Density-density Correlation Research Articles

New Estimator for Gravitational Lensing Using Galaxy and Intensity Mapping Surveys.

We introduce the galaxy intensity mapping cross-correlation estimator (GIMCO), which is a new tomographic estimator for the gravitational lensing potential, based on a combination of intensity mapping (IM) and galaxy number counts. The estimator can be written schematically as IM(z_{f})×galaxy(z_{b})-galaxy(z_{f})×IM(z_{b}) for a pair of distinct redshifts (z_{f},z_{b}); this combination allows to greatly reduce the contamination by density-density correlations, thus isolating the lensing signal. As an estimator constructed only from cross-correlations, it is additionally less susceptible to systematic effects. We show that the new estimator strongly suppresses cosmic variance and consequently improves the signal-to-noise ratio (SNR) for the detection of lensing, especially on linear scales and intermediate redshifts. For cosmic variance dominated surveys, the SNR of our estimator is a factor of 30 larger than the SNR obtained from the correlation of galaxy number counts only. Shot noise and interferometer noise reduce the SNR. For the specific example of the dark energy survey (DES) cross-correlated with the hydrogen intensity mapping and real time analysis experiment (HIRAX), the SNR is around four, whereas for Euclid cross-correlated with HIRAX it reaches 52. This corresponds to an improvement of a factor of 4-5 compared to the SNR from DES alone. For Euclid cross-correlated with HIRAX the improvement with respect to Euclid alone strongly depends on the redshift. We find that the improvement is particularly important for redshifts below 1.6, where it reaches a factor of 5. This makes our estimator especially valuable to test dark energy and modified gravity, that are expected to leave an impact at low and intermediate redshifts.

The solvent mediated interaction potential between solute particles: theory and applications.

In this paper we develop a theory to calculate the solvent mediated interaction potential between solute particles dispersed in a solvent. The potential is a functional of the instantaneous distribution of solute particles and is expressed in terms of the solute-solvent direct pair correlation function and the density-density correlation function of the bulk solvent. The dependence of the direct pair correlation function on multi-point correlations of the solute distribution is simplified with a mean field approximation. A self consistent approach is developed to calculate the effective potential between solute particles, the solute-solvent and the solute-solute correlation functions. The significance of the solvent fluctuations on the range of the effective potential is elucidated. The theory is applied to calculate equilibrium properties of the Asakura-Oosawa (AO) model for several values of solute and solvent densities and for several values of the particles size ratio. The results give a quantitative description of many-body effect on the effective potential and on the pair correlation functions.

Evolution of Critical Correlations at the QCD Phase Transition

We investigate the evolution of the density-density correlations in the isoscalar critical condensate formed at the QCD critical point. The initial equilibrium state of the system is characterized by a fractal measure determining the distribution of isoscalar particles (sigmas) in configuration space. Non-equilibrium dynamics is induced through a sudden symmetry breaking leading gradually to the deformation of the initial fractal geometry. After constructing an ensemble of configurations describing the initial state of the isoscalar field we solve the equations of motion and show that remnants of the critical state and the associated fractal geometry survive for time scales larger than the time needed for the mass of the isoscalar particles to reach the two-pion threshold. This result is more transparent in an event-by-event analysis of the phenomenon. Thus, we conclude that the initial fractal properties can eventually be transferred to the observable pion-sector through the decay of the sigmas even in the case of a quench.

Charge density response and fake plasmons in holographic models with strong translation symmetry breaking

We study the charge density response in holographic models with explicit trans- lation symmetry breaking which is relevant in IR. In particular, we focus on Q-lattices and the Bianchy VII helix. We show that the hydrodynamic sound mode is removed from the spectrum due to the strong momentum relaxation and therefore, the usual treatment of the plasmon as Coulomb-dressed zero sound does not apply. Furthermore, the dominant coherent modes in the longitudinal channel, which control the neutral density-density correlator, are the diffusive modes. We show these modes are strongly suppressed when the boundary Coulomb interaction is turned on. This renders the low frequency charge density response spectrum completely incoherent and featureless.At intermediate frequencies, we observe a broad feature — the fake plasmon — in the dressed correlator, which could be confused with an overdamped plasmon. However, its gap is set by the scale of translation symmetry breaking instead of the plasma frequency. This broad feature originates from the non-hydrodynamic sector of the holographic spectrum, and therefore, its behaviour, typical of strongly correlated quantum critical systems with holographic duals, deviates from the standard Fermi-liquid paradigm.

