Point Correlation Function Research Articles

Exactly solvable inhomogeneous fermion systems

Abstract 15 exactly solvable inhomogeneous (spinless) fermion systems on one-dimensional lattices are constructed explicitly based on the discrete orthogonal polynomials of Askey scheme, e.g. the Krawtchouk, Hahn, Racah, Meixner, q-Racah polynomials. The Schrödinger and Heisenberg equations are solved explicitly, as the entire set of the eigenvalues and eigenstates are known explicitly. The ground state two point correlation functions are derived explicitly. The multi point correlation functions are obtained by Wick’s Theorem. Corresponding 15 exactly solvable XX spin systems are also displayed. They all have nearest neighbour interactions. The exact solvability of Schrödinger equation means that of the corresponding Fokker-Planck equation. This leads to 15 exactly solvable Birth and Death fermions and 15 Birth and Death spin models. These provide plenty of materials for calculating interesting quantities, e.g. entanglement entropy, etc.

Inverse problem of correlation functions in holography

This paper shows that the bulk metric of a planar/spherically/hyperbolically symmetric asymptotically anti-de Sitter static black brane/hole can be reconstructed from its boundary frequency 2-point correlation functions of two probe scalar operators by solving Gel’fand-Levitan-Marchenko integral equation. Since the frequency correlation function is easily handled in experiments and theories, this paper not only proposes a new method to “measure” the corresponding holographic spacetime for a material that has holographic dual but also provides an approach to experimentally check if a system has holographic dual.

Quantifying the impact of AGN feedback on the large-scale matter distribution using two- and three-point statistics

Abstract Feedback from active galactic nuclei (AGN) plays a critical role in shaping the matter distribution on scales comparable to and larger than individual galaxies. Upcoming surveys such as Euclid and LSST aim to precisely quantify the matter distribution on cosmological scales, making a detailed understanding of AGN feedback effects essential. Hydrodynamical simulations provide an informative framework for studying these effects, in particular by allowing us to vary the parameters that determine the strength of these feedback processes and, consequently, to predict their corresponding impact on the large-scale matter distribution. We use the EAGLE simulations to explore how changes in subgrid viscosity and AGN heating temperature affect the matter distribution, quantified via 2- and 3-point correlation functions, as well as higher order cumulants of the matter distribution. We find that varying viscosity has a small impact ($\approx 10~{{\%}}$) on scales larger than 1h−1 Mpc, while changes to the AGN heating temperature lead to substantial differences, with up to 70% variation in gas clustering on small scales (≲ 1h−1 Mpc). By examining the suppression of the power spectrum as a function of time, we identify the redshift range z = 1.5 − 1 as a key epoch where AGN feedback begins to dominate in these simulations. The 3-point function provides complementary insight to the more familiar 2-point statistics, and shows more pronounced variations between models on the scale of individual haloes. On the other hand, we find that effects on even larger scales are largely comparable.

A foray on SCFT3 via super spinor-helicity and Grassmann twistor variables

In this paper, we develop a momentum super space formalism for N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1, 2 superconformal field theories in three dimensions. First, we solve for super-correlators in the usual momentum superspace variables. However, we found that expressing quantities in super space spinor helicity variables greatly simplifies the analysis. Further, by performing a “half” Fourier transform of the Grassmann coordinates which is analogous to the Twistor transform, an even more remarkable simplification occurs. Using this formalism, we first compute all three point correlation functions involving conserved super-currents with arbitrary spins in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1, 2 theories. We discover interesting double copy relations in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 super-correlators. Further, we discovered super double copy relations that take us from N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 to N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 super-correlators. We also extend our results to correlators involving scalars as well as to higher points. Further, we comment on the connection of our results with the flat space super amplitudes in one higher dimension.

