Showing papers on "Correlation function (statistical mechanics) published in 2018"

Many-body chaos and energy dynamics in holography

Abstract: Recent developments have indicated that in addition to out-of-time ordered correlation functions (OTOCs), quantum chaos also has a sharp manifestation in the thermal energy density two-point functions, at least for maximally chaotic systems. The manifestation, referred to as pole-skipping, concerns the analytic behaviour of energy density two-point functions around a special point ω = iλ, k = iλ/vB in the complex frequency and momentum plane. Here λ and vB are the Lyapunov exponent and butterfly velocity characterising quantum chaos. In this paper we provide an argument that the phenomenon of pole-skipping is universal for general finite temperature systems dual to Einstein gravity coupled to matter. In doing so we uncover a surprising universal feature of the linearised Einstein equations around a static black hole geometry. We also study analytically a holographic axion model where all of the features of our general argument as well as the pole-skipping phenomenon can be verified in detail.

A practical computational method for the anisotropic redshift-space three-point correlation function

Abstract: Author(s): Slepian, Z; Eisenstein, DJ | Abstract: We present an algorithm enabling computation of the anisotropic redshift-space galaxy threepoint correlation function (3PCF) scaling as N2, with N the number of galaxies. Our previous work showed how to compute the isotropic 3PCF with this scaling by expanding the radially binned density field around each galaxy in the survey into spherical harmonics and combining these coefficients to form multipole moments. The N2 scaling occurred because this approach never explicitly required the relative angle between a galaxy pair about the primary galaxy. Here, we generalize this work, demonstrating that in the presence of azimuthally symmetric anisotropy produced by redshift-space distortions (RSD), the 3PCF can be described by two triangle side lengths, two independent total angular momenta, and a spin. This basis for the anisotropic 3PCF allows its computation with negligible additional work over the isotropic 3PCF. We also present the covariance matrix of the anisotropic 3PCF measured in this basis. Our algorithm tracks the full 5D redshift-space 3PCF, uses an accurate line of sight to each triplet, is exact in angle, and easily handles edge correction. It will enable use of the anisotropic large-scale 3PCF as a probe of RSD in current and upcoming large-scale redshift surveys.

Spatially heterogeneous dynamics in a metallic glass forming liquid imaged by electron correlation microscopy.

Abstract: Supercooled liquids exhibit spatial heterogeneity in the dynamics of their fluctuating atomic arrangements. The length and time scales of the heterogeneous dynamics are central to the glass transition and influence nucleation and growth of crystals from the liquid. Here, we report direct experimental visualization of the spatially heterogeneous dynamics as a function of temperature in the supercooled liquid state of a Pt-based metallic glass, using electron correlation microscopy with sub-nanometer resolution. An experimental four-point space-time correlation function demonstrates a growing dynamic correlation length, ξ, upon cooling of the liquid toward the glass transition temperature. ξ as a function of the relaxation time τ are in good agreement with Adam-Gibbs theory, inhomogeneous mode-coupling theory and random first-order transition theory of the glass transition. The same experiments demonstrate the existence of a nanometer thickness near-surface layer with order of magnitude shorter relaxation time than inside the bulk.

On the Hydrogen Bond Strength and Vibrational Spectroscopy of Liquid Water.

Abstract: In the present work, we introduce two new metrics i.e. hydrogen-bond strength and charge-transfer between the donor/acceptor water molecules as a measure of hydrogen-bond rearrangement dynamics. Further, we also employ a simple model based on energy flux through the donor-acceptor water pairs to quantify the extent of the local hydrogen-bond network reorganization. Most importantly, we report a linear relationship between the OH stretch frequency and the charge and energy transfer through donor-acceptor water pairs. We demonstrate that the vibrational frequency fluctuations, which are used to determine third-order non-linear spectroscopic observables like the short-time slope of three pulse photon echo, can be used as an analog of the fluctuations in the hydrogen-bond strength and charge-transfer. The timescales obtained from our hydrogen-bond strength correlation and charge-transfer correlation decay are in excellent agreement with the computed frequency-time correlation function, as well as with recent vibrational echo experiments.