Structure factor of fluctuating interfaces: From liquid surfaces to suspended graphene

We obtain the density-density correlation structure in molecular dynamics (MD) simulations of graphene, and analyze it within the capillary wave theory (CWT), developed for fluid surfaces, to describe the thermal corrugations of the graphene sheet with a wave-vector-dependent surface tension $\ensuremath{\gamma}({q}_{x})$. The density correlation function (from the atomic positions) is compared with the theoretical prediction by Bedeaux and Weeks (BW), within the CWT, in terms of $\ensuremath{\gamma}({q}_{x})$ and the density profile. The agreement is very good, even for relatively large ${q}_{x}\ensuremath{\approx}0.2{\AA{}}^{\ensuremath{-}1}$, and with very little role for the correlation background, which sets an important difficulty for liquid surfaces. We present and test a generic prediction for the structure factor $S({q}_{x},{q}_{z})$ from $\ensuremath{\gamma}({q}_{x})$, that contains and goes beyond the classical asymptotic expression, developed by Sinha, for the analysis of x-ray surface scattering. We compare our prediction with the formula used in the interpretation of experimental data, that assumes a direct relationship between $\ensuremath{\gamma}({q}_{x})$ and the correlation structure for the same wave vector ${q}_{x}$. That relation is exact only for the first (Wertheim's) term of the BW series, and we use our results to test the accuracy of the function $\ensuremath{\gamma}({q}_{x})$ estimated through that method.

Microscopic determination of correlations in the fluid interfacial region in the presence of liquid-gas asymmetry.

In a recent article, we showed how the properties of the density-density correlation function and its integral, the local structure factor, in the fluid interfacial region, in systems with short-ranged forces, can be understood microscopically by considering the resonances of the local structure factor [A. O. Parry and C. Rascón, Nat. Phys. 15, 287 (2019)NPAHAX1745-247310.1038/s41567-018-0361-z]. Here, we illustrate, using mean-field square-gradient theory and the more microscopic Sullivan density functional model, and how this approach generalizes when there is liquid-gas asymmetry, i.e., when the bulk correlation lengths of the coexisting liquid and gas phases are different. In particular, we are able to express the correlation function exactly as a simple average of contributions arising from two effective Ising-symmetric systems referred to as the symmetric gas and symmetric liquid. When combined with our earlier results, this generates analytical approximations for the correlation function and the local structure factor, which are near indistinguishable from the numerical solution to the Ornstein-Zernike equations over the whole range of wave vectors. Our results highlight how asymmetry affects the correlation function structure and describes the crossover from a long-ranged Goldstone mode to short-ranged properties determined by the local density as the wave vector increases.

Floquet-engineered light-cone spreading of correlations in a driven quantum chain

We investigate the light-cone-like spread of electronic correlations in a laser-driven quantum chain. Using the time-dependent density matrix renormalization group, we show that high-frequency driving leads to a Floquet-engineered spread velocity that determines the enhancement of density-density correlations when the ratio of potential and kinetic energies is effectively increased both by either a continuous or a pulsed drive. For large times we numerically show the existence of a Floquet steady state at not too long distances on the lattice with minimal heating. Intriguingly, we find a discontinuity of dynamically scaled correlations at the edge of the light cone, akin to the discontinuity known to exist for quantum quenches in Luttinger liquids. Our work demonstrates the potential of pump-probe experiments for investigating light-induced correlations in low-dimensional materials and puts quantitative speed limits on the manipulation of long-ranged correlations through Floquet engineering.

Correlation-function structure in square-gradient models of the liquid-gas interface: Exact results and reliable approximations.