Loops in AdS: from the spectral representation to position space. Part III

We study loop amplitudes in anti de-Sitter space via the spectral representation. We consider loops of spinning fields and in particular gauge fields, and derive various identities connecting different families of loop diagrams, at different number of loops, different spins, different masses. Such identities are useful for the computation of Witten diagrams. Considering the theory of large-Nf conformal scalar QED defined on AdS space, we derive an analytic expression for the exact 4-point correlation function at sub-leading order in 1Nf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{N_f} $$\\end{document}. Additionally, we derive analytic expressions for bulk 2-point functions and boundary 4-point functions for various families of diagrams, which we denote as “blob diagrams”. Finally we study 4-point ladder diagrams with spinning fields, and we derive integral expressions for the spectral representation of a k-loop ladder diagram.

Generalized autocorrelation function in the family of deterministic and stochastic anomalous diffusion processes

We investigate the observables of the one-dimensional model for anomalous transport in semiconductor devices where diffusion arises from scattering at dislocations at fixed random positions, known as the Lévy-Lorentz gas. To gain insight into the microscopic properties of such a stochastically complex system, deterministic dynamics known as the slicer map and fly-and-die dynamics are used. We analytically derive the generalized position autocorrelation function of these dynamics and study the special case, the 3-point position correlation function. For this, we derive single-parameter-dependent scaling and compare it with the numerically estimated 3-point position autocorrelation of the Lévy-Lorentz gas, for which the analytical expression is still an open question. Here we obtained a remarkable agreement between them, irrespective of any functional relationship with time. Moreover, we demonstrate that the position moments and the position autocorrelations of these systems scale in the same fashion, provided the times are large enough and far enough apart. Other observables, such as velocity moments and correlations, are reported to distinguish the systems. Published by the American Physical Society 2024

Averages of products of characteristic polynomials and the law of real eigenvalues for the real Ginibre ensemble

We review an elementary derivation of the Borodin–Sinclair–Forrester–Nagao Pfaffian point process, which characterizes the law of real eigenvalues for the real Ginibre ensemble in the large matrix size limit, in terms of averages of products of characteristic polynomials. This derivation relies on a number of interesting structures associated with the real Ginibre ensemble such as the hidden symplectic symmetry of the statistics of real eigenvalues. It leads to a representation for the [Formula: see text]-point correlation function for any [Formula: see text] in terms of an integral over the symmetric space [Formula: see text] and this paper gives the proof of asymptotic exactness for this integral.

Equation and solution for the 4-point correlation function of galaxies in the Gaussian approximation and its parity-odd part

Equation and solution for the 4-point correlation function of galaxies in the Gaussian approximation and its parity-odd part

Cosmological constraints from the EFT power spectrum and tree-level bispectrum of 21 cm intensity maps

We explore the information content of 21 cm intensity maps in redshift space using the 1-loop Effective Field Theory power spectrum model and the bispectrum at tree level. The 21 cm signal contains signatures of dark matter, dark energy and the growth of large-scale structure in the Universe. These signatures are typically analysed via the 2-point correlation function or power spectrum. However, adding the information from the 3-point correlation function or bispectrum will be crucial to exploiting next-generation intensity mapping experiments. The bispectrum could offer a unique opportunity to break key parameter degeneracies that hinder the measurement of cosmological parameters and improve on the precision. We use a Fisher forecast analysis to estimate the constraining power of the HIRAX survey on cosmological parameters, dark energy and modified gravity.

The DESI one-per cent survey: exploring the halo occupation distribution of luminous red galaxies and quasi-stellar objects with AbacusSummit

