Space Correlation Function Research Articles

THE SIZE AND ORIGIN OF METAL-ENRICHED REGIONS IN THE INTERGALACTIC MEDIUM FROM SPECTRA OF BINARY QUASARS

We present tomography of the circum-galactic metal distribution at redshift 1.7 to 4.5 derived from echellete spectroscopy of binary quasars. We find CIV systems at similar redshifts in paired sightlines more often than expected for sightline-independent redshifts. As the separation of the sightlines increases from 36 kpc to 907 kpc, the amplitude of this clustering decreases. At the largest separations, the CIV systems cluster similar to Lyman-break galaxies (Adelberger et al. 2005a). The CIV systems are significantly less correlated than these galaxies, however, at separations less than R_1 ~ 0.42 +/- 0.15 h-1 comoving Mpc. Measured in real space, i.e., transverse to the sightlines, this length scale is significantly smaller than the break scale estimated from the line-of-sight correlation function in redshift space (Scannapieco et al. 2006a). Using a simple model, we interpret the new real-space measurement as an indication of the typical physical size of enriched regions. We adopt this size for enriched regions and fit the redshift-space distortion in the line-of-sight correlation function. The fitted velocity kick is consistent with the peculiar velocity of galaxies as determined by the underlying mass distribution and places an upper limit on the outflow (or inflow) speed of metals. The implied time scale for dispersing metals is larger than the typical stellar ages of Lyman-break galaxies (Shapley et al. 2001), and we argue that enrichment by galaxies at z > 4.3 played a greater role in dispersing metals. To further constrain the growth of enriched regions, we discuss empirical constraints on the evolution of the CIV correlation function with cosmic time. This study demonstrates the potential of tomography for measuring the metal enrichment history of the circum-galactic medium.

Sodium migration pathways in multicomponent silicate glasses: Car–Parrinello molecular dynamics simulations

The mechanism of sodium migration in low-silica alkali-alkaline earth silicate glasses is investigated through Car-Parrinello molecular dynamics (MD) simulations. The transport of sodium to the glass surface and its subsequent release is critical for the use of these glasses in biomedical applications. The analysis of the MD trajectory, mainly through a combination of space and time correlation functions, reveals a complex mechanism, with some common features to the migration in mixed-alkali silicate glasses and several important differences. The low site selectivity of Na cations in this glass allows them to use both Na and Ca sites in the migration process. The high fragmentation and the corresponding flexibility of the silicate network enable an additional mechanism for ion migration, not favorable in the more rigid network of common higher-silica glasses, involving the creation of empty transient sites through the correlated forward-backward motion of an Na or a Ca cation. We also show that because sodium migration must involve an undercoordinated intermediate, sharing of oxygen atoms in the initial and final coordination shells is a way to reduce the energetic cost of losing favorable Na-O interactions and Na migration proceeds between corner-sharing NaO(x) polyhedra, where x=5-7. For these low-silica compositions, the present simulations suggest that due to the participation of calcium in the Na migration, the latter will not be significantly hampered by extensive mixing with less mobile Ca ions, or, in any event, the effect will be less marked than for higher-silica glasses.

Variational approach to the ground state of an impurity in a Bose–Einstein condensate

In this paper, we consider the effect of self-localization of a quantum impurity in a Bose–Einstein condensate. The space correlation function of the impurity is evaluated with the help of the imaginary-time path integral approach. Employing Feynman's variational method, we calculate the impurity correlation function as well as the energy of the system associated with the impurity. The effect of self-localization predicted before within the Gross–Pitaevskii approach is recovered by our treatment. The strong coupling regime with negative ground state energy is reached by the variational method, and the corresponding correlation function is calculated.

