Density Correlation Function Research Articles

Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models.

We argue that the dynamics of particle imbalance in quadratic fermionic models is, for the majority of initial many-body product states in the site occupation basis, virtually indistinguishable from the dynamics of survival probabilities of single-particle states. We then generalize our statement to a similar relationship between the non-equal time and space density correlation functions in many-body states, and the transition probabilities of single-particle states at nonzero distances. Finally, we study the equal-time connected density-density correlation functions in many-body states, which exhibit certain qualitative analogies with the survival and transition probabilities of single-particle states. Our results are numerically tested for two paradigmatic models of single-particle localization: the 3D Anderson model and the 1D Aubry-André model. This work gives an affirmative answer to the question of whether it is possible to measure features of single-particle survival and transition probabilities by the dynamics of observables in many-body states.

Elasticity of bilayer lipid membranes from their density correlation function

ABSTRACT We study the density correlation function (DCF) of DPPC lipid bilayers. We compare Molecular Dynamics (MD) results with theoretical predictions obtained with a mesoscopic description, in terms of the lipid membrane elasticity. One key objective of our work is the quantification of the lipid membrane elasticity directly from the DCF, both for the membrane undulations and local membrane thickness. Our method does not require the definition of instantaneous surfaces or internal variables defining lipid orientations. Building on our previous work, here we focus on the intralayer correlations, i.e. the DCF of lipids residing on the same monolayer, by tracking only the position of the phosphorus atoms in a lipid head group. We demonstrate the relevance of the intralayer two-dimensional (2D) correlations to the total DCF. We further show that all-atom (AA) and coarse grained (CG) lipid forcefields, feature distintively different DCFs. The CG forcefield predicts results in good agreement with the mesoscopic predictions, for the entire wavevector range; the AA forcefield (CHARMM36) predict strong peristaltic fluctuations at long wavevectors q ≳ 0.8 nm − 1 , which are absent in the CG lipid model (MARTINI).

Stochastic processes and mean square calculus on fractal curves

Abstract In this paper, random and stochastic processes are defined on fractal curves. Fractal calculus is used to define the cumulative distribution function, probability density function, moments, variance, and correlation function of stochastic processes on fractal curves. A new framework, which is a generalization of mean square calculus, is formulated. The sequence of random variables on the fractal curve, fractal mean square continuity, mean square F α {F^{\alpha}} -derivative, and fractal mean square integral are discussed. The mean square solution of a fractal stochastic equation is derived and plotted to illustrate the details.

An exact method for bosonizing the Fermi surface in arbitrary dimensions

Inspired by the recent work by Delacretaz et. al. [Phys. Rev. Res. 4, 033131 (2022)], we rigorously derive an exact and simple method to bosonize a non-interacting fermionic system with a Fermi surface starting from a microscopic Hamiltonian. In the long-wavelength limit, we show that the derived bosonized action is exactly equivalent to the action obtained by Delacretaz et. al. In addition, we propose diagrammatic rules to evaluate correlation functions using our bosonized theory and demonstrate these rules by calculating the three- and four-point density correlation functions. We also consider a general density-density interaction and show that the simplest approximation in our bosonic theory is identical to RPA results.

A new test of gravity – II. Application of marked correlation functions to luminous red galaxy samples

ABSTRACT We apply the marked correlation function test proposed by Armijo et al. (Paper I) to samples of luminous red galaxies (LRGs) from the final data release of the Sloan Digital Sky Survey (SDSS) III. The test assigns a density-dependent mark to galaxies in the estimation of the projected marked correlation function. Two gravity models are compared: general relativity (GR) and $f(R)$ gravity. We build mock catalogues which, by construction, reproduce the measured galaxy number density and two-point correlation function of the LRG samples, using the halo occupation distribution model (HOD). A range of HOD models give acceptable fits to the observational constraints, and this uncertainty is fed through to the error in the predicted marked correlation functions. The uncertainty from the HOD modelling is comparable to the sample variance for the SDSS-III LRG samples. Our analysis shows that current galaxy catalogues are too small for the test to distinguish a popular $f(R)$ model from GR. However, upcoming surveys with a better measured galaxy number density and smaller errors on the two-point correlation function, or a better understanding of galaxy formation, may allow our method to distinguish between viable gravity models.