In a recent article, we described how the microscopic structure of density-density correlations in the fluid interfacial region, for systems with short-ranged forces, can be understood by considering the resonances of the local structure factor occurring at specific parallel wave vectors q [Nat. Phys. 15, 287 (2019)1745-247310.1038/s41567-018-0361-z]. Here we investigate this further by comparing approximations for the local structure factor and pair correlation function against three new examples of analytically solvable models within square-gradient theory. Our analysis further demonstrates that these approximations describe the pair correlation function and structure factor across the whole spectrum of wave vectors, encapsulating the crossover from the Goldstone mode divergence (at small q) to bulklike behavior (at larger q). As shown, these approximations are exact for some square-gradient model potentials and never more than a few percent inaccurate for the others. Additionally, we show that they describe very accurately the correlation function structure for a model describing an interface near a tricritical point. In this case, there are no analytical solutions for the correlation functions, but the approximations are nearly indistinguishable from the numerical solutions of the Ornstein-Zernike equation.

Dynamical BCS Theory of a Two-Dimensional Attractive Fermi Gas: Effective Interactions from Quantum Monte Carlo Calculations

The primary work presented in this paper focuses on the calculation of density-density dynamical correlations in an attractive two dimensional Fermi gas in several physically interesting regimes, including the strongly correlated BEC-BCS crossover regime. We use state-of-the-art dynamical BCS theory and we address the possibility to renormalize the interaction strength, using unbiased Quantum Monte Carlo results as an asset to validate the predictions. We propose that a suitable interplay between dynamical BCS theory, which is computationally very cheap and yields results directly in real time domain, and Quantum Monte Carlo methods, which are exact but way more demanding and limited to imaginary time domain, can be a very promising idea to study dynamics in many body systems. We illustrate the idea and provide quantitative results for a few values of the interaction strength in the cold gas.

Self-diffusion and structure of monovalent ions in two dimensions: A molecular dynamics study

The knowledge of the self-diffusion coefficient is indispensable for different processes in chemical engineering and in the design of new materials, which sometimes occur in restricted or confined geometries. In this work we studied the self-diffusion and structural properties of monovalent ions moving in two dimensions. The two-dimensional soft primitive model was used to describe the interaction between ions and molecular dynamics simulations of the electroneutral mixture were performed to calculate the properties. Radial distribution functions, density-density and charge-charge correlation functions as well as the mean square displacement, the velocity autocorrelation function and the diffusion coefficient were evaluated at supercritical conditions. For the lowest reduced temperature, the formation of clusters, chains and rings of ions influenced the cation-anion radial distribution function, particularly at low densities, where very high values of the first maximum were observed. Clusters and free ions were evaluated. These arrays also influence the density-density and charge-charge correlation functions. Concerning the self-diffusion, it increases as temperature is higher and decreases when density increases, as physically expected. The behavior of the self-diffusion coefficient was analyzed by trying different fitting models. We found that the density dependence is well described by a third-degree polynomial or a linear-logarithmic fit. When the simultaneous dependence with density and temperature is considered, we found that the diffusion is a unique function of the variable ργ/T, where the exponent γ is about 1.7, in contrast with three-dimensional m − 6 Lennard-Jones fluids, where it has been found to be in the range 3.4–13.5. We also investigated the type of diffusive motion. The features observed in both, the velocity autocorrelation function and the mean square displacement, indicated that the diffusion of the ions takes place as normal diffusion, in contrast with other two-dimensional fluids, where superdiffusive and subdiffusive motion have been observed.

Testing Rigidity Transitions in Glass and Crystal Forming Dense Liquids: Viscoelasticity and Dynamical Gaps

A computational study of rigidity for dense fluids of monodisperse and bidisperse hard-disks near a phase and a glass transition respectively is presented. To achieve this goal, the transversal part of the dynamical structure factor is calculated. In both cases, a viscoelastic behavior is obtained, with a dynamical gap determined by a critical wavevector $k_c$. Transversal waves exist for $k>k_c$ while density-density correlations happens at frequency $\omega=0$ for $k<k_c$. In both cases $k_c$ goes to zero as the freezing point is approached. Both systems are able to fulfill a scaled dynamical law. The obtained results indicate that this method gives an alternative to study rigidity in dense fluids, since it is possible to assign a number of floppy modes to the liquid. Also, this suggests that the critical wavevector $k_c$ can serve as a suitable order parameter.