Geometry-Based Statistical Modeling of Non-WSSUS Mobile-to-Mobile Rayleigh Fading Channels

Abstract: In this paper, we present a novel geometry-based statistical model for small-scale non-wide-sense stationary uncorrelated scattering (non-WSSUS) mobile-to-mobile (M2M) Rayleigh fading channels. The proposed model builds on the principles of plane wave propagation to capture the temporal evolution of the propagation delay and Doppler shift of the received multipath signal. This is different from existing non-WSSUS geometry-based statistical channel models, which are based on a spherical wave propagation approach, that in spite of being more realistic is more mathematically intricate. By considering an arbitrary geometrical configuration of the propagation area, we derive general expressions for the most important statistical quantities of nonstationary channels, such as the first-order probability density functions of the envelope and phase, the four-dimensional (4-D) time-frequency correlation function (TF-CF), local scattering function (LSF), and time-frequency-dependent delay and Doppler profiles. We also present an approximate closed-form expression of the channel's 4-D TF-CF for the particular case of the geometrical one-ring scattering model. The obtained results provide new theoretical insights into the correlation and spectral properties of non-WSSUS M2M Rayleigh fading channels.

The Zeldovich approximation and wide-angle redshift-space distortions

Abstract: Author(s): Castorina, E; White, M | Abstract: The contribution of line-of-sight (LOS) peculiar velocities to the observed redshift of objects breaks the translational symmetry of the underlying theory, modifying the predicted two-point functions. These 'wide-angle effects' have mostly been studied using linear perturbation theory in the context of the multipoles of the correlation function and power spectrum. In this work, we present the first calculation of wide-angle terms in the Zeldovich approximation, which is known to be more accurate than linear theory on scales probed by the next generation of galaxy surveys.We present the exact result for dark matter and perturbatively biased tracers as well as the small angle expansion of the configuration- and Fourier-space two-point functions and the connection to the multifrequency angular power spectrum. We compare different definitions of the LOS direction and discuss how to translate between them. We show that wide-angle terms can reach tens of percent of the total signal in a measurement at low redshift in some approximations, and that a generic feature of wide-angle effects is to slightly shift the Baryon Acoustic Oscillation scale.

Dipolar-coupled moment correlations in clusters of magnetic nanoparticles

Abstract: Here, we resolve the nature of the moment coupling between 10-nm dimercaptosuccinic acid--coated magnetic nanoparticles. The individual iron oxide cores were composed of $g95\phantom{\rule{0.16em}{0ex}}%$ maghemite and agglomerated to clusters. At room temperature the ensemble behaved as a superparamagnet according to M\"ossbauer and magnetization measurements, however, with clear signs of dipolar interactions. Analysis of temperature-dependent ac susceptibility data in the superparamagnetic regime indicates a tendency for dipolar-coupled anticorrelations of the core moments within the clusters. To resolve the directional correlations between the particle moments we performed polarized small-angle neutron scattering and determined the magnetic spin-flip cross section of the powder in low magnetic field at 300 K. We extract the underlying magnetic correlation function of the magnetization vector field by an indirect Fourier transform of the cross section. The correlation function suggests nonstochastic preferential alignment between neighboring moments despite thermal fluctuations, with anticorrelations clearly dominating for next-nearest moments. These tendencies are confirmed by Monte Carlo simulations of such core clusters.

Influence of grain morphology on ultrasonic wave attenuation in polycrystalline media with statistically equiaxed grains

Abstract: The influence of a polycrystals' grain structure on elastic wave scattering is studied with analytical and numerical methods in a broad frequency range. A semi-analytical attenuation model, based on an established scattering theory, is presented. This technique accurately accounts for the grain morphology without prior assumptions on grain statistics. This is achieved by incorporating a samples' exact spatial two-point correlation function into the theory. The approach is verified by using a finite element method (FEM) to simulate P-wave propagation in 3D Voronoi crystals with equal mean grain diameter, but different grain shape uniformity. Aluminum and Inconel serve as representatives for weak and strong scattering cubic class materials for simulations and analytical calculations. It was found that the shape of the grains has a strong influence on the attenuation curve progression in the Rayleigh-stochastic transition region, which was attributed to mode conversion scattering. Comparisons between simulations and theory show excellent agreement for both materials. This demonstrates the need for accurately taking the microstructure of heterogeneous materials into account, to get precise analytical predictions for their scattering behaviour. It also demonstrates the impressive accuracy and flexibility of the scattering theory which was used.