Many-body localization transition in a lattice model of interacting fermions: Statistics of renormalized hoppings in configuration space

We consider the one-dimensional lattice model of interacting fermions with disorder studied previously by Oganesyan and Huse [Phys. Rev. B 75, 155111 (2007)]. To characterize a possible many-body localization transition as a function of the disorder strength $W$, we use an exact renormalization procedure in configuration space that generalizes the Aoki real-space RG procedure for Anderson localization one-particle models [H. Aoki, J. Phys. C13, 3369 (1980)]. We focus on the statistical properties of the renormalized hopping $V_L$ between two configurations separated by a distance $L$ in configuration space (distance being defined as the minimal number of elementary moves to go from one configuration to the other). Our numerical results point towards the existence of a many-body localization transition at a finite disorder strength $W_c$. In the localized phase $W>W_c$, the typical renormalized hopping $V_L^{typ} \equiv e^{\bar{\ln V_L}}$ decays exponentially in $L$ as $ (\ln V_L^{typ}) \simeq - \frac{L}{\xi_{loc}}$ and the localization length diverges as $\xi_{loc}(W) \sim (W-W_c)^{-\nu_{loc}}$ with a critical exponent of order $\nu_{loc} \simeq 0.5$. In the delocalized phase $W<W_c$, the renormalized hopping remains a finite random variable as $L \to \infty$, and the typical asymptotic value $V_{\infty}^{typ} \equiv e^{\bar{\ln V_{\infty}}}$ presents an essential singularity $(\ln V_{\infty}^{typ}) \sim - (W_c-W)^{-\kappa}$ with an exponent of order $\kappa \sim 1.4$. Finally, we show that this analysis in configuration space is compatible with the localization properties of the simplest two-point correlation function in real space.

PARTICLE MESH SIMULATIONS OF THE Lyα FOREST AND THE SIGNATURE OF BARYON ACOUSTIC OSCILLATIONS IN THE INTERGALACTIC MEDIUM

We present a set of ultra-large particle-mesh simulations of the LyA forest targeted at understanding the imprint of baryon acoustic oscillations (BAO) in the inter-galactic medium. We use 9 dark matter only simulations which can, for the first time, simultaneously resolve the Jeans scale of the intergalactic gas while covering the large volumes required to adequately sample the acoustic feature. Mock absorption spectra are generated using the fluctuating Gunn-Peterson approximation which have approximately correct flux probability density functions (PDFs) and small-scale power spectra. On larger scales there is clear evidence in the redshift space correlation function for an acoustic feature, which matches a linear theory template with constant bias. These spectra, which we make publicly available, can be used to test pipelines, plan future experiments and model various physical effects. As an illustration we discuss the basic properties of the acoustic signal in the forest, the scaling of errors with noise and source number density, modified statistics to treat mean flux evolution and misestimation, and non-gravitational sources such as fluctuations in the photo-ionizing background and temperature fluctuations due to HeII reionization.

A Monte Carlo algorithm for computing spin echo small angle neutron scattering correlation functions in real space: Hard sphere liquids

A Monte Carlo algorithm is developed to compute the autocorrelation function of liquids and the corresponding spatial correlation function from spin echo small angle neutron scattering (SESANS) spectra. The accuracy of the simulation algorithm is tested with isolated hard spheres and single dumbbells consisting of two hard spheres separated by a given distance. The simulation results accurately reproduce the exact expressions of these two models. To further test the algorithm for many-body systems, two liquid models are considered including hard sphere fluids and hard spheres with an attractive tail. The many-particle Monte Carlo simulation is carried out to obtain the ensemble average of these correlation functions. Meanwhile, the Percus-Yevic (PY) integral equation theory is resorted to compute the autocorrelation function and SESANS spatial correlation function for a density that the PY theory is reasonably applicable. The agreement between simulation and theory indicates that the algorithm is quite robust and can be extended to more complex fluids in the future. Furthermore, we find that the SESANS spatial correlation function is highly sensitive to the interaction potential between particles, which may serve as a useful tool to explore particle interactions in a liquid.

Redshift space correlations and scale-dependent stochastic biasing of density peaks

