Two-particle Correlation Function Research Articles

Differential two-particle number and momentum correlations with the AMPT, UrQMD, and EPOS models in Pb-Pb collisions at sNN=2.76 TeV

We report studies of charge-independent (CI) and charge-dependent (CD) two-particle differential number correlation functions, $R_{2} \left( \Delta \eta, \Delta \varphi \right)$, and transverse momentum correlation functions, $P_2 \left( \Delta \eta, \Delta \varphi \right)$ of charged particles produced in \PbPb\ collisions at the LHC centre-of-mass energy $\sqrt{s_{\rm NN}} =$ 2.76 TeV with the UrQMD, AMPT and EPOS models. Model predictions for $R_2$ and $P_2$ correlation functions are presented for inclusive charged hadrons ($h^\pm$) in selected transverse momentum ranges and with full azimuthal coverage in the pseudorapidity range $|\eta|< 1.0$. We compare these predictions for the strength, shape, and particularly the width of the correlation functions with recent measurements of these observables by the ALICE collaboration. Our analysis indicate that comparative studies of $R_2$ and $P_2$ correlation functions provide valuable insight towards the understanding of particle production in Pb--Pb collisions. We find, in particular, that these models have quantitatively different predictions for these three observables but none reproduce the measured correlation functions reported by the ALICE collaboration. Accounting for quantum number conservation in models, particularly charge conservation, is mandatory to reproduce the detailed measurements of number and transverse momentum correlation functions.

Two component quantum walk in one-dimensional lattice with hopping imbalance

We investigate the two-component quantum walk in one-dimensional lattice. We show that the inter-component interaction strength together with the hopping imbalance between the components exhibit distinct features in the quantum walk for different initial states. When the walkers are initially on the same site, both the slow and fast particles perform independent particle quantum walks when the interaction between them is weak. However, stronger inter-particle interactions result in quantum walks by the repulsively bound pair formed between the two particles. For different initial states when the walkers are on different sites initially, the quantum walk performed by the slow particle is almost independent of that of the fast particle, which exhibits reflected and transmitted components across the particle with large hopping strength for weak interactions. Beyond a critical value of the interaction strength, the wave function of the fast particle ceases to penetrate through the slow particle signalling a spatial phase separation. However, when the two particles are initially at the two opposite edges of the lattice, then the interaction facilitates the complete reflection of both of them from each other. We analyze the above mentioned features by examining various physical quantities such as the on-site density evolution, two-particle correlation functions and transmission coefficients.

Experimental investigation of abnormal transverse flow enhancement of α particles in heavy-ion collisions

The mass dependence of the transverse flow for $Z=1$--5 fragments from the collisions of $^{40}\mathrm{Ar}+^{27}\mathrm{Al}, ^{40}\mathrm{Ar}+^{48}\mathrm{Ti}$, and $^{40}\mathrm{Ar}+^{58}\mathrm{Ni}$ at 47 MeV/nucleon is investigated experimentally in this article. The transverse flow values are determined using the in-plane components of the fragment transverse momenta, where three conventional methods, i.e., the kinetic flow tensor method, the transverse momentum analysis method, and the azimuthal correlation method, are applied to reconstruct the reaction plane in an event-by-event basis. It is demonstrated from the comparison of the present experimental mass dependent flow measurements and the model simulations using an improved antisymmetrized molecular dynamics model that the experimentally observed abnormal $\ensuremath{\alpha}$ transverse flow enhancement is closely related to the reaction plane reconstruction procedure in the flow extraction. We further investigate the physical existence of the abnormal $\ensuremath{\alpha}$ flow behavior using a two-particle azimuthal correlation method, which allows us to provide the relative flow magnitude information with an identification of fragment charge number without the knowledge of the reaction plane differing from the three conventional methods. It is found that the relative flow magnitudes deduced from the two-particle azimuthal correlation functions with an identification of $Z$, with the correction for the recoil effect imposed by the momentum conservation, show a monotonically increasing trend as a function of fragment charge number, with no exception of the $\ensuremath{\alpha}$ flow enhancement. These results, in addition to those from the improved antisymmetrized molecular dynamics model simulations, definitely provide experimental evidences for the inexistence of the abnormal $\ensuremath{\alpha}$ flow behavior in the heavy-ion collisions at the present incident energy region in nature.