Atomic Dynamics in Simple Liquid: de Gennes Narrowing Revisited.

Abstract: The de Gennes narrowing phenomenon is frequently observed by neutron or x-ray scattering measurements of the dynamics of complex systems, such as liquids, proteins, colloids, and polymers. The characteristic slowing down of dynamics in the vicinity of the maximum of the total scattering intensity is commonly attributed to enhanced cooperativity. In this Letter, we present an alternative view on its origin through the examination of the time-dependent pair correlation function, the van Hove correlation function, for a model liquid in two, three, and four dimensions. We find that the relaxation time increases monotonically with distance and the dependence on distance varies with dimension. We propose a heuristic explanation of this dependence based on a simple geometrical model. This finding sheds new light on the interpretation of the de Gennes narrowing phenomenon and the α-relaxation time.

The Evolution of States in a Spatial Population Model

Abstract: The evolution of states in a spatial population model is studied. The model describes an infinite system of point entities in $$\mathbb {R}^d$$ which reproduce themselves at distant points (disperse) and die with rate that includes a competition term. The system’s states are probability measures on the space of configurations, and their evolution is obtained from a hierarchical chain of differential equations for the corresponding correlation functions derived from the Fokker–Planck equation for the states. Under natural conditions imposed on the model parameters it is proved that the correlation functions evolve in a scale of Banach spaces in such a way that at each moment of time the correlation function corresponds to a unique sub-Poissonian state. Some further properties of the evolution of states constructed in this way are described.

Molecular dynamics simulation of geminal dicationic ionic liquids [Cn(mim)2][NTf2]2 - structural and dynamical properties.

Abstract: In this work, the structural and dynamical properties of two imidazolium-based geminal dicationic ionic liquids (GDILs), i.e. [Cn(mim)2][NTf2]2 with n = 3 and 5, have been studied to obtain a fundamental understanding of the molecular basis of the macroscopic and microscopic properties of the bulk liquid phase. To achieve this purpose, molecular dynamics (MD) simulation, density functional theory (DFT) and atoms in molecule (AIM) methods were used. Interaction energies, charge transfers and hydrogen bonds between the cation and anions of each studied GDIL were investigated by DFT calculations and also AIM. The mean square displacement (MSD), self-diffusion coefficient, and transference number of the cation and anions, and also the density, viscosity and electrical conductivity of the studied GDILs, were computed at 333.15 K and at 1 atm. The simulated values were in good agreement with the experimental data. The effect of linkage alkyl chain length on the thermodynamic, transport and structural properties of these GDILs has been investigated. The structural features of these GDILs were characterized by calculating the partial site–site radial distribution functions (RDFs) and spatial distribution functions (SDFs). The heterogeneity order parameter (HOP) has been used to describe the spatial structures of these GDILs and the distribution of the angles formed between two cation heads and the middle carbon atom of the linkage alkyl chain was analyzed in these ILs. To investigate the temporal heterogeneity of the studied GDILs, the deviation of the self-part of the van Hove correlation function, Gs(,t), from the Gaussian distribution of particle displacement and also the second-order non-Gaussian parameter, α2(t), were used. Since, the transport and interfacial properties and ionic characteristics of these GDILs were studied experimentally in our previous studies as a function of linkage chain length and temperature, in this work, we try to give a better perspective of the structure and dynamics of these systems at a molecular level.

Testing modified gravity using a marked correlation function

Abstract: In theories of modified gravity with the chameleon screening mechanism, the strength of the fifth force depends on environment This induces an environment dependence of structure formation, which differs from Λ-cold-dark-matter (ΛCDM) We show that these differences could be captured by the marked correlation function With the galaxy correlation functions and number densities calibrated to match between f(R) and ΛCDM models in simulations, we show that the marked correlation functions by using either the local galaxy number density or halo mass as the marks encode extra information, which can be used to test these theories We discuss possible applications of these statistics in observations

Splashback radius of nonspherical dark matter halos from cosmic density and velocity fields

