scholarly journals A Supersymmetric Hierarchical Model for Weakly Disordered 3d Semimetals

2020 ◽  
Vol 21 (11) ◽  
pp. 3499-3574
Author(s):  
Giovanni Antinucci ◽  
Luca Fresta ◽  
Marcello Porta
Keyword(s):  
Multiscale Analysis ◽  
Three Dimensional ◽  
Quantum Systems ◽  
Supersymmetric Model ◽  
Energy Bands ◽  
Algebraic Decay ◽  
Group Methods ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Renormalization Group Methods

Abstract In this paper, we study a hierarchical supersymmetric model for a class of gapless, three-dimensional, weakly disordered quantum systems, displaying pointlike Fermi surface and conical intersections of the energy bands in the absence of disorder. We use rigorous renormalization group methods and supersymmetry to compute the correlation functions of the system. We prove algebraic decay of the two-point correlation function, compatible with delocalization. A main technical ingredient is the multiscale analysis of massless bosonic Gaussian integrations with purely imaginary covariances, performed via iterative stationary phase expansions.

scholarly journals Wide-angle effects on galaxy ellipticity correlations

2021 ◽  
Author(s):  
Maresuke Shiraishi ◽  
Atsushi Taruya ◽  
Teppei Okumura ◽  
Kazuyuki Akitsu
Keyword(s):  
Cosmological Parameters ◽  
Three Dimensional ◽  
New Physics ◽  
Opening Angle ◽  
Wide Angle ◽  
Galaxy Surveys ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Cross Correlations ◽  
Three Dimensional Configuration

Abstract We show an efficient way to compute wide-angle or all-sky statistics of galaxy intrinsic alignment in three-dimensional configuration space. For this purpose, we expand the two-point correlation function using a newly introduced spin-dependent tripolar spherical harmonic basis. Therefore, the angular dependences on the two line-of-sight (LOS) directions pointing to each pair of objects, which are degenerate with each other in the conventional analysis under the small-angle or plane-parallel (PP) approximation, are unambiguously decomposed. By means of this, we, for the first time, compute the wide-angle auto and cross correlations between intrinsic ellipticities, number densities and velocities of galaxies, and compare them with the PP-limit results. For the ellipticity-ellipticity and density-ellipticity correlations, we find more than $10\%$ deviation from the PP-limit results if the opening angle between two LOS directions exceeds 30○ − 50○. It is also shown that even if the PP-limit result is strictly zero, the non-vanishing correlation is obtained over the various scales, arising purely from the curved-sky effects. Our results indicate the importance of the data analysis not relying on the PP approximation in order to determine the cosmological parameters more precisely and/or find new physics via ongoing and forthcoming wide-angle galaxy surveys.

scholarly journals Photometric Calibration and Large-Scale Clustering in the Universe

1994 ◽  
Vol 161 ◽  
pp. 295-300
Author(s):  
R. Fong ◽  
N. Metcalfe ◽  
T. Shanks
Keyword(s):  
Correlation Function ◽  
Large Scale ◽  
Three Dimensional ◽  
High Signal ◽  
Galaxy Surveys ◽  
Photometric Calibration ◽  
Peculiar Velocities ◽  
Redshift Surveys ◽  
Point Correlation ◽  
Point Correlation Function

The machine measurements of UK Schmidt plates have produced two very large galaxy surveys, the APM survey and the Edinburgh-Durham Southern Galaxy Catalogue (or COSMOS survey). These surveys can constrain the power on large scales of ≳ 10h −1 Mpc better than current redshift surveys, simply because such large numbers, ≳ 2 million galaxies to bJ ≤ 20.5, provide very high signal/noise in the estimated two-point correlation function for galaxies. Furthermore, the results for the three-dimensional galaxy two point correlation function, ξ(r), obtained from the measured projected function, ω(θ), should be quite robust for reasonable model number-redshift distributions, N(z), for these magnitude limits (see, e.g., Roche et al. 1993). Another clear advantage of measuring ω(θ) is that it is unaffected by the peculiar velocities of the galaxies, whereas they have an important effect on the corresponding ξ,(s) using galaxy redshift surveys.

scholarly journals CORRELATION FUNCTIONS OF A CONFORMAL FIELD THEORY IN THREE DIMENSIONS

1996 ◽  
Vol 11 (13) ◽  
pp. 1047-1059 ◽  
Author(s):  
S. GURUSWAMY ◽  
P. VITALE
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Correlation Functions ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Radius Of Curvature ◽  
Nonlinear Sigma Model ◽  
Long Distance ◽  
Point Correlation ◽  
Point Correlation Function