Universal correlations along the BEC-BCS crossover

Universality of the long-distance behavior across the Bardeen–Cooper–Schrieffer (BEC)-Bose–Einstein condensate (BCS) smooth transition for two-body density correlation functions and the Cooper-pair probability density is demonstrated in a balanced mixture of a two-component Fermi gas at T = 0. It is numerically shown at the mean-field level that these two-body quantities exhibit an exponential decay in terms of the chemical potential and the low-energy behavior of the gap. A general expression is found for the two-body distributions holding for different features of finite-range potentials, such as divergences at the origin, discontinuities at a finite radius, power-law decay, and exponential decay. The correlation length characterizing the long-distance behavior unravels the dependence on the energy needed to break pairs along the BEC-BCS crossover, a quantity meaningful to the stability of the many-body state.

Random packing dynamics of [Formula: see text]-triplets.

In this paper, we used a combination of DEM and the multi-sphere method to investigate the random packing dynamics of [Formula: see text]-triplets. These triplets consist of three overlapping primary spheres, forming a bent structure with a bond angle of [Formula: see text] and belonging to the [Formula: see text] symmetry group. The motivation for choosing such a structural arrangement is twofold: first, to understand how bent-shaped structures influence packing dynamics, and secondly, to investigate how mesoscopic or macroscopic particles possessing symmetry similar to that found in more elementary particles impact packing observables. To ensure non-overlapping particles at the beginning of the simulations, the confinement box was divided into basic cells. Each triplet was then inserted into a basic cell with a random orientation. After that, the system is allowed to settle under gravity toward the bottom of the box. An implicit leapfrog algorithm with quaternion acceleration was used to numerically integrate the rotational motion equations. Through a molecular approach, we consider the impact of long-range cohesive forces by employing a Lennard-Jones (LJ)-type potential. Packing processes are studied assuming different long-range interaction strengths. Different quantities are studied including packing density and orientation pair correlation function. In addition, the force probability distributions in the random packing structures have been analyzed.

Physical insights from imaginary-time density–density correlation functions

An accurate theoretical description of the dynamic properties of correlated quantum many-body systems, such as the dynamic structure factor S(q, ω), is important in many fields. Unfortunately, highly accurate quantum Monte Carlo methods are usually restricted to the imaginary time domain, and the analytic continuation of the imaginary-time density–density correlation function F(q, τ) to real frequencies is a notoriously hard problem. Here, it is argued that often no such analytic continuation is required because by definition, F(q, τ) contains the same physical information as does S(q, ω), only represented unfamiliarly. Specifically, it is shown how one can directly extract key information such as the temperature or quasi-particle excitation energies from the τ domain, which is highly relevant for equation-of-state measurements of matter under extreme conditions [T. Dornheim et al., Nat. Commun. 13, 7911 (2022)]. As a practical example, ab initio path-integral Monte Carlo results for the uniform electron gas (UEG) are considered, and it is shown that even nontrivial processes such as the roton feature of the UEG at low density [T. Dornheim et al., Commun. Phys. 5, 304 (2022)] are manifested straightforwardly in F(q, τ). A comprehensive overview is given of various useful properties of F(q, τ) and how it relates to the usual dynamic structure factor. In fact, working directly in the τ domain is advantageous for many reasons and opens up multiple avenues for future applications.

Correlation of local densities of states on mesoscopic energy scales in random band matrices

We are interested in the phase transition of the correlation function of local densities of states at mesoscopic scales of random band matrices of width W in dimension 2. As a result, we show that the local densities of states are alternately positively and negatively correlated in the diffusive regime O(log (L/W)) times, L being the size of the system.