Abstract: We investigate the splashback features of dark-matter halos based on cosmic density and velocity fields. Besides the density correlation function binned by the halo orientation angle, which was used in the literature, we introduce, for the first time, the corresponding velocity statistic, alignment momentum correlation function, to take into account the asphericity of halos. Using large-volume, high-resolution $N$-body simulations, we measure the alignment statistics of density and velocity. On halo scales, $x\ensuremath{\sim}{R}_{200\mathrm{m}}\ensuremath{\sim}1\text{ }\text{ }{h}^{\ensuremath{-}1}\text{ }\mathrm{Mpc}$, we detect a sharp steepening in the momentum correlation associated with the physical halo boundary, or the splashback feature, which is found more prominent than in the density correlation. We also find that the splashback radius determined from the density correlation becomes $\ensuremath{\sim}3.5%$ smaller than that from the momentum correlation, with their correlation coefficient being 0.605. Moreover, the orientation-dependent splashback feature due to halo asphericity is measured when the density profile is determined by dark-matter particles, which can be used as a test of collisional cold dark matter since the halo shape is predicted to be rounder in such a model.

Numerical and analytic modelling of elastodynamic scattering within polycrystalline materials.

Abstract: The elastodynamic behavior of polycrystalline cubic materials is studied through the fundamental propagation properties, the attenuation and wave speed, of a longitudinal wave. Predictions made by different analytical models are compared to both numerical and experimental results. The numerical model is based on a three-dimensional Finite Element (FE) simulation which provides a full-physics solution to the scattering problem. The three main analytical models include the Far-Field Approximation (FFA), the Self-Consistent Approximation (SCA) to the reference medium, and the herein derived Second Order Approximation (SOA). The classic Stanke and Kino model is also included, which by comparison to the SOA, reveals the importance of the distribution of length-scales described in terms of the two-point correlation function in determining scattering behavior. Further comparison with the FE model demonstrates that the FFA provides a simple but satisfactory approximation, whereas the SOA shows all-around excellent agreement. The experimental wave velocity data evaluated against the SOA and SC reveal a better agreement when the Voigt reference is used in second order models. The use of full-physics numerical simulations has enabled the study of wave behavior in these random media which will be important to inform the ongoing development of analytical models and the understanding of observations.

Bulk dynamics of Brownian hard disks: Dynamical density functional theory versus experiments on two-dimensional colloidal hard spheres.

Abstract: Using dynamical density functional theory (DDFT), we theoretically study Brownian self-diffusion and structural relaxation of hard disks and compare to experimental results on quasi two-dimensional colloidal hard spheres. To this end, we calculate the self-van Hove correlation function and distinct van Hove correlation function by extending a recently proposed DDFT-approach for three-dimensional systems to two dimensions. We find that the theoretical results for both self-part and distinct part of the van Hove function are in very good quantitative agreement with the experiments up to relatively high fluid packing fractions of roughly 0.60. However, at even higher densities, deviations between the experiment and the theoretical approach become clearly visible. Upon increasing packing fraction, in experiments, the short-time self-diffusive behavior is strongly affected by hydrodynamic effects and leads to a significant decrease in the respective mean-squared displacement. By contrast, and in accordance with previous simulation studies, the present DDFT, which neglects hydrodynamic effects, shows no dependence on the particle density for this quantity.

A Novel 3D Non-Stationary Vehicle-to-Vehicle Channel Model and its Spatial-Temporal Correlation Properties

Abstract: In this paper, a new non-stationary Vehicle-to-Vehicle (V2V) channel model is proposed. It could generate more smooth fading phase between the adjacent channel states and guarantee more accurate Doppler frequency, which is a great improvement comparing with those of the existing non-stationary geometry-based stochastic models (GBSMs) for V2V channels. Meanwhile, the spatial–temporal correlation function (STCF) as well as a temporal correlation function (TCF) and a spatial correlation function (SCF) are derived in details based on the power angle spectrums of both the mobile transmitter (MT) and mobile receiver (MR) following the Von Mises Fisher (VMF) distribution. Simulation results have demonstrated that the time-variant correlation properties of our proposed channel model have an excellent agreement with the theoretical results, which verifies the correctness of theoretical derivations and simulations. Finally, the TCF and stationary interval of the proposed model are verified by the measured results.

Precise algorithms to compute surface correlation functions of two-phase heterogeneous media and their applications.