ABSTRACT We present the first comprehensive halo occupation distribution (HOD) analysis of the Dark Energy Spectroscopic Instrument (DESI) One-Percent Survey luminous red galaxy (LRG) and Quasi Stellar Object (QSO) samples. We constrain the HOD of each sample and test possible HOD extensions by fitting the redshift-space galaxy 2-point correlation functions in 0.15 < r < 32 h−1 Mpc in a set of fiducial redshift bins. We use AbacusSummit cubic boxes at Planck 2018 cosmology as model templates and forward model galaxy clustering with the AbacusHOD package. We achieve good fits with a standard HOD model with velocity bias, and we find no evidence for galaxy assembly bias or satellite profile modulation at the current level of statistical uncertainty. For LRGs in 0.4 < z < 0.6, we infer a satellite fraction of $f_\mathrm{sat} = 11\pm 1~{y{\ \mathrm{per\,cent}}}$, a mean halo mass of $\log _{10}\overline{M}_h/M_\odot =13.40^{+0.02}_{-0.02}$, and a linear bias of $b_\mathrm{lin} = 1.93_{-0.04}^{+0.06}$. For LRGs in 0.6 < z < 0.8, we find $f_\mathrm{sat}=14\pm 1~{{\ \mathrm{per\,cent}}}$, $\log _{10}\overline{M}_h/M_\odot =13.24^{+0.02}_{-0.02}$, and $b_\mathrm{lin}=2.08_{-0.03}^{+0.03}$. For QSOs, we infer $f_\mathrm{sat}=3^{+8}_{-2}\mathrm{per\,cent}$, $\log _{10}\overline{M}_h/M_\odot = 12.65^{+0.09}_{-0.04}$, and $b_\mathrm{lin} = 2.63_{-0.26}^{+0.37}$ in redshift range 0.8 < z < 2.1. Using these fits, we generate a large suite of high fidelity galaxy mocks, forming the basis of systematic tests for DESI Y1 cosmological analyses. We also study the redshift-evolution of the DESI LRG sample from z = 0.4 up to z = 1.1, revealling significant and interesting trends in mean halo mass, linear bias, and satellite fraction.

A comparative study of two correlation functions applying to the quantitative characterization of the pore structure within hardened concrete

The paper presents a comparative study between the autocorrelation function (ACF) and the 2-point correlation function (2PCF) for the quantitative analysis of the pore structure within hardened concrete via the image analysis technique. This work was carried out on five cross-sectional images of concrete specimens with varying area porosities ranging from 2.6% to 21.2%. This research indicates that: (i) the ACF provides a comprehensive and effective tool that is capable of capturing the contribution of the area porosity, size, and orientation of the pores in quantifying the pore structure within hardened concrete, while the 2PCF only enables quantifying the size and spacing between the pores; (ii) the ACF requires the cross-sectional images to be square, whereas the 2PCF can analyze images of any size and shape; (iii) for an area porosity below 20%, the characteristic size of the pore structure within hardened concrete, determined by both the ACF and 2PCF approaches, is not significantly different; (iv) on average, the correlation length estimated by 2PCF is more than 1.6 times greater than the corresponding value determined by ACF; and (v) the characteristic size provides a more accurate and comprehensive quantification of the pore structure within hardened concrete specimens than the correlation length.

Wave-optics limit of the stochastic gravitational wave background

The stochastic gravitational wave background (SGWB) is a rich resource of cosmological information, encoded both in its source statistics and anisotropies induced by propagation effects. We provide a theoretical description of it, without employing tools which rely on the geometric optics assumption. Our formalism is based on the so-called classical matter approximation and it is able to capture wave-optics effects, such as interference and diffraction. We show that the interaction between the gravitational waves and the cosmic structures along the line-of-sight produce observable scalar and vector polarization modes, on top of modulating the tensorial ones. We build the two point correlation function describing the statistics of the SGWB, and introduce the intensity and gravitational Stokes parameters for all its components. In the case of an unpolarized, Gaussian and statistically homogeneous SGWB, we show that the interaction with matter modulates its intensity and does not generate a net difference between left- and right-helicity tensor and vector modes, as expected. We demonstrate that, in order to produce QT- and UT-tensor polarization modes the background must possess a hexadecapole anisotropy, while a quadrupole anisotropy can source the vector QV- and UV-Stokes parameters.

Primordial non-Gaussianities with weak lensing: information on non-linear scales in the Ulagam full-sky simulations