Ab initio path integral Monte Carlo approach to the static and dynamic density response of the uniform electron gas

In a recent Letter [T. Dornheim et al., Phys. Rev. Lett. 121, 255001 (2018)] we have presented ab initio results for the dynamic structure factor $S(\mathbf{q},\ensuremath{\omega})$ of the uniform electron gas for conditions ranging from the warm dense matter regime to the strongly correlated electron liquid. This was achieved on the basis of exact path integral Monte Carlo data by stochastically sampling the dynamic local field correction $G(\mathbf{q},\ensuremath{\omega})$. In this paper we introduce in detail this reconstruction method and provide several practical demonstrations. Moreover, we thoroughly investigate the associated imaginary-time density-density correlation function $F(\mathbf{q},\ensuremath{\tau})$. The latter also gives us access to the static density-response function $\ensuremath{\chi}(\mathbf{q})$ and static local field correction $G(\mathbf{q})$, which are compared to standard dielectric theories like the widespread random phase approximation. In addition, we study the high-frequency limit of $G(\mathbf{q},\ensuremath{\omega})$ and provide extensive results for the dynamic structure factor for different densities and temperatures. Finally, we discuss the implications of our findings for warm dense matter research and the interpretation of experiments.

Probing the Roton Excitation Spectrum of a Stable Dipolar Bose Gas.

We measure the excitation spectrum of a stable dipolar Bose-Einstein condensate over a wide momentum range via Bragg spectroscopy. We precisely control the relative strength ε_{dd} of the dipolar to the contact interactions and observe that the spectrum increasingly deviates from the linear phononic behavior for increasing ε_{dd}. Reaching the dipolar-dominated regime ε_{dd}>1, we observe the emergence of a roton minimum in the spectrum and its softening towards instability. We characterize how the excitation energy and the strength of the density-density correlations at the roton momentum vary with ε_{dd}. Our findings are in excellent agreement with numerical calculations based on mean-field Bogoliubov theory. When including beyond-mean-field corrections, in the form of a Lee-Huang-Yang potential, we observe a quantitative deviation from the experiment, questioning the validity of such a description in the roton regime.

Q-Independent Slow Dynamics in Atomic and Molecular Systems.

Investigating million-atom systems for very long simulation times, we demonstrate that the collective density-density correlation time (τ_{α}) in simulated supercooled water and silica becomes wave-vector independent (q^{0}) when the probing wavelength is several times larger than the interparticle distance. The q independence of the collective density-density correlation functions, a feature clearly observed in light-scattering studies of some soft-matter systems, is thus a genuine feature of many (but not all) slow-dynamics systems, either atomic, molecular, or colloidal. Indeed, we show that when the dynamics of the density fluctuations includes particle-type diffusion, as in the case of the Lennard-Jones binary-mixture model, the q^{0} regime does not set in and the relaxation time continues to scale as τ_{α}∼q^{-2} even at small q.

Giant number fluctuations in dry active polar fluids: A shocking analogy with lightning rods.

It has been shown [H. Chaté et al., Phys. Rev. E 77, 046113 (2008) and F. Ginelli, Eur. Phys. J.: Spec. Top. 225, 2099 (2016)] that the hydrodynamic equations of dry active polar fluids (i.e., moving flocks without momentum conservation) imply giant number fluctuations. Specifically, the rms fluctuations ⟨(δN)2⟩ of the number N of active particles in a region containing a mean number of active particles ⟨N⟩ scale according to the law ⟨(δN)2⟩=K'⟨N⟩ϕ(d) with ϕ(d)=710+15d in d ≤ 4 spatial dimensions. This is much larger than the "law of large numbers" scaling ⟨(δN)2⟩=K⟨N⟩ found in most equilibrium and nonequilibrium systems. In this paper, it is demonstrated that giant number fluctuations also depend singularly on the shape of the box in which one counts the particles, vanishing in the limit of very thin and very fat boxes. These fluctuations arise not from large density fluctuations-indeed, the density fluctuations in polar ordered dry active fluids are not in general particularly large-but from long ranged spatial correlations between those fluctuations. These are shown to be closely related in two spatial dimensions to the electrostatic potential near a sharp upward pointing conducting wedge of opening angle 3π4=135° and in three dimensions to the electrostatic potential near a sharp upward pointing charged cone of opening angle 37.16°. This very precise prediction can be stringently tested by alternative box counting experiments that directly measure the direction dependence, as well as the scaling with distance, of the density-density correlation function.