Scaling of factorial moments in cumulative variables

A search for power-law fluctuations within the framework of the intermittency method is ongoing to locate the critical point of the strongly interacting matter. In particular, experimental data on proton and pion production in heavy-ion collisions are analyzed in transverse-momentum, pT, space.In this regard, we have studied the dependence of the second scaled factorial moment F2 of particle multiplicity distribution on the number of subdivisions of transverse momentum-interval used in the analysis. The study is performed using a simple model with a power-law two-particle correlation function in pT. We observe that F2 values depend on the size and position of the pT interval. However, when we convert the non-uniform transverse-momentum distribution to uniform one using cumulative transformation, F2 calculated in subdivisions of the cumulative pT becomes independent of the cumulative-pT interval. The scaling behaviour of F2 for the cumulative variable is observed. Moreover, F2 follows a power law with the number of subdivisions of the cumulative-pT interval with the intermittency index close to the correlation function's exponent.

Cumulants and correlation functions of net-proton, proton, and antiproton multiplicity distributions in Au+Au collisions at energies available at the BNL Relativistic Heavy Ion Collider

We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton multiplicity distributions, and correlation functions, $\kappa_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm {NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_{n}$ and $\kappa_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_{T}$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the BNL Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y| <$ 0.5) and transverse momentum 0.4 $<$ $p_{\rm T}$ $<$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ($\sqrt{s_{\mathrm {NN}}}$ = 7.7 -- 62.4 GeV) of the net-proton $C_{4}$/$C_{2}$ with the significance of 3.1$\sigma$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with $\sqrt{s_{\mathrm {NN}}}$. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\kappa_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\kappa_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be understood by the effect of baryon number conservation.

Two-particle azimuthal correlations in photonuclear ultraperipheral Pb+Pb collisions at 5.02 TeV with ATLAS

Two-particle long-range azimuthal correlations are measured in photonuclear collisions using 1.7 nb$^{-1}$ of 5.02 TeV Pb+Pb collision data collected by the ATLAS experiment at the LHC. Candidate events are selected using a dedicated high-multiplicity photonuclear event trigger, a combination of information from the zero-degree calorimeters and forward calorimeters, and from pseudorapidity gaps constructed using calorimeter energy clusters and charged-particle tracks. Distributions of event properties are compared between data and Monte Carlo simulations of photonuclear processes. Two-particle correlation functions are formed using charged-particle tracks in the selected events, and a template-fitting method is employed to subtract the non-flow contribution to the correlation. Significant nonzero values of the second- and third-order flow coefficients are observed and presented as a function of charged-particle multiplicity and transverse momentum. The results are compared with flow coefficients obtained in proton-proton and proton-lead collisions in similar multiplicity ranges, and with theoretical expectations. The unique initial conditions present in this measurement provide a new way to probe the origin of the collective signatures previously observed only in hadronic collisions.