Primordial non-Gaussianities (PNGs) are signatures in the density field that encode particle physics processes from the inflationary epoch. Such signatures have been extensively studied using the Cosmic Microwave Background, through constraining their amplitudes, fX NL, with future improvements expected from large-scale structure surveys; specifically, the galaxy correlation functions. We show that weak lensing fields can be used to achieve competitive and complementary constraints. This is shown via the Ulagam suite of N-body simulations, a subset of which evolves primordial fields with four types of PNGs. We create full-sky lensing maps and estimate the Fisher information from three summary statistics measured on the maps: the moments, the cumulative distribution function, and the 3-point correlation function. We find that the year 10 sample from the Rubin Observatory Legacy Survey of Space and Time (LSST) can constrain PNGs to σ(f NL eq) ≈ 110, σ(f NL or, lss) ≈ 120, σ(f NL loc) ≈ 40. For the former two, this is better than or comparable to expected galaxy clustering-based constraints from the Dark Energy Spectroscopic Instrument (DESI). The PNG information in lensing fields is on non-linear scales and at low redshifts (z ≲ 1.25), with a clear origin in the evolution history of massive halos. The constraining power degrades by ∼60% under scale cuts of ≳ 20 Mpc, showing there is still significant information on scales mostly insensitive to small-scale systematic effects (e.g., baryons). We publicly release the Ulagam suite to enable more survey-focused analyses.

Effective field theory of particle mixing

We introduce an effective field theory to study mixing of two fields induced by their couplings to a common decay channel in a medium. The extension of the method of Lee, Oehme, and Yang, the cornerstone of analysis of CP violation in flavored mesons, to include the mixing of particles with different masses provides a guide to and benchmark for the effective field theory. The analysis reveals subtle caveats in the description of mixing in terms of the widely used non-Hermitian effective Hamiltonian, more acute in the nondegenerate case. The effective field theory describes the dynamics of field mixing where the common intermediate states populate a bath in thermal equilibrium, as an . We obtain the effective action up to second order in the couplings, where indirect mixing is a consequence of off-diagonal self-energy components. We find that if only one of the mixing fields features an initial expectation value, indirect mixing induces an expectation value of the other field. The equal time two point correlation functions exhibit an asymptotic approach to a stationary thermal state, and the emergence of long-lived coherence which displays quantum beats as a consequence of interference of quasinormal modes in the medium. The amplitudes of the quantum beats are resonantly enhanced in the nearly degenerate case with potential observational consequences. Published by the American Physical Society 2024

The sound horizon scale at the baryon drag epoch

We study how to measure the sound horizon scale at the baryon drag epoch, rs , a parameter considered a cosmological standard ruler, from the 2-point correlation function analysis. This important parameter is originated in the baryon acoustic oscillations (BAO) phenomenon, which supports the large-scale structure scenario of the ΛCDM cosmological model, and provides valuable information of the dynamical evolution of the Universe. For this, one of the aims of current astronomical surveys is to know this parameter with high precision. Here we study how to correctly extract the BAO sound horizon scale in case where the signature is weak because there are few correlated pairs, sourced from the BAO phenomenon, probably due to non-linear evolution processes.

CFT thermal 2-point function

This is a short review of our recent work [B. Bajc and A. R. Lugo, arXiv:2212.13639 [hep-th]] with some new original results. We numerically calculate the conformal two point correlation function of operators with arbitrary scale dimension up to order [Formula: see text] in the low temperature expansion. We analytically compute its large scale dimension limit up to the same order.

Impact of tidal environment on galaxy clustering in GAMA

ABSTRACT We constrain models of the galaxy distribution in the cosmic web using data from the Galaxy and Mass Assembly (GAMA) survey. We model the redshift-space behaviour of the 2-point correlation function (2pcf) and the recently proposed Voronoi volume function (VVF) – which includes information beyond two-point statistics. We extend the standard halo model using extra satellite degrees of freedom and two assembly bias parameters: αcen and αsat, which correlate the occupation numbers of central and satellite galaxies with their host halo’s tidal environment, respectively. We measure $\alpha _{\rm sat}=1.44^{+0.25}_{-0.43}$ and $\alpha _{\rm cen}=-0.79^{+0.29}_{-0.11}$ using a combination of 2pcf and VVF measurements, representing a detection of assembly bias at the 3.3σ (2.4σ) significance level for satellite (central) galaxies. This result remains robust to possible anisotropies in the halocentric distribution of satellites as well as technicalities of estimating the data covariance. We show that the growth rate (fσ8) deduced using models with assembly bias is about 7 per cent (i.e. 1.5σ) lower than if assembly bias is ignored. When projected on to the Ωm–σ8 plane, the model constraints without assembly bias overlap with Planck expectations, while allowing assembly bias introduces significant tension with Planck, preferring either a lower Ωm or a lower σ8. Finally, we find that the all-galaxy weak-lensing signal is unaffected by assembly bias, but the central and satellite sub-populations individually show significantly different signals in the presence of assembly bias. Our results illustrate the importance of accurately modelling galaxy formation for cosmological inference from future surveys.