On the statistical theory of self-gravitating collisionless dark matter flow

Dark matter, if it exists, accounts for five times as much as the ordinary baryonic matter. Compared to hydrodynamic turbulence, the flow of dark matter might possess the widest presence in our universe. This paper presents a statistical theory for the flow of dark matter that is compared with N-body simulations. By contrast to hydrodynamics of normal fluids, dark matter flow is self-gravitating, long-range, and collisionless with a scale-dependent flow behavior. The peculiar velocity field is of constant divergence nature on small scale and irrotational on large scale. The statistical measures, i.e., correlation, structure, dispersion, and spectrum functions, are modeled on both small and large scales, respectively. Kinematic relations between statistical measures are fully developed for incompressible, constant divergence, and irrotational flow. Incompressible and constant divergence flow share the same kinematic relations for even order correlations. The limiting correlation of velocity ρL=1/2 on the smallest scale (r = 0) is a unique feature of collisionless flow (ρL=1 for incompressible flow). On large scale, transverse velocity correlation has an exponential form T2∝e−r/r2 with a constant comoving scale r2=21.3 Mpc/h that may be related to the horizon size at matter–radiation equality. All other correlation, structure, dispersion, and spectrum functions for velocity, density, and potential fields are derived analytically from kinematic relations for irrotational flow. On small scale, longitudinal structure function follows one-fourth law of S2l∝r1/4. All other statistical measures can be obtained from kinematic relations for constant divergence flow. Vorticity is negatively correlated for scale r between 1 and 7 Mpc/h. Divergence is negatively correlated for r > 30 Mpc/h that leads to a negative density correlation.

Computational study of Na diffusion and conduction in P2- and O3-Na2x[NixTi1-x]O2 materials with machine-learning interatomic potentials

Sodium-ion batteries (SIBs) provide a feasible solution for large-scale energy storage applications of sustainable energy resources like wind and solar energy. Layered sodium nickel titanates (Na2x[NixTi1-x]O2) (SNTL) are considered a promising electrode material for SIBs since they can function as either a positive or negative electrode due to the coexistence of high redox potential element Ni (V = 3.7 V vs. Na/Na+) and low redox potential element Ti (V = 0.7 V vs. Na/Na+). There have been both experimental and computational studies on the family of Na2x[NixTi1-x]O2 materials, investigating their structures, electrochemical performance, electronic and ionic conductivity, etc. However, the current understanding of the Na migration mechanism is still very limited at an atomic level because of the restrictions of simulation methods: density-functional theory (DFT) simulation is restricted to a small length and time scale, whereas the conventional empirical interatomic potential (IP) is restricted by a limited accuracy. To solve this efficiency-versus-accuracy dilemma, herein we developed a neural network (NN)-based machine-learning interatomic potential (MLIP), which is trained using DFT data. Our MLIP demonstrates a DFT-approaching accuracy in terms of atomic forces. Moreover, the extracted Na self-diffusivity, ionic conductivity, and activation energy values from MLIP-MD simulation agree well with experimental data. In general, P2-SNTL demonstrates a higher Na self-diffusivity and ionic conductivity than O3-SNTL, mainly due to the larger bottleneck size through which Na ions migrate. We also employed the incoherent density correlation function to study the Na migration mechanism. The Singwi-Sjölander (SS) model and Chudley-Elliot (CE) model were used to fit the jump-diffusion behavior in P2- and O3-SNTL, respectively. The obtained jump distance values match well with the typical distance between the nearest Na sites in P2- and O3-SNTL, confirming that the hopping events happen mostly between neighboring Na sites in SNTL. The decrease of residence time and jump distance values with temperature is a result of higher ion mobility and level of delocalization, as validated by the nuclear density maps. In addition, our study also confirmed that both the “straight” and “curved” Na migration paths exist in O3-SNTL, in contrast to previous studies which only mention the “curved” migration path. In the end, our calculated Haven ratios have a value <1, indicating that it is more likely for the Na hopping events to occur via a concerted migration of several atoms other than the jump of an isolated atom.

Full view on the dynamics of an impurity coupled to two one-dimensional baths

We consider a model for the motion of an impurity interacting with two parallel, one-dimensional baths, described as two Tomonaga-Luttinger liquid systems. The impurity is able to move along the baths, and to jump from one to the other. We provide a perturbative expression for the evolution of the system when the impurity is injected in one of the baths, with a given wave packet. We obtain an approximation formally of infinite order in the impurity-bath coupling, which allows us to reproduce the orthogonality catastrophe. We monitor and discuss the dynamics of the impurity and its effect on the baths, in particular for a Gaussian wave packet. Besides the motion of the impurity, we also analyze the dynamics of the bath density and momentum density (i.e., the particle current), and show that it fits an intuitive semiclassical interpretation. We also quantify the correlation that is established between the baths by calculating the interbath, equal-time spatial correlation functions of both bath density and momentum, finding a complex pattern. We show that this pattern contains information on both the impurity motion and on the baths, and that these can be unveiled by taking appropriate ``slices'' of the time evolution.