Accelerated impurity solver for DMFT and its diagrammatic extensions

We present ComCTQMC, a GPU accelerated quantum impurity solver. It uses the continuous-time quantum Monte Carlo (CTQMC) algorithm wherein the partition function is expanded in terms of the hybridisation function (CT-HYB). ComCTQMC supports both partition and worm-space measurements, and it uses improved estimators and the reduced density matrix to improve observable measurements whenever possible. ComCTQMC efficiently measures all one and two-particle Green's functions, all static observables which commute with the local Hamiltonian, and the occupation of each impurity orbital. ComCTQMC can solve complex-valued impurities with crystal fields that are hybridized to both fermionic and bosonic baths. Most importantly, ComCTQMC utilizes graphical processing units (GPUs), if available, to dramatically accelerate the CTQMC algorithm when the Hilbert space is sufficiently large. We demonstrate acceleration by a factor of over 600 (100) in a simulation of δ-Pu at 600 K with (without) crystal fields. In easier problems, the GPU offers less impressive acceleration or even decelerates the CTQMC. Here we describe the theory, algorithms, and structure used by ComCTQMC in order to achieve this set of features and level of acceleration. Program summaryProgram Title: ComCTQMCCPC Library link to program files:https://doi.org/10.17632/x2gzgm8njh.1Licensing provisions: GPLv3Programming language: C++/CUDANature of problem: In dynamical mean-field theory (DMFT), the computational bottleneck is the repeated solution of a quantum impurity problem [1]. The continuous-time quantum Monte-Carlo (CTQMC) algorithm has emerged as one of the most efficient methods for solving multiorbital impurity problems at moderate-to-high temperatures [2]. However, the low-temperature regime remains inaccessible, particularly for f-shell systems, and the measurement of two-particle correlation functions on an impurity adds a substantial computational burden. The bottleneck of the CTQMC solver is itself the computation of the local trace which includes the multiplication of many moderate-to-large sized matrices. The efficient solution of the impurity, measurement of the two-particle correlation functions, and acceleration of the trace computation are therefore critical.Solution method: ComCTQMC uses the hybridisation expansion of the impurity action to explore partition space [3]. It uses the worm algorithm [4] to explore the union of the partition space with observables spaces, e.g., the two-particle correlation functions. It uses improved estimators to more accurately measure the one- and two-particle Green's functions [5]. Identical impurities are solved across all MPI ranks (for ideal weak scaling) and the trace computations of these impurities are distributed to and accelerated by GPUs (when available). The lazy-trace algorithm [6] is used to further reduce the burden of the local trace calculation.Additional comments including restrictions and unusual features: ComCTQMC solves nearly arbitrary impurities, including those with complex valued and time-dependent interactions. However, there are two restrictions: (1) The retarded part of the interaction is described by a set of bilinears (a paired creation and annihilation operator), and these bilinears must commute with the local Hamiltonian and have real quantum numbers; (2) If a local Green's function vanishes, then the corresponding hybridisation function also vanishes.

Ab Initio Full Cell GW+DMFT for Correlated Materials

Quantitative prediction of electronic properties in correlated materials requires simulations without empirical truncations and parameters. We present a method to achieve this goal through a new ab initio formulation of dynamical mean-field theory (DMFT). Instead of using small impurities defined in a low-energy subspace, which require complicated downfolded interactions which are often approximated, we describe a full cell $GW$+DMFT approach, where the impurities comprise all atoms in a unit cell or supercell of the crystal. Our formulation results in large impurity problems, which we treat here with efficient quantum chemistry impurity solvers that work on the real-frequency axis, combined with a one-shot $G_0W_0$ treatment of long-range interactions. We apply our full cell approach to bulk Si, two antiferromagnetic correlated insulators NiO and $\alpha$-Fe$_2$O$_3$, and the paramagnetic correlated metal SrMoO$_3$, with impurities containing up to 10 atoms and 124 orbitals. We find that spectral properties, magnetic moments, and two-particle spin correlation functions are obtained in good agreement with experiments. In addition, in the metal oxide insulators, the balanced treatment of correlations involving all orbitals in the cell leads to new insights into the orbital character around the insulating gap.