Spectral representation of Matsubara n-point functions: Exact kernel functions and applications

In the field of quantum many-body physics, the spectral (or Lehmann) representation simplifies the calculation of Matsubara nn-point correlation functions if the eigensystem of a Hamiltonian is known. It is expressed via a universal kernel function and a system- and correlator-specific product of matrix elements. Here we provide the kernel functions in full generality, for arbitrary nn, arbitrary combinations of bosonic or fermionic operators and an arbitrary number of anomalous terms. As an application, we consider bosonic 3- and 4-point correlation functions for the fermionic Hubbard atom and a free spin of length SS, respectively.

Beyond 3×2-point cosmology: the integrated shear and galaxy 3-point correlation functions

We present the integrated 3-point correlation functions (3PCF) involving both the cosmic shear and the galaxy density fields. These are a set of higher-order statistics that describe the modulation of local 2-point correlation functions (2PCF) by large-scale features in the fields, and which are easy to measure from galaxy imaging surveys. Based on previous works on the shear-only integrated 3PCF, we develop the theoretical framework for modelling 5 new statistics involving the galaxy field and its cross-correlations with cosmic shear. Using realistic galaxy and cosmic shear mocks from simulations, we determine the regime of validity of our models based on leading-order standard perturbation theory with an MCMC analysis that recovers unbiased constraints of the amplitude of fluctuations parameter A s and the linear and quadratic galaxy bias parameters b 1 and b 2. Using Fisher matrix forecasts for a DES-Y3-like survey, relative to baseline analyses with conventional 3×2PCFs, we find that the addition of the shear-only integrated 3PCF can improve cosmological parameter constraints by 20–40%. The subsequent addition of the new statistics introduced in this paper can lead to further improvements of 10–20%, even when utilizing only conservatively large scales where the tree-level models are valid. Our results motivate future work on the galaxy and shear integrated 3PCFs, which offer a practical way to extend standard analyses based on 3×2PCFs to systematically probe the non-Gaussian information content of cosmic density fields.

Probing cosmic homogeneity in the Local Universe

ABSTRACT We investigate the transition scale to homogeneity, RH, using as cosmic tracer the spectroscopic sample of blue galaxies from the Sloan Digital Sky Survey (SDSS). Considering the spatial distribution of the galaxy sample, we compute the two point correlation function ξ(r), the scaled counts in spheres $\mathcal {N}(\lt r)$, and the fractal dimension $\mathcal {D}_2(r)$ to quantify the homogeneity scale in the Local Universe (0.04 < z < 0.20). The sample in analysis is compared with random and mock catalogues with the same geometry, and the same number of synthetic cosmic objects as the data set, to calculate the covariance matrix for the errors determination. The criteria adopted for the transition-to-homogeneity follows the literature, it is attained when $\mathcal {D}_2(r)$ reaches the 1 per cent level of the limit value 3 (i.e. where it reaches 2.97) as the scale increases. We obtain RH = 70.33 ± 10.74 Mpc h−1, at the effective redshift zeff = 0.128, for a sample containing $150\, 302$ SDSS blue galaxies with 0.04 < z < 0.20. Additionally, we perform robustness tests by analysing the homogeneity scale in sub-volumes of the original one, obtaining coherent results; we also check for a possible artefact in our procedure examining a homogeneous synthetic data set as a pseudo-data, verifying that such systematic is absent. Because our analyses concentrate in data at low redshifts, z < 0.20, we find interesting to use cosmography to calculate the radial comoving distances; therefore in this subject our analyses do not use fiducial cosmological model. For completeness, we evaluate the difference of the comoving distances estimation using cosmography and fiducial cosmology.