Abstract: The quantitative characterization of the microstructure of random heterogeneous media in d-dimensional Euclidean space R^{d} via a variety of n-point correlation functions is of great importance, since the respective infinite set determines the effective physical properties of the media. In particular, surface-surface F_{ss} and surface-void F_{sv} correlation functions (obtainable from radiation scattering experiments) contain crucial interfacial information that enables one to estimate transport properties of the media (e.g., the mean survival time and fluid permeability) and complements the information content of the conventional two-point correlation function. However, the current technical difficulty involved in sampling surface correlation functions has been a stumbling block in their widespread use. We first present a concise derivation of the small-r behaviors of these functions, which are linked to the mean curvature of the system. Then we demonstrate that one can reduce the computational complexity of the problem, without sacrificing accuracy, by extracting the necessary interfacial information from a cut of the d-dimensional statistically homogeneous and isotropic system with an infinitely long line. Accordingly, we devise algorithms based on this idea and test them for two-phase media in continuous and discrete spaces. Specifically for the exact benchmark model of overlapping spheres, we find excellent agreement between numerical and exact results. We compute surface correlation functions and corresponding local surface-area variances for a variety of other model microstructures, including hard spheres in equilibrium, decorated "stealthy" patterns, as well as snapshots of evolving pattern formation processes (e.g., spinodal decomposition). It is demonstrated that the precise determination of surface correlation functions provides a powerful means to characterize a wide class of complex multiphase microstructures.

Coupled charge and spin dynamics in a photoexcited doped Mott insulator

Abstract: Using a nonequilibrium implementation of the extended dynamical mean-field theory (EDMFT) we simulate the relaxation after photoexcitation in a strongly correlated electron system with antiferromagnetic spin interactions. We consider the $t\ensuremath{-}J$ model and focus on the interplay between the charge and spin dynamics in different excitation and doping regimes. The appearance of string states after a weak photoexcitation manifests itself in a nontrivial scaling of the relaxation time with the exchange coupling and leads to a correlated oscillatory evolution of the kinetic energy and spin-spin correlation function. A strong excitation of the system, on the other hand, suppresses the spin correlations and results in a relaxation that is controlled by hole scattering. We discuss the possibility of detecting string states in optical and cold-atom experiments.

Topological Order Generated by a Random Field in a 2D Exchange Model.

Abstract: We study a 2D exchange model with a weak static random field on lattices containing over ${10}^{8}$ spins. Ferromagnetic correlations persist on the Imry-Ma scale inversely proportional to the random-field strength and decay exponentially at greater distances. We find that the average energy of the correlated area is close to the ground-state energy of a Skyrmion, while the topological charge of the area is close to $\ifmmode\pm\else\textpm\fi{}1$. The correlation function of the topological charge density changes sign at a distance determined by the ferromagnetic correlation length, while its Fourier transform exhibits a maximum. These findings suggest that static randomness transforms a 2D ferromagnetic state into a Skyrmion--anti-Skyrmion glass.

An analytic implementation of the IR-resummation for the BAO peak

Abstract: We develop an analytic method for implementing the IR-resummation of arXiv:1404.5954, which allows one to correctly and consistently describe the imprint of baryon acoustic oscillations (BAO) on statistical observables in large-scale structure. We show that the final IR-resummed correlation function can be computed analytically without relying on numerical integration, thus allowing for an efficient and accurate use of these predictions on real data in cosmological parameter fitting. In this work we focus on the one-loop correlation function and the BAO peak. We show that, compared with the standard numerical integration method of IR-resummation, the new method is accurate to better than 0.2 %, and is quite easily improvable. We also give an approximate resummation scheme which is based on using the linear displacements of a fixed fiducial cosmology, which when combined with the method described above, is about six times faster than the standard numerical integration. Finally, we show that this analytic method is generalizable to higher loop computations.

Momentum distribution and contacts of one-dimensional spinless Fermi gases with an attractive p -wave interaction

Abstract: We present a rigorous study of momentum distribution and p-wave contacts of one dimensional (1D) spinless Fermi gases with an attractive p-wave interaction. Using the Bethe wave function, we analytically calculate the large-momentum tail of momentum distribution of the model. We show that the leading ($\sim 1/p^{2}$) and sub-leading terms ($\sim 1/p^{4}$) of the large-momentum tail are determined by two contacts $C_2$ and $C_4$, which we show, by explicit calculation, are related to the short-distance behaviour of the two-body correlation function and its derivatives. We show as one increases the 1D scattering length, the contact $C_2$ increases monotonically from zero while $C_4$ exhibits a peak for finite scattering length. In addition, we obtain analytic expressions for p-wave contacts at finite temperature from the thermodynamic Bethe ansatz equations in both weakly and strongly attractive regimes.

