Three-particle Correlation Functions Research Articles

Elucidating lipid conformations in the ripple phase: Machine learning reveals four lipid populations

A new mixed radial-angular, three-particle correlation function method in combination with unsupervised machine learning was applied to examine the emergence of the ripple phase in dipalmitoylphosphatidylcholine (DPPC) lipid bilayers using data from atomistic molecular dynamics simulations of system sizes ranging from 128 to 4096 lipids. Based on the acyl tail conformations, the analysis revealed the presence of four distinct conformational populations of lipids in the ripple phases of the DPPC lipid bilayers. The expected gel-like (ordered; Lo) and fluid-like (disordered; Ld) lipids are found along with their splayed tail equivalents (Lo,s and Ld,s). These lipids differ, based on their gauche distribution and tail packing. The disordered (Ld) and disordered-splayed (Ld,s) lipids spatially cluster in the ripple in the groove side, that is, in an asymmetric manner across the bilayer leaflets. The ripple phase does not contain large numbers of Ld lipids; instead they only exist on the interface of the groove side of the undulation. The bulk of the groove side is a complex coexistence of Lo,Lo,s, and Ld,s lipids. The convex side of the undulation contains predominantly Lo lipids. Thus, the structure of the ripple phase is neither a simple coexistence of ordered and disordered lipids nor a coexistence of ordered interdigitating gel-like (Lo) and ordered-splayed (Lo,s) lipids, but instead a coexistence of an ordered phase and a complex mixed phase. Principal component analysis further confirmed the existence of the four lipid groups.

Structural and mass transport properties of liquid ytterbium in the temperature range 1123 K–1473 K

We have studied the structural and atomic transport properties of liquid f-shell Yb in the temperature range 1123 K–1473 K. Pair interactions between atoms are derived using a local pseudopotential. The potential parameters are fitted to the phonon dispersion curve at room temperature. The local pseudopotential used in the present study is computationally more efficient with only three parameters, and it is found to be transferable to the liquid phase without changing the parameters. Since the various computed properties agree with reported theoretical and experimental findings, the adopted fitting scheme is justified. As a significant outcome of the study, we find that (i) the melting in Yb is governed by the Lindemann’s law, (ii) the mass transport mechanism obeys the Arrhenius law, (iii) the role of the three-particle correlation function in deriving the velocity autocorrelation function is small, (iv) the mean-square atomic displacement is more sensitive to the choice of interaction potential than the other bulk properties, and (v) liquid Yb does not show liquid–liquid phase transition within the studied temperature range. Further, due to the good description of the structural and mass transport properties, we propose that Yb remains divalent at reduced density.

Derivation of a constitutive model for the rheology of jammed soft suspensions from particle dynamics

Considering the rheology of two-dimensional soft suspensions above the jamming density, we derive a tensorial constitutive model from the microscopic particle dynamics. Starting from the equation governing the N-particle distribution, we derive an evolution equation for the stress tensor. This evolution equation is not closed, as it involves the pair and three-particle correlation functions. To close this equation, we first employ the standard Kirkwood closure relation to express the three-particle correlation function in terms of the pair correlation function. Then we use a simple and physically motivated parametrization of the pair correlation function to obtain a closed evolution equation for the stress tensor. The latter is naturally expressed as separate evolution equations for the pressure and for the deviatoric part of the stress tensor. These evolution equations provide us with a non-linear tensorial constitutive model describing the rheological response of a jammed soft suspension to an arbitrary uniform deformation. One of the advantages of this microscopically-rooted description is that the coefficients appearing in the constitutive model are known in terms of packing fraction and microscopic parameters.

A Fourier-cumulant analysis for multiharmonic flow fluctuation

The Fourier analysis of the final particle distribution followed by cumulant study of the Fourier coefficient event-by-event fluctuation is one of the main approaches for testing the collective evolution in the heavy-ion collision. Using a multidimensional generating function, we propose a method to extract any possible cumulant of multiharmonic flow fluctuations and classify them in terms of the order of cumulants and harmonics involved in them. In particular, we show that there are 33 distinct cumulants with order 2, 3, 4, 5 and harmonics 2, 3, 4, 5. We compute the normalized version of these cumulants from hydrodynamic simulation for Pb–Pb collisions based on T_mathtt{R}ENTo+VISH2+1+UrQMD. We compare the simulation with those normalized cumulants that the LHC has measured and predict the unmeasured ones. Comparing the initial and final state fluctuation normalized cumulants, we compute the linear and nonlinear hydrodynamic response couplings. We finally introduce the genuine three-particle correlation function containing information of all third-order cumulants.