Time- and frequency-domain two-particle correlations of a driven dissipative Bose-Hubbard model

We investigate theoretically the time- and frequency-domain two-particle correlations of a driven-dissipative Bose-Hubbard model at and near a dissipative phase transition (DPT). We compute the Hanbury Brown--Twiss (HBT)-type two-particle temporal correlation function ${g}^{2}(\ensuremath{\tau})$ which, as a function of time delay $\ensuremath{\tau}$, exhibits oscillations with frequencies determined by the imaginary part of the Liouvillian gap. As the gap closes near a transition point, the oscillations at that point die down. For parameters slightly away from the transition point, the HBT correlations show oscillations from superbunching to antibunching regimes. We show that the Fourier transform of HBT correlations into the frequency domain provide information about DPT and Liouvillian dynamics. We numerically solve the many-body Lindblad master equation and calculate the Wigner distribution of the system in the steady state to ascertain the DPT. Below a certain drive strength, the Fourier transform shows a two-peak structure, while above that strength it exhibits either a Lorentzian-like single-peak structure or a structure with two dips. The width of the single-peak structure is minimal at the phase-transition point and the peak of this structure always lies at zero frequency. The positions of the two symmetrical peaks in case of a two-peak structure are given by the imaginary parts of the Liouvillian gap while their half width at half maximum is given by the real part of the gap. The positions and widths of the two dips are also related to low-lying eigenvalues of the Liouvillian operator. We discuss quantum statistical properties of the model in terms of the HBT correlation function and its Fourier transform.

INSTABILITY IN A DISLOCATION ENSEMBLE AT PLASTIC DEFORMATION IN METALS

A problem related to the development of instability of a homogeneous state in an ensemble of screw dislocations under plastic deformation of metals is considered . The study of the development of instability and structure formation in the dislocation ensemble is carried out on the basis of the method developed for charged particles in plasma and associated with the correlation interaction of electrons and positively charged ions. Accordingly, the screw dislocation ensemble is represented as a system of dislocations with an opposite Burgers vector, i.e., as a plasma-like medium with opposite dislocation charges. The total dislocation charge of the dislocation ensemble is equal to zero due to the law of conservation of the Burgers vector. In this situation, the elastic field of dislocations is “cut off”. The stress field of a single dislocation is shielded by a uniformly distributed dislocation “background” and is characterized by a certain effective potential. It is found that at long distances it decreases exponentially. Therefore, the value in the argument of the falling potential can be considered as the radius of screening of the elastic field of dislocations. It is shown that the screening radius is equal to the correlation radius, which makes it possible to construct a two-particle correlation function and find the energy of the correlation interaction of dislocations. A system of kinetic equations for a dislocation ensemble is formulated, taking into account the elastic and correlation interaction of dislocations, as well as the processes of their generation and annihilation. The criterion of instability of the homogeneous distribution of dislocations for the formulated system of equations is established. The instability criterion is met under the condition that the dislocation density exceeds a certain critical value that depends on the square of the flow stress and material constants (such as the Burgers vector modulus and shear modulus, as well as indirectly, the packing defect energy). In the framework of linear analysis, it is shown that when one system of sliding screw dislocations is taken into account, a one – dimensional periodic dislocation dissipative structure is formed at the moment of instability occurrence, and when multiple sliding is taken into account, solutions appear in the form of various variants of polyhedral lattices (cellular structures). It is established that the characteristic size of the cellular structure coincides with the experimental dependence both qualitatively and quantitatively ( the cell size is proportional to the square root of the dislocation density, and the proportionality coefficient is about ten). It is shown that the origin of spatially inhomogeneous dislocation structures, based on correlation instability, depends mainly on the features of the elastic interaction of dislocations and is not critical to the choice of the mechanisms of their kinetics (i.e., the mechanisms of generation, annihilation, and runoff of dislocations).

Correlation analysis of high-energy heavy-ion collisions within the integrated hydrokinetic model

The interferometry radii, obtained from the Gaussian fits to the two-particle momentum correlation functions for different high-energy heavy-ion collision experiments at the LHC and the top RHIC energies, are described in the integrated hydrokinetic model. The role of the different geometrical sizes of the colliding ions in the formation of the observed femtoscopy scales is investigated by comparing the results for Au+Au, Pb+Pb and Xe+Xe collisions at close values of the mean charged particle multiplicity.