We derive explicit forms of the two-point correlation functions of the O(N) nonlinear sigma model at the critical point, in the large-N limit, on various three-dimensional manifolds of constant curvature. The two-point correlation function, G(x, y), is the only n-point correlation function which survives in this limit. We analyze the short distance and long distance behaviors of G(x, y). It is shown that G(x, y) decays exponentially with the Riemannian distance on the spaces R2×S1, S1×S1×R, S2×R, H2×R. The decay on R3 is of course a power law. We show that the scale for the correlation length is given by the geometry of the space and therefore the long distance behavior of the critical correlation function is not necessarily a power law even though the manifold is of infinite extent in all directions; this is the case of the hyperbolic space where the radius of curvature plays the role of a scale parameter. We also verify that the scalar field in this theory is a primary field with weight [Formula: see text]; we illustrate this using the example of the manifold S2×R whose metric is conformally equivalent to that of R3–{0} up to a reparametrization.

scholarly journals UV background fluctuations and three-point correlations in the large-scale clustering of the Lyman α forest

2019 ◽  
Vol 487 (4) ◽  
pp. 5346-5362 ◽  
Author(s):  
Suk Sien Tie ◽  
David H Weinberg ◽  
Paul Martini ◽  
Wei Zhu ◽  
Sébastien Peirani ◽  
...  
Keyword(s):  
Correlation Function ◽  
Large Scale ◽  
Signal To Noise Ratio ◽  
Mass Density ◽  
Three Dimensional ◽  
Mean Free Path ◽  
Density Fluctuations ◽  
Data Sets ◽  
Point Correlation ◽  
Point Correlation Function

ABSTRACT Using the Lyman α (Lyα) Mass Association Scheme, we make theoretical predictions for the three-dimensional three-point correlation function (3PCF) of the Lyα forest at redshift z = 2.3. We bootstrap results from the (100 h−1 Mpc)3 Horizon hydrodynamic simulation to a (1 h−1 Gpc)3N-body simulation, considering both a uniform ultraviolet background (UVB) and a fluctuating UVB sourced by quasars with a comoving nq ≈ 10−5h3 Mpc−3 placed either in massive haloes or randomly. On scales of 10–30 h−1 Mpc, the flux 3PCF displays hierarchical scaling with the square of the two-point correlation function (2PCF), but with an unusual value of Q ≡ ζ123/(ξ12ξ13 + ξ12ξ23 + ξ13ξ23) ≈ −4.5 that reflects the low bias of the Lyα forest and the anticorrelation between mass density and transmitted flux. For halo-based quasars and an ionizing photon mean free path of λ = 300 h−1 Mpc comoving, UVB fluctuations moderately depress the 2PCF and 3PCF, with cancelling effects on Q. For λ = 100 or 50 h−1 Mpc, UVB fluctuations substantially boost the 2PCF and 3PCF on large scales, shifting the hierarchical ratio to Q ≈ −3. We scale our simulation results to derive rough estimate of the detectability of the 3PCF in current and future observational data sets for the redshift range z = 2.1–2.6. At r = 10 and 20 h−1 Mpc, we predict a signal-to-noise ratio (SNR) of ∼9 and ∼7, respectively, for both Baryon Oscillation Spectroscopic Survey (BOSS) and extended BOSS (eBOSS), and ∼37 and ∼25 for Dark Energy Spectroscopic Instrument (DESI). At r = 40 h−1 Mpc the predicted SNR is lower by a factor of ∼3–5. Measuring the flux 3PCF would provide a novel test of the conventional paradigm of the Lyα forest and help separate the contributions of UVB fluctuations and density fluctuations to Lyα forest clustering, thereby solidifying its foundation as a tool of precision cosmology.

scholarly journals Galaxy Clustering to B = 27M

1994 ◽  
Vol 161 ◽  
pp. 635-643
Author(s):  
N. Roche ◽  
T. Shanks ◽  
N. Metcalfe ◽  
R. Fong
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Redshift Distribution ◽  
Galaxy Clustering ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Luminosity Evolution

The angular two-point correlation function, ω(θ), for galaxies can be used as a probe of their redshift distribution N(z) and, therefore, of galaxy luminosity evolution. Without redshift data, we can still observe the projection onto the two-dimensional sky of the three-dimensional clustering of galaxies. The autocorrelation of this projected distribution is described by ω(θ). Observations have indicated that ω(θ) follows a θ−0.8 power-law (Peebles 1980) and that the index of the power-law remains approximately constant to the faintest limits of photographic surveys (Jones, Shanks & Fong 1987).

Simulation and Modeling of Turbulent Flows

1996 ◽  
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Simulation And Modeling ◽  
Simulation Techniques ◽  
Rational Development ◽  
Group Methods ◽  
Turbulent Closure ◽  
The Subject ◽  
Renormalization Group Methods

This book provides students and researchers in fluid engineering with an up-to-date overview of turbulent flow research in the areas of simulation and modeling. A key element of the book is the systematic, rational development of turbulence closure models and related aspects of modern turbulent flow theory and prediction. Starting with a review of the spectral dynamics of homogenous and inhomogeneous turbulent flows, succeeding chapters deal with numerical simulation techniques, renormalization group methods and turbulent closure modeling. Each chapter is authored by recognized leaders in their respective fields, and each provides a thorough and cohesive treatment of the subject.

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

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