Slow dynamics of a mobile impurity interacting with an Anderson insulator

We investigate dynamics of a single mobile impurity immersed in a bath of Anderson localized particles and focus on the regime of relatively strong disorder and interactions. In that regime, the dynamics of the system is particularly slow, suggesting, at short times, an occurrence of many-body localization. Considering longer time scales, we show that the latter is a transient effect and that, eventually, the impurity spreads sub-diffusively and induces a gradual delocalization of the Anderson insulator. The phenomenology of the system in the considered regime of slow dynamics includes a sub-diffusive growth of mean square displacement of the impurity, power-law decay of density correlation functions of the Anderson insulator and a power-law growth of entanglement entropy in the system. We observe a similar regime of slow dynamics also when the disorder in the system is replaced by a sufficiently strong quasi-periodic potential.

Tracking locality in the time evolution of disordered systems

Using local density correlation functions for a one-dimensional spin system, we introduce a correlation function difference (CFD) which compares correlations on a given site between a full system of size $L$ and its restriction to $\ell<L$ sites. We show that CFD provides useful information on transfer of information in quantum many-body systems by considering the examples of ergodic, Anderson, and many-body localized regimes in disordered XXZ spin chain. In the ergodic phase, we find that the propagation of CFD is asymptotically faster than the spin transport but slower than the ballistic propagation implied by the Lieb-Robinson bound. In contrast, in the localized cases, we unravel an exponentially slow relaxation of CFD. Connections between CFD and other observables detecting non-local correlations in the system are discussed.

Ergodicity in glass relaxation

We derive an equation for the glass relaxation. In the derivation, the Zwanzig-Mori projection method is not applied explicitly, which makes our equation different from the mode coupling theory. Due to the nonlinearity, it is difficult to solve the equation to get the full behaviors of the glass relaxation. But we can simplify the equation when time approaches infinity and obtain the static result analytically. The static result shows that the density correlation function decays to zero finally, meaning that the glass relaxation is ergodic. In this study, we also find that the force fluctuation of one individual particle averaged in the glass is sensitive to the temperature and is suggested to be a parameter to reflect the structural transition for the glass relaxation.

Anomalous fluctuations in homogeneous fluid phase of active Brownian particles

Giant number fluctuations (GNF) are an anomaly universally observed in active fluids with polar or nematic order. In this paper, we show that GNF arise in the fluid phase of active Brownian particles (ABP), where the polar order is absent. GNF in ABP extends over a large but finite length which characterizes the growing velocity correlations. To suppress unwanted phase separation and allow ones to explore the disordered fluid phase at large activities, we impart the inertia, or the mass, to the ABP. A linearized hydrodynamic theory captures our findings, but only qualitatively. We find numerically a nontrivial scaling relation for the density correlation function, which the linearized theory cannot explain. The results suggest ubiquitousness of the anomalous fluctuations even in the disordered homogeneous fluid phase in the absence of the directional order.

The Hydrophobic Effect Studied by Using Interacting Colloidal Suspensions.

Interactions between nanoparticles (NPs) determine their self-organization and dynamic processes. In these systems, a quantitative description of the interparticle forces is complicated by the presence of the hydrophobic effect (HE), treatable only qualitatively, and due to the competition between the hydrophobic and hydrophilic forces. Recently, instead, a sort of crossover of HE from hydrophilic to hydrophobic has been experimentally observed on a local scale, by increasing the temperature, in pure confined water and studying the occurrence of this crossover in different water-methanol solutions. Starting from these results, we then considered the idea of studying this process in different nanoparticle solutions. By using photon correlation spectroscopy (PCS) experiments on dendrimer with OH terminal groups (dissolved in water and methanol, respectively), we show the existence of this hydrophobic-hydrophilic crossover with a well defined temperature and nanoparticle volume fraction dependence. In this frame, we have used the mode coupling theory extended model to evaluate the measured time-dependent density correlation functions (ISFs). In this context we will, therefore, show how the measured spectra are strongly dependent on the specificity of the interactions between the particles in solution. The observed transition demonstrates that just the HE, depending sensitively on the system thermodynamics, determines the hydrophobic and hydrophilic interaction properties of the studied nanostructures surface.