Bosonic Pfaffian state in the Hofstadter-Bose-Hubbard model

Topological states of matter, such as fractional quantum Hall states, are an active field of research due to their exotic excitations. In particular, ultracold atoms in optical lattices provide a highly controllable and adaptable platform to study such new types of quantum matter. However, finding a clear route to realize non-Abelian quantum Hall states in these systems remains challenging. Here we use the density-matrix renormalization-group (DMRG) method to study the Hofstadter-Bose-Hubbard model at filling factor $\nu = 1$ and find strong indications that at $\alpha=1/6$ magnetic flux quanta per plaquette the ground state is a lattice analog of the continuum non-Abelian Pfaffian. We study the on-site correlations of the ground state, which indicate its paired nature at $\nu = 1$, and find an incompressible state characterized by a charge gap in the bulk. We argue that the emergence of a charge density wave on thin cylinders and the behavior of the two- and three-particle correlation functions at short distances provide evidence for the state being closely related to the continuum Pfaffian. The signatures discussed in this letter are accessible in current cold atom experiments and we show that the Pfaffian-like state is readily realizable in few-body systems using adiabatic preparation schemes.

Predicting the slope of the radial distribution function of a hard disk fluid

The slope of the radial distribution function at contact is investigated for a pure component two-dimensional hard disk fluid. Using the framework of scaled particle theory (SPT), an exact equation for g'(σ +) is derived in terms of SPT quantities. This new expression requires the value of the average of a three-particle correlation function for which an ideal gas approximation is developed. The resultant predictions for g'(σ +) are compared to those generated from literature equations and to simulation data generated for this work. In addition to simulation data for g'(σ +), simulation values for the three-particle correlation function are presented for comparison to the approximation. The simple fourth-order integer coefficient polynomial is an accurate predictor of g'(σ +), on the order of or better than what is calculated by existing equations.

Computation of the equilibrium three-particle entropy for dense atomic fluids by molecular dynamics simulation.

We have computed the two- and three-particle contribution to the entropy of a Weeks-Chandler-Andersen fluid via molecular dynamics simulations. The three-particle correlation function and entropy were computed with a new method which simplified the calculation. Results are qualitatively similar to Lennard-Jones systems. We observed a numerical instability in the three-particle contribution. This phenomenon has been previously detected when the traditional method is used; thus, it is likely to be intrinsic in the computation. While the effect of statistical fluctuations can be removed through an extrapolation procedure, the discretization error due to the finite bin size is more difficult to characterize. With a correct choice of the bin size, a good estimate of the three-particle entropy contribution can be achieved at any state, even close to the freezing point. We observed that, despite the fact that the magnitude of the three-particle contribution increases significantly compared to that of the two-particle contribution as freezing is approached, the error induced from overestimation of the excess entropy by the two- and three-body terms exceeds that induced by approximating the excess entropy with the two body term alone.

Particle spatial arrangement metrics for near-crack-tip stress

Motivated by the lack of spatial information in fracture mechanics formulations, this work updates near-crack-tip stress field equations by introducing two scalar order metrics that capture particle arrangement. These metrics are based on the two-particle and three-particle spatial correlation functions. By evaluating these order metrics in particle distributions generated as stochastic perturbations of a regular grid, we study their behavior as a function of a perturbation parameter. To incorporate the scalar measures into the closed-form solution of the stress field near the crack tip, we introduce a correction factor containing both measures. The limits of these factors are established using existing results from computational fracture toughness experiments. The present study provides new tools to improve the description of material microstructure and allows us to describe the sensitivity of crack-tip stress to the particle arrangement. This will be useful for manufacturing techniques like additive manufacturing, where feature description of material microstructure is required.

