low levels; – accurate pure seawater backscattering values are critical in determining particulate backscattering coefficients in the open ocean (not only in these very clear waters); the pure water scattering values determined by Buiteveld et al. (1994) with a [1 + 0.3S/37] adjustment for salinity based on Morel (1974) appear to be the most accurate estimates, with aggregate accuracies as low as a few percent; and – closure was demonstrated with subsurface reflectance measurements reported by Morel et al. (2007) within instrument precisions, a useful factor in validating the backscattering measurements. This methodology enabled several observations with respect to the hydrography and the use of backscattering as a biogeochemical proxy: – The clearest waters sampled were found at depths between 300 and 350 m, from 23.5° S, 118° W to 26° S, 114° W, where total backscattering at 650 nm was not distinguishable from pure seawater; – Distributions of particulate backscattering bbp across the central gyre exhibited a broad particle peak centered ~100 m; – The particulate backscattering ratio typically ranged between 0.4% and 0.6% through the majority of the central gyre from the surface to ~210 m, indicative of "soft" water-filled particles with low bulk refractive index; and – bbp at 532 and 650 nm showed a distinct secondary deeper layer centered ~230 m that was absent in particulate attenuation cp data. The particulate backscattering ratio was significantly higher in this layer than in the rest of the water column, reaching 1.2% in some locations. This high relative backscattering, along with the pigment composition and ecological niche of this layer, appear to be consistent with the coccolithophorid F. profunda. Moreover, results were consistent with several expectations extrapolated from theory and previous work in oceanic and coastal regions, supporting the conclusion that particulate and total backscattering could be resolved in these extremely clear natural waters