Exploring the Λ -deuteron interaction via correlations in heavy-ion collisions

$\Lambda$-deuteron two-particle momentum correlation functions, to be measured in high-energy heavy-ion collisions, are investigated. In particular, the question is addressed whether such correlations can serve as an additional and alternative source of information on the elementary $\Lambda N$ interaction. The study is performed within the Lednicky-Lyuboshits formalism, utilizing an effective range expansion for the two relevant $S$-wave $\Lambda d$ amplitudes with parameters taken from the literature. It is found that in collisions characterized by a large emitting source the $\Lambda d$ correlation function is predominatly sensitive to the quartet state ($^4S_{3/2}$). In contrast, for small source sizes the contribution from the doublet partial wave ($^2S_{1/2}$) could be significant. Though the latter is constrained by the hypertriton binding energy, its present experimental uncertainty impedes an accurate determination of the doublet amplitude and, in turn, complicates conclusions on the quartet state.

Long-range azimuthal correlations for partially coherent pion emission in proton-proton collisions

In this paper, we investigate the influence of coherent pion emission on long-range azimuthal correlations in relativistic proton-proton collisions. We study the pion momentum distribution for a coherent source with both transverse and Bjorken longitudinal expansions, and calculate the two-particle correlation function C(Δη,Δϕ). A “ridge” structure is observed in the correlation function C(Δη,Δϕ) of the coherent pion emission, whether the coherent source is expanding or static. The onset of this long-range azimuthal correlation can be traced back to the asymmetric initial transverse profile of the coherent source, owing to the interference in coherent emission. We further construct a partially coherent pion-emitting source by incorporating a chaotic emission component. From the experimental data of the two-pion Hanbury-Brown-Twiss correlations in pp collisions at s=7 TeV, we extract a coherent fraction of pion emission, which increases with increasing charged-particle multiplicity, as an input of the partially coherent source model. The ridge structure is observed in the correlation function C(Δη,Δϕ) for the partially coherent source. The correlation becomes stronger at higher multiplicities because of the larger degrees of coherence. The results in this work are meaningful for fully understanding the collectivity in the small system of pp collisions.

Femtoscopic correlations and the varLambda _c N interaction

We study the prospects for deducing constraints on the interaction of charmed baryons with nucleons from measurements of two-particle momentum correlation functions for varLambda _c p. The correlation functions are calculated for varLambda _c N and varSigma _c N interactions that have been extrapolated from lattice QCD simulations at unphysical masses of m_pi =410-570 MeV to the physical point using chiral effective field theory as guideline. In addition, we consider phenomenological Y_c N models from the literature to explore the sensitivity of the results to the properties of the interaction in detail. We find that a measurement of the varLambda _c p correlation functions could indeed allow one to discriminate between strongly attractive varLambda _c N forces, as predicted by some phenomenological models, and a weakly attractive interaction as suggested by the presently available lattice simulations.

Quantum walks of interacting Mott-insulator defects with three-body interactions

Quantum walks of interacting particles may display non-trivial features due to the interplay between the statistical nature and the many-body interactions associated to them. We analyze the quantum walk of interacting defects on top of an uniform bosonic Mott insulator at unit filling in an one dimensional graph. While the quantum walk of single particle defect shows trivial features, the case of two particles exhibits interesting phenomenon of quantum walk reversal as a function of additional onsite three-body attractive interactions. In the absence of the three-body interaction a quantum walk of pairs of particles is obtained and as the strength of the three-body interaction becomes more and more attractive, the independent particle behavior in quantum walk appears. Interestingly, further increase in the three-body interaction leads to the re-appearance of the quantum walk associated to a pair of particles. This quantum-walk reversal phenomenon is studied using the real-space density evolution, Bloch oscillation as well as two-particle correlation functions.