Predictions on three-particle azimuthal correlations in proton--proton collisions

The ridge signal, which is long-ranged in rapidity, in the di-hadron correlations in high-multiplicity p-p and p-A collisions opened up a whole new research area in high-energy QCD. Although the ridge had been observed in A-A collisions and interpreted as a result of the radial flow of quark-gluon plasma, it had not appeared until recently in the data of small collision systems such as p-p and p-A, nor had it been predicted theoretically or seen in the event generators. There are two competing approaches that attempt to explain the systematics of the di-hadron ridge signal; hydrodynamics and gluon saturation physics (color glass condensate/glasma). In this work, we present predictions for the transverse momentum and rapidity dependence of the three-particle correlation function within the gluon saturation physics. Tri-hadron correlations can be measured, and the data can possibly rule out one of the two alternative approaches.

Application of the Two-Particle Correlation Function Approach to the Description of a Single-Pass Free Electron Laser Operated in SASE Mode

We describe the theory of a superluminescent single-pass free electron laser based on the Bogolyubov chain of equations for multiparticle distribution functions. Special choice of the variables eliminates the retardation of interaction. A small parameter (inverse number of particles per signal growth length in the accompanying reference system) for the chain truncation is found. Expansion over this parameter makes it possible to neglect three-particle correlation functions and solve only the equations containing a single-particle distribution function and two-particle correlation functions. The calculation results are in good agreement with the conclusions based on the previously developed quasilinear theory.

Three-particle correlations in liquid and amorphous aluminium

Analysis of three-particle correlations is performed on the basis of simulation data of atomic dynamics in liquid and amorphous aluminium. A three-particle correlation function is introduced to characterize the relative positions of various three particles—the so-called triplets. Various configurations of triplets are found by calculation of pair and three-particle correlation functions. It was found that in the case of liquid aluminium with temperatures 1000 K, 1500 K, and 2000 K the three-particle correlations are more pronounced within the spatial scales, comparable with a size of the second coordination sphere. In the case of amorphous aluminium with temperatures 50 K, 100 K, and 150 K these correlations in the mutual arrangement of three particles are manifested up to spatial scales, which are comparable with a size of the third coordination sphere. Temporal evolution of three-particle correlations is analyzed by using a time-dependent three-particle correlation function, for which an integro-differential equation of type of the generalized Langevin equation is output with help of projection operators technique. A solution of this equation by means of mode-coupling theory is compared with our simulation results. It was found that this solution correctly reproduces the behavior of the time-dependent three-particle correlation functions for liquid and amorphous aluminium.

Classical non-Markovian Boltzmann equation

The modeling of particle transport involves anomalous diffusion, ⟨x2(t) ⟩ ∝ tα with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advection-dispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.

Second-order response Bethe-Salpeter equation

A Bethe-Salpeter equation for the three-particle correlation function is derived, representing a second-order response generalization of the usual Bethe-Salpeter equation. The equation can be solved formally, giving the three-particle correlation function in terms of the two-particle correlation function and many-body interaction kernels. The similarity to second-order response time-dependent density-functional theory can be used to improve the understanding of the higher-order exchange and correlation kernels of this theory. An exact expression for such a kernel is derived.

Intercepts of the momentum correlation functions in the $ \mu$ -Bose gas model and their asymptotics

The so-called \mu-deformed oscillator (or \mu-oscillator) introduced by A.Jannussis, though possesses rather exotic properties with respect to other better known deformed oscillator models, also has good potential for diverse physical applications. In this paper, the corresponding \mu-Bose gas model based on \mu-oscillators is explored. Within this model, the intercepts \lambda^(2)(K) and \lambda^(3)(K) of two- and three-particle momentum correlation functions are calculated with the goal of possible application for modeling the non-Bose type behavior of the intercepts of two- and three-pion correlations, observed in the experiments on relativistic heavy ion collisions. In derivation of intercepts, different orders of approximation in the deformation parameter \mu are considered. Our analysis also yields asymptotical behavior of the intercepts \lambda^(2)(K) and \lambda^(3)(K). The results for \lambda^(2)(K) are compared with experimental data, and with earlier known results drawn using other deformed Bose gas models.

Transport through a Kondo quantum dot: Functional RG approach

We apply the functional renormalization group (FRG) method to calculate the conductance of a quantum dot in the Kondo regime. Starting from the exact FRG equations in Keldysh formulation for the Kondo exchange Hamiltonian in pseudo-fermion (pf) representation, we solve the coupled equations for the pf self energy and the coupling function, neglecting three-particle and higher correlation functions. The conductance $G$ as a function of temperature $T$ and bias voltage $V$ is calculated using a renormalized Golden Rule expression. The limiting behavior at $T$ and/or $V$ $\gg T_{K}$ ($T_{K}$ : Kondo temperature) agrees with known results. The difficulties when approaching strong coupling are analyzed and improvements are suggested.

