Two-particle Correlation Function Research Articles

QUANTIZED HYDRODYNAMIC THEORY OF BOSONS IN QUASI-ONE-DIMENSIONAL HARMONIC TRAP

We analytically study effects of density and phase fluctuations of quasi-one-dimensional degenerate atomic Bose gases in the mean-field as well as in the hard-core bosons regimes. We obtain the analytic expressions for dynamic structure factors in both the regimes. We also calculate single-particle density matrix and momentum distribution by taking care of the phase fluctuations upto fourth-order term, the density fluctuations as well as the non-condensate density in both the regimes. In the mean-field regime, there is a long-tail in the momentum distributions at large temperature, which can be used to identify the quasi-condensate from a pure condensate. The single-particle correlation functions of hard-core bosons is almost zero even at zero temperature due to the fermionization of the bosonic systems. Two-particle correlation function in the hard-core bosons regime shows many deep valleys at various relative separations. These valleys at various relative separations imply shell structure due to the Pauli blocking in real space.

Generalized exclusion statistics and degenerate signature of strongly interacting anyons

We show that below the degenerate temperature the distribution profiles of strongly interacting anyons in one-dimension coincide with the most probable distributions of ideal particles obeying generalized exclusion statistics (GES). In the strongly interacting regime the thermodynamics and the local two-particle correlation function derived from the GES are seen to agree for low temperatures with the results derived for the anyon model using the thermodynamic Bethe ansatz. The anyonic and dynamical interactions implement a continuous range of GES, providing a signature of strongly interacting anyons, including the strongly interacting one-dimensional Bose gas.

Combined Analysis of Two- and Three-Particle Correlations in q,p-Bose Gas Model

q-deformed oscillators and the q-Bose gas model enable effective description of the observed non-Bose type behavior of the intercept (strength) � (2) ≡ C (2) (K,K) − 1 of two-particle correlation function C (2) (p1,p2) of identical pions produced in heavy-ion collisions. Three- and n-particle correlation functions of pions (or kaons) encode more in- formation on the nature of the emitting sources in such experiments. And so, the q-Bose gas model was further developed: the intercepts of n-th order correlators of q-bosons and the n-particle correlation intercepts within the q,p-Bose gas model have been obtained, the result useful for quantum optics, too. Here we present the combined analysis of two- and three-pion correlation intercepts for the q-Bose gas model and its q,p-extension, and con- front with empirical data (from CERN SPS and STAR/RHIC) on pion correlations. Similar to explicit dependence of � (2) on mean momenta of particles (pions, kaons) found earlier, here we explore the peculiar behavior, versus mean momentum, of the 3-particle correlation intercept � (3) (K). The whole approach implies complete chaoticity of sources, unlike other joint descriptions of two- and three-pion correlations using two phenomenological parameters (e.g., core-halo fraction plus partial coherence of sources).

A model study of short range correlations with a multi determinantal method

Using a simple model of fermions interacting with a strong short range repulsive potential, we discuss how short range correlations can be described with a linear combination of Slater determinants using variational methods. The many-body wavefunction obtained in this way is used to evaluate the two-particle correlation function which shows the typical depletion at distances between particles comparable with the range of the repulsive potential.