Multiplicity Correlations with Strongly Intensive Quantities

The strongly intensive observable between multiplicities in two acceptance windows separated in rapidity is calculated in the model with quark-gluon strings acting as particle emitting sources. The dependence of this observable on the two-particle correlation function of a string, the width of observation windows and the rapidity gap between them is presented. String fusion effects violate the property of strong intensity. Changes in the behaviour of this observable with energy and collision centrality, arising due to the string fusion phenomena, are discussed. Predictions for the NICA collision energy range are presented.

Tsallis meets Boltzmann: q-index for a finite ideal gas and its thermodynamic limit.

Nonadditive Tsallis q-statistics has successfully been applied for a plethora of systems in natural sciences and other branches of knowledge. Nevertheless, its foundations have been severely criticized by some authors based on the standard additive Boltzmann-Gibbs approach, thereby remaining a quite controversial subject. In order to clarify some polemical concepts, the distribution function for an ideal gas with a finite number of point particles and its q-index are analytically determined. The two-particle correlation function is also derived. The degree of correlation diminishes continuously with the growth of the number of particles. The ideal finite gas system is usually correlated, becomes less correlated when the number of particles grows, and is finally fully uncorrelated when the molecular chaos regime is reached. It is also advocated that both approaches can be confronted through a careful kinetic spectroscopic experiment. The analytical results derived here suggest that Tsallis q-statistics may play a physical role more fundamental than usually discussed in the literature.

K^{-}p Correlation Function from High-Energy Nuclear Collisions and Chiral SU(3) Dynamics.

The two-particle momentum correlation function of a K^{-}p pair from high-energy nuclear collisions is evaluated in the K[over ¯]N-πΣ-πΛ coupled-channel framework. The effects of all coupled channels together with the Coulomb potential and the threshold energy difference between K^{-}p and K[over ¯]^{0}n are treated completely for the first time. Realistic potentials based on the chiral SU(3) dynamics are used which fit the available scattering data. The recently measured correlation function is found to be well reproduced by allowing variations of the source size and the relative weight of the source function of πΣ with respect to that of K[over ¯]N. The predicted K^{-}p correlation function from larger systems indicates that the investigation of its source size dependence is useful in providing further constraints in the study of the K[over ¯]N interaction.

Two-particle correlation functions in cluster perturbation theory: Hubbard spin susceptibilities

Cluster Perturbation Theory (CPT) is a computationally economic method commonly used to estimate the momentum and energy resolved single-particle Green's function. It has been used extensively in direct comparisons with experiments that effectively measure the single-particle Green's function, e.g., angle-resolved photoemission spectroscopy. However, many experimental observables are given by two-particle correlation functions. CPT can be extended to compute two-particle correlation functions by approximately solving the Bethe-Salpeter equation. We implement this method and focus on the transverse spin-susceptibility, measurable via inelastic neutron scattering or with optical probes of atomic gases in optical lattices. We benchmark the method with the one-dimensional Fermi-Hubbard model at half filling by comparing with known results.

Beam-energy dependence of identified two-particle angular correlations in sNN=7.7–200 GeV Au+Au collisions

The two-particle angular correlation functions, $R_2$, of pions, kaons, and protons in Au+Au collisions at $\sqrt{s_{NN}}=$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV were measured by the STAR experiment at RHIC. These correlations were measured for both like-sign and unlike-sign charge combinations and versus the centrality. The correlations of pions and kaons show the expected near-side ({\it i.e.}, at small relative angles) peak resulting from short-range mechanisms. The amplitudes of these short-range correlations decrease with increasing beam energy. However, the proton correlation functions exhibit strong anticorrelations in the near-side region. This behavior is observed for the first time in an A+A collision system. The observed anticorrelation is $p_{T}$-independent and decreases with increasing beam energy and centrality. The experimental results are also compared to the Monte Carlo models UrQMD, Hijing, and AMPT.