We calculate the redshift space correlation function and the power spectrum of density peaks of a Gaussian random field. In the linear regime k < 0.1 h/Mpc, the redshift space power spectrum is P^s_{pk}(k,u) = exp(-f^2 s_{vel}^2 k^2 u^2) * [b_{pk}(k) + b_{vel}(k) f u^2]^2 * P_m(k), where u is the angle with respect to the line of sight, s_{vel} is the one-dimensional velocity dispersion, f is the growth rate, and b_{pk}(k) and b_{vel}(k) are k-dependent linear spatial and velocity bias factors. For peaks, the value of s_{vel} depends upon the functional form of b_{vel}. The peaks model is remarkable because it has unbiased velocities -- peak motions are driven by dark matter flows -- but, in order to achieve this, b_{vel} is k-dependent. We speculate that this is true in general: k-dependence of the spatial bias will lead to k-dependence of b_{vel} even if the biased tracers flow with the dark matter. Because of the k-dependence of the linear bias parameters, standard manipulations applied to the peak model will lead to k-dependent estimates of the growth factor that could erroneously be interpreted as a signature of modified dark energy or gravity. We use the Fisher formalism to show that the constraint on the growth rate f is degraded by a factor of two if one allows for a k-dependent velocity bias of the peak type. We discuss a simple estimate of nonlinear evolution and illustrate the effect of the peak bias on the redshift space multipoles. For k < 0.1 h/Mpc, the peak bias is deterministic but k-dependent, so the configuration space bias is stochastic and scale dependent, both in real and redshift space. We provide expressions for this stochasticity and its evolution (abridged).

THE TWO- AND THREE-POINT CORRELATION FUNCTIONS OF THE POLARIZED FIVE-YEARWMAPSKY MAPS

We present the two- and three-point real space correlation functions of the five-year WMAP sky maps, and compare the observed functions to simulated LCDM concordance model ensembles. In agreement with previously published results, we find that the temperature correlation functions are consistent with expectations. However, the pure polarization correlation functions are acceptable only for the 33GHz band map; the 41, 61, and 94 GHz band correlation functions all exhibit significant large-scale excess structures. Further, these excess structures very closely match the correlation functions of the two (synchrotron and dust) foreground templates used to correct the WMAP data for galactic contamination, with a cross-correlation statistically significant at the 2sigma-3sigma confidence level. The correlation is slightly stronger with respect to the thermal dust template than with the synchrotron template.

ERRATUM: “RELIABILITY OF THE DETECTION OF THE BARYON ACOUSTIC PEAK” (2009, ApJ, 696, L93)

The correlation function of the distribution of matter in the universe shows, at large scales, baryon acoustic oscillations, which were imprinted prior to recombination. This feature was first detected in the correlation function of the luminous red galaxies (LRG) of the Sloan Digital Sky Survey (SDSS). The final release (DR7) of the SDSS has been recently made available, and the useful volume is about two times bigger than in the old sample. We present here, for the first time, the redshift space correlation function of this sample at large scales together with that for one shallower, but denser volume-limited subsample drawn from the 2dF redshift survey. We test the reliability of the detection of the acoustic peak at about 100 Mpc/h and the behaviour of the correlation function at larger scales by means of careful estimation of errors. We confirm the presence of the peak in the latest data although broader than in previous detections.

Dynamical spin-spin correlation functions in the Kondo model out of equilibrium

We calculate the dynamical spin-spin correlation functions of a Kondo dot coupled to two noninteracting leads held at different chemical potentials. To this end we generalize a recently developed real-time renormalization group method in frequency space (RTRG-FS) to allow the calculation of dynamical correlation functions of arbitrary dot operators in systems describing spin and/or orbital fluctuations. The resulting two-loop RG equations are analytically solved in the weak-coupling regime. This implies that the method can be applied provided either the voltage $V$ through the dot or the external magnetic field $h_0$ are sufficiently large, $\max\{V,h_0\}\gg T_K$, where the Kondo temperature $T_K$ is the scale where the system enters the strong-coupling regime. Explicitly, we calculate the longitudinal and transverse spin-spin correlation and response functions as well as the resulting fluctuation-dissipation ratios. The correlation functions in real-frequency space can be calculated in Matsubara space without the need of any analytical continuation. We obtain analytic results for the line-shape, the small- and large-frequency limits and several other features like the height and width of the peak in the transverse susceptibility at $\Omega\approx\tilde{h}$, where $\tilde{h}$ denotes the reduced magnetic field. Furthermore, we discuss how the developed method can be generalized to calculate dynamical correlation functions of other operators involving reservoir degrees of freedom as well.