Mesoscopic eigenvalue density correlations of Wigner matrices

Abstract: We investigate to what extent the microscopic Wigner-Gaudin-Mehta-Dyson (WGMD) (or sine kernel) statistics of random matrix theory remain valid on mesoscopic scales To that end, we compute the connected two-point spectral correlation function of a Wigner matrix at two mesoscopically separated points In the mesoscopic regime, density correlations are much weaker than in the microscopic regime Our result is an explicit formula for the two-point function This formula implies that the WGMD statistics are valid to leading order on all mesoscopic scales, that in the real symmetric case there are subleading corrections matching precisely the WGMD statistics, while in the complex Hermitian case these subleading corrections are absent We also uncover non-universal subleading correlations, which dominate over the universal ones beyond a certain intermediate mesoscopic scale The proof is based on a hierarchy of Schwinger-Dyson equations for a sufficiently large class of polynomials in the entries of the Green function The hierarchy is indexed by a tree, whose depth is controlled using stopping rules A key ingredient in the derivation of the stopping rules is a new estimate on the density of states, which we prove to have bounded derivatives of all order on all mesoscopic scales

Rigorous proof for the nonlocal correlation function in the transverse Ising model with ring frustration

Abstract: An unusual correlation function was conjectured by Campostrini et al. [Phys. Rev. E 91, 042123 (2015)PLEEE81539-375510.1103/PhysRevE.91.042123] for the ground state of a transverse Ising chain with geometrical frustration. Later, we provided a rigorous proof for it and demonstrated its nonlocal nature based on an evaluation of a Toeplitz determinant in the thermodynamic limit [J. Stat. Mech. (2016) 11310210.1088/1742-5468/2016/11/113102]. In this paper, we further prove that all the low excited energy states forming the gapless kink phase share the same asymptotic correlation function with the ground state. As a consequence, the thermal correlation function almost remains constant at low temperatures if one assumes a canonical ensemble.

Relationship between morphology and transparency in glass-ceramic materials

Abstract: This paper is an attempt to understand and interpret optical scattering in composite materials. It focuses on phase-separated glasses and glass-ceramics that maintain transparency at high crystal content. Two approaches aimed at understanding optical scattering are investigated for each example material: (1) a single particle approach and (2) a correlation function approach based on the spatial distribution of the refractive index profile of the material pioneered by Debye. Both methods have shortcomings: the single particle approach cannot take the material’s morphology into account, and it is nontrivial to determine the correlation function. Regardless, the preferred approach is determined for each of the materials investigated. It is shown that optical scattering in glass-ceramics can be controlled to produce a transparent material if the glass-ceramic has a bulk fine-grained structure without an easily recognized “grain size.”

The peculiar velocity correlation function

Abstract: We present an analysis of the two-point peculiar velocity correlation function using data from the CosmicFlows catalogues. The Millennium and MultiDark Planck 2 N-body simulations are used to estimate cosmic variance and uncertainties due to measurement errors. We compare the velocity correlation function to expectations from linear theory to constrain cosmological parameters. Using the maximum likelihood method, we find values of $\Omega_m= 0.315^{+0.205}_{-0.135}$ and $\sigma_8=0.92^{+0.440}_{-0.295}$, consistent with the Planck and Wilkinson Microwave Anisotropy Probe CMB derived estimates. However, we find that the cosmic variance of the correlation function is large and non-Gaussian distributed, making the peculiar velocity correlation function less than ideal as a probe of large-scale structure.

Full Dysonian dynamics of the complex Ginibre ensemble

Abstract: We find stochastic equations governing eigenvalues and eigenvectors of a dynamical complex Ginibre ensemble reaffirming the intertwined role played between both sets of matrix degrees of freedom. We solve the accompanying Smoluchowski-Fokker-Planck equation valid for any initial matrix. We derive evolution equations for the averaged extended characteristic polynomial and for a class of $k$-point eigenvalue correlation functions. From the latter we obtain a novel formula for the eigenvector correlation function which we inspect for Ginibre and spiric initial conditions and obtain macro- and microscopic limiting laws.