The importance of the three-particle correlation function in the theory of monatomic classical liquids like argon

The present study was motivated by the work of Fortov et al. (2008) on the use of experimental methods of analysis of spatial correlation of dust particles in plasma. Here, we therefore focus on the importance of the three-particle correlation function g 3 in the theory of monatomic classical liquids like argon, in the framework of two-body central forces. We cover (i) the asymptotic relation of g 3 to the Ornstein–Zernike direct correlation function c(r); (ii) the use of g 3 to determine the specific heat difference c P − c V ; and (iii) g 3 related to the pressure dependence of the pair correlation function.

Dynamics of a dilute sheared inelastic fluid. II. The effect of correlations

The effect of correlations on the viscosity of a dilute sheared inelastic fluid is analyzed using the ring-kinetic equation for the two-particle correlation function. The leading-order contribution to the stress in an expansion in =(1-e);{12} is calculated, and it is shown that the leading-order viscosity is identical to that obtained from the Green-Kubo formula, provided the stress autocorrelation function in a sheared steady state is used in the Green-Kubo formula. A systemmatic extension of this to higher orders is also formulated, and the higher-order contributions to the stress from the ring-kinetic equation are determined in terms of the terms in the Chapman-Enskog solution for the Boltzmann equation. The series is resummed analytically to obtain a renormalized stress equation. The most dominant contributions to the two-particle correlation function are products of the eigenvectors of the conserved hydrodynamic modes of the two correlated particles. In Part I, it was shown that the long-time tails of the velocity autocorrelation function are not present in a sheared fluid. Using those results, we show that correlations do not cause a divergence in the transport coefficients; the viscosity is not divergent in two dimensions, and the Burnett coefficients are not divergent in three dimensions. The equations for three-particle and higher correlations are analyzed diagrammatically. It is found that the contributions due to the three-particle and higher correlation functions to the renormalized viscosity are smaller than those due to the two-particle distribution function in the limit -->0 . This implies that the most dominant correlation effects are due to the two-particle correlations.

Transverse radial flow effects on two- and three-particle angular correlations

We use a simple a transverse radial boost scenario coupled to PYTHIA events to illustrate the impact radial flow may have of two- and three-particle correlation functions measured in heavy-ion collisions. We show that modest radial velocities can impart strong modifications to the correlation functions, some of which may be interpreted as same side ridge and away side structure that can mimic conical emission.

Tracer diffusion in ordered lattice-gas systems with defect-controlled transport mechanisms

Tracer diffusion in an ordered two-dimensional lattice-gas system with square lattice symmetry is studied theoretically and by means of computer simulations. It is well known that the ordering with $c(2\ifmmode\times\else\texttimes\fi{}2)$ symmetry formed in the vicinity of half-filling of lattice sites is due to strong nearest neighbor repulsive interaction. In this case, the tracer migration occurs mainly by elementary displacements of structural defects. This paper focuses on the dimer transport mechanism which was accounted for with insufficient accuracy in previous publications. The long-time asymptotics of the dimer-tracer correlation function (i.e., a three-particle correlation function), which describes concerted tracer-dimer motion, is obtained analytically. We analyze a specific exchange mechanism, relevant to tracer diffusion only. Also, the contribution of generation-recombination jumps to tracer diffusion is taken into account. The theoretical data agree well with the results of intensive Monte Carlo simulations.

COHERENCE OF PION SOURCES FROM MULTI-PION INTERFEROMETRY IN RELATIVISTIC HEAVY ION COLLISIONS AT SPS AND RHIC

We study degree of coherence of pion sources by making use of two- and three-particle momentum intensity correlation functions in S + Pb , Pb + Pb , and Au + Au collisions at SPS and RHIC. For each system, we calculate a chaotic fraction ε and the number of coherent sources α from the chaoticity λ of the two-pion correlation function and the weight factor ω of the three-pion correlator. We take account of long-lived resonance decay contribution to the λ factor by making a correction with the help of a statistical model. The result gives strong constraints on the source and shows roughly increasing number of coherent sources as multiplicity increases.