FLUID HELIUM-4 IN THERMAL EQUILIBRIUM

The microscopic quantum structure of fluid 4 He may be clearly revealed by a proper decomposition of its spatial correlations into quantum statistical components and direct quantum correlations. This decomposition permits to elucidate the competition between the short-ranged statistical (or particle exchange) correlations and the quantum correlations brought about by the existing strong interparticle repulsion at short relative particle-particle distances. The appropriate method of choice is provided by correlated density-matrix (CDM) theory. It does not only permit a detailed formal analysis of this competition but also allows for a quantitative numerical computation of correlation functions, structure functions, and momentum and energy distributions. The theoretical CDM results for 4 He are, so far as possible, compared with results from path-integral Monte Carlo (PIMC) calculations and with available experimental results. Reported are CDM results on relevant structure functions, correlation functions in coordinate space, kinetic energy distributions, and gross quantitities such as the exchange energy for fluid 4 He . The calculations are performed for normal helium at various temperatures in the range T BE = 2.17 K ≤ T &lt; 14 K .

X-Ray Scattering Studies of the Surface Structure of Complex Oxide Films during Layer-by-Layer Growth via Pulsed Laser Deposition

We report time-resolved X-ray reflectivity and surface diffuse X-ray scattering measurements of the surface evolution during pulsed laser deposition of SrTiO3 thin films. After developing the scattering theory, we illustrate how these data may used to characterize the kinetics of interlayer transport and of the island size distribution during deposition. We then calculate the density-density correlation function in real space and show that it exhibits the expected features.

Constraints on primordial non-Gaussianity from a needlet analysis of theWMAP-5 data

We look for a non-Gaussian signal in the WMAP 5-year temperature anisotropy maps by performing a needlet-based data analysis. We use the foreground-reduced maps obtained by the WMAP team through the optimal combination of the W, V and Q channels, and perform realistic non-Gaussian simulations in order to constrain the non-linear coupling parameter $\fnl$. We apply a third-order estimator of the needlet coefficients skewness and compute the $\chi^2$ statistics of its distribution. We obtain $-80<\fnl<120$ at 95% confidence level, which is consistent with a Gaussian distribution and comparable to previous constraints on the non-linear coupling. We then develop an estimator of $\fnl$ based on the same simulations and we find consistent constraints on primordial non-Gaussianity. We finally compute the three point correlation function in needlet space: the constraints on $\fnl$ improve to $-50<\fnl<110$ at 95% confidence level.

Structural evolution of Cu–Zr metallic glasses under tension

The structural behaviour of Cu 50Zr 50 and Cu 65Zr 35 metallic glasses under uniaxial tensile stress was investigated in situ by high-energy X-ray synchrotron diffraction. The components of the elastic strain tensor were determined from both the change of positions of first maximum of the structure factor in reciprocal space as well as from the maxima of the atomic pair correlation function in real space. The atomic scale strain agrees with the macroscopic strain values. The topological and chemical short-range order of the Cu–Zr glasses changes upon loading. The number density of Cu–Zr and Zr–Zr nearest neighbour atomic pair becomes oriented along the loading direction whereas the partial nearest neighbour distances are only weakly influenced.

Causality and primordial tensor modes

We introduce the real space correlation function of B-mode polarization of the cosmic microwave background (CMB) as a probe of superhorizon tensor perturbations created by inflation.By causality, any non-inflationary mechanism for gravitational wave production after reheating, like global phase transitions or cosmic strings,must have vanishing correlations for angular separations greater than the angle subtended by the particle horizon at recombination, i.e. θ ≳ 2°.Since ordinary B-modes are defined non-locally in terms of the Stokes parameters Q and U and therefore don't have to respect causality, special care is taken to define `causal B̃-modes' for the analysis.We compute the real space B̃-mode correlation function for inflation and discuss its detectability on superhorizon scales where it provides an unambiguous test of inflationary gravitational waves.The correct identification of inflationary tensor modes is crucial since it relates directly to the energy scale of inflation. Wrongly associating tensor modes from causal seeds with inflation would imply an incorrect inference of the energy scale of inflation.We find that the superhorizon B̃-mode signal is above cosmic variance for the angular range 2° < θ < 4° and is therefore in principle detectable. In practice, the signal will be challenging to measure since it requires accurately resolving the recombination peak of the B-mode power spectrum.However, a future CMB satellite (CMBPol), with noise level ΔP ≃ 1μK-arcmin and sufficient resolution to efficiently correct for lensing-induced B-modes, should be able to detect the signal at more than 3σ if the tensor-to-scalar ratio isn't smaller than r ≃ 0.01.