Meson deformation by magnetic fields in lattice QCD

We study light meson properties in a magnetic field, focusing on a charged pion and a charged and polarized rho meson, in quenched lattice QCD. The gauge-invariant density-density correlators are calculated to investigate the deformation caused by the magnetic field. We find that these mesons acquire elongated shapes along the magnetic field. The magnitude of the deformation is about 10-20 % when the strength of the magnetic field is of the order of the squared unphysical pion mass.

Statistics of noisy growth with mechanical feedback in elastic tissues

Tissue growth is a fundamental aspect of development and is intrinsically noisy. Stochasticity has important implications for morphogenesis, precise control of organ size, and regulation of tissue composition and heterogeneity. However, the basic statistical properties of growing tissues, particularly when growth induces mechanical stresses that can in turn affect growth rates, have received little attention. Here, we study the noisy growth of elastic sheets subject to mechanical feedback. Considering both isotropic and anisotropic growth, we find that the density-density correlation function shows power law scaling. We also consider the dynamics of marked, neutral clones of cells. We find that the areas (but not the shapes) of two clones are always statistically independent, even when they are adjacent. For anisotropic growth, we show that clone size variance scales like the average area squared and that the mode amplitudes characterizing clone shape show a slow [Formula: see text] decay, where n is the mode index. This is in stark contrast to the isotropic case, where relative variations in clone size and shape vanish at long times. The high variability in clone statistics observed in anisotropic growth is due to the presence of two soft modes-growth modes that generate no stress. Our results lay the groundwork for more in-depth explorations of the properties of noisy tissue growth in specific biological contexts.

Proposal for an analog Schwarzschild black hole in condensates of light

By etching a hole in the mirrors or by placing a scatterer in the center of a cavity, we can create a sink for light. In a Bose-Einstein condensate of photons this sink results in the creation of a so-called radial vortex, which is a two-dimensional analogue of a Schwarzschild black hole. We theoretically investigate the Hawking radiation and the associated greybody factor of this Schwarzschild black hole. In particular, we determine the density-density and velocity-velocity correlation functions of the Hawking radiation, which can be measured by observing the spatial correlations in the fluctuations in the light emitted by the cavity.

Semiclassical quench dynamics of Bose gases in optical lattices

We analyze the time evolution of the Bose-Hubbard model after a sudden quantum quench to a weakly interacting regime. Specifically, motivated by a recent experiment at Kyoto University, we numerically simulate redistribution of the kinetic and onsite-interaction energies at an early time, which was observed in non-equilibrium dynamics of ultracold Bose gases in a cubic optical lattice starting with a singly-occupied Mott-insulator state. In order to compute the short-time dynamics corresponding to the experimental situation, we apply the truncated-Wigner approximation (TWA) to the Bose-Hubbard model on a cubic lattice. We show that our semiclassical approach quantitatively reproduces the fast redistribution dynamics. We further analyze spatial spreading of density-density correlations at equal time in the Bose-Hubbard model on a square lattice with a large filling factor. When the system is initially prepared in a coherent state, we find that a propagation velocity of the correlation wave packet in the correlation function strongly depends on the final interaction strength, and it is bounded by twice the maximum group velocity of the elementary excitations. In contrast, when the system is initially in a Mott-insulator state, the propagation velocity of the wave packet is approximately independent of the final interaction strength.

Method for validating a first principles theory of the lambda transition in liquid helium 4

This paper explains how a first principles theory for critical fluctuations consisting of isothermal fourth sound waves in bulk liquid He II can be tested experimentally. The first principles theory is able to predict the detailed behavior of isothermal fourth sound wave signals very near the lambda transition. Experimental detection of the predicted signals would validate this theory to a high degree of confidence and thereby provide a new paradigm for understanding the physical mechanism responsible for critical properties in liquid helium 4. Theoretical and experimental results that support the predictions of this theory are presented. The method of detection rests on formulas derived here for the time-dependent density-density correlation function and associated pressure fluctuations in superfluid He II that is in thermodynamic equilibrium near the lambda transition temperature. Plots of predicted signals are presented and experimental apparatus that uses an electron-tunneling sensor that can detect the pressure fluctuations is described. Some implications of how validation of this first principles theory would impact general understanding of critical fluctuations and lambda transitions are discussed.