Semi-analytic forecasts for Roman – the beginning of a new era of deep-wide galaxy surveys

ABSTRACT The Nancy Grace Roman Space Telescope, NASA’s next flagship observatory, will redefine deep-field galaxy survey with a field of view two orders of magnitude larger than Hubble and an angular resolution of matching quality. These future deep-wide galaxy surveys necessitate new simulations to forecast their scientific output and to optimize survey strategies. In this work, we present five realizations of 2-deg2 light cones, containing a total of ≳25 million simulated galaxies with −16 ≳ MUV ≳ −25 spanning z ∼ 0 to 10. This data set enables a new set of experiments with the impacts of survey size on the derived galaxy formation and cosmological constraints. The intrinsic and observable galaxy properties are predicted using a well-established, physics-based semi-analytic modelling approach. We provide forecasts for number density, cosmic SFR, field-to-field variance, and angular two-point correlation functions, and demonstrate how the future wide-field surveys will be able to improve these measurements relative to current generation surveys. We also present a comparison between these light cones and others that have been constructed with empirical models. The mock light cones are designed to facilitate the exploration of multi-instrument synergies and connecting with current generation instruments and legacy surveys. In addition to Roman, we also provide photometry for a number of other instruments on upcoming facilities, including Euclid and Rubin, as well as the instruments, that are part of many legacy surveys. Full object catalogues and data tables for the results presented in this work are made available through a web-based, interactive portal.

Coarse-grained Hamiltonian and effective one component theory of colloidal suspensions

We develop a theory to trace out the solvent degrees of freedom from the grand partition function of colloid-solvent mixtures. Our approach to coarse-graining is based on density functional formalism of density profile and the grand thermodynamic potential of solvent. The solvent-induced interaction which is many-body in character is expressed in terms of two functionals; one that couples the solvent to the colloidal density distribution and the second represents the density–density correlation function of the solvent. The nature, strength, and range of the potential depend on these functionals and therefore on the thermodynamic state of the solvent. The solvent-induced contribution to free energy functional is also derived. A self-consistent procedure is developed to calculate the effective potential between colloidal particles, colloid-solvent, and colloid-colloid correlation functions. The theory is used to investigate both additive and nonadditive binary hard-sphere mixtures. Results are reported for the two systems for several values of packing fractions ηb and ηs and particles diameter ratio q=σsσb where symbols b and s refer to colloid and solvent, respectively. Several interesting features are found: The short-range attractive part of the potential shows non-monotonic dependence on ηb; when ηb is increased from zero, initially the potential becomes more attractive but beyond a certain value of ηb that depends on q, the attraction starts weakening. The repulsive peaks formed at R∼(1+12nq) where R is a distance between centers of colloidal particles expressed in units of σb and n is an integer, become stronger on increasing ηb. These results show that many-body contribution to the effective potential depends in a subtle way on packing fractions ηb,ηs, size ratio q, and on nature of the interaction model and makes a non-negligible contribution to the coarse-grained Hamiltonian.

Spin relaxation rate for heavy quarks in weakly coupled QCD plasma

We compute the relaxation rate of the spin density of heavy quarks in a perturbative QCD plasma to leading-log order in the coupling constant g. The spin relaxation rate Γs in spin hydrodynamics is shown to be Γs ~ g4 log(1/g)T(T/M)2 in the heavy-quark limit T/M ≪ 1, which is smaller than the relaxation rate of other non- hydrodynamic modes by additional powers of T/M. We demonstrate three different methods to evaluate the spin relaxation rate: 1) the Green-Kubo formula in the spin hydrodynamic regime, 2) the spin density correlation function in the strict hydrodynamic limit, and 3) quantum kinetic theory of the spin distribution function in momentum space. We highlight the interesting differences between these methods, while they are ultimately connected to each other by the underlying Ward-Takahashi identity for the non-conserved spin density.