Hierarchical phase space structure of dark matter haloes: Tidal debris, caustics, and dark matter annihilation

Most of the mass content of dark matter haloes is expected to be in the form of tidal debris. The density of debris is not constant, but rather can grow due to formation of caustics at the apocenters and pericenters of the orbit, or decay as a result of phase mixing. In the phase space, the debris assemble in a hierarchy which is truncated by the primordial temperature of dark matter. Understanding this phase structure can be of significant importance for the interpretation of many astrophysical observations and in particular dark matter detection experiments. With this purpose in mind, we develop a general theoretical framework to describe the hierarchical structure of the phase space of cold dark matter haloes. We do not make any assumption of spherical symmetry and/or smooth and continuous accretion. Instead, working with correlation functions in the action-angle space, we can fully account for the hierarchical structure (predicting a two-point correlation function ~ (\Delta J)^{-1.6} in the action space), as well as the primordial discreteness of the phase space. As an application, we estimate the boost to the dark matter annihilation signal due to the structure of the phase space within virial radius: the boost due to the hierarchical tidal debris is of order unity, whereas the primordial discreteness of the phase structure can boost the total annihilation signal by up to an order of magnitude. The latter is dominated by the regions beyond 20% of the virial radius, and is largest for the recently formed haloes with the least degree of phase mixing.

Recovering the real-space correlation function from photometric redshift surveys

Measurements of clustering in large-scale imaging surveys that make use of photometric redshifts depend on the uncertainties in the redshift determination. We have used light-cone simulations to show how the deprojection method successfully recovers the real space correlation function when applied to mock photometric redshift surveys. We study how the errors in the redshift determination affect the quality of the recovered two-point correlation function. Considering the expected errors associated to the planned photometric redshift surveys, we conclude that this method provides information on the clustering of matter useful for the estimation of cosmological parameters that depend on the large scale distribution of galaxies.

Clustering of luminous red galaxies - II. Small-scale redshift-space distortions

This is the second paper of a series where we study the clustering of LRG galaxies in the latest spectroscopic SDSS data release, DR6, which has 75000 LRG galaxies covering over 1 $Gpc^3/h^3$ for $0.15<z<0.47$. Here we focus on modeling redshift space distortions in $\xisp$, the 2-point correlation in separate line-of-sight and perpendicular directions, at small scales and in the line-of-sight. We show that a simple Kaiser model for the anisotropic 2-point correlation function in redshift space, convolved with a distribution of random peculiar velocities with an exponential form, can describe well the correlation of LRG at all scales. We show that to describe with accuracy the so called "fingers-of-God" (FOG) elongations in the radial direction, it is necessary to model the scale dependence of both bias $b$ and the pairwise rms peculiar velocity $\sigma_{12}$ with the distance. We show how both quantities can be inferred from the $\xisp$ data. From $r \simeq 10$ Mpc/h to $r \simeq 1$ Mpc/h, both the bias and $\sigma_{12}$ are shown to increase by a factor of two: from $b=2$ to $b=4$ and from $\sigma_{12}=400$ to 800 Km/s. The later is in good agreement, within a 5 percent accuracy in the recovered velocities, with direct velocity measurements in dark matter simulations with $\Omega_m=0.25$ and $\sigma_8$=0.85.

Space-Time Correlations in Two Subsonic Jets Using Dual Particle Image Velocimetry Measurements

half-velocity diameter in reference to length in the shear layer and on the jet axis, respectively. From these results, a discussion on the modeling of turbulence in jets is addressed. The self-similarity of some space correlation functions in the shear layer and on the jet axis is shown. Furthermore, far enough downstream in the shear layer, some of the ratios between the space and time scales are relatively close to the values expected in homogeneous and isotropic turbulence. It is also found that the ratio between the integral length and the time scales in the fixed frame is of the order of the local mean flow velocity. In the convected frame, the appropriate scaling factor is the rms velocity.

3D pion source functions from the AMPT model

We use the AMPT model to study pion source functions in Au+Au collisions at RHIC together with the corresponding correlation functions in momentum space. Partonic interactions are shown to significantly affect the three-dimensional source functions as well as the correlation functions. Results from the AMPT with string melting agree reasonably with the RHIC data in the side and long directions, but they exhibit different shapes than the data in the out direction. These comparisons provide the basis for further investigations of the cause of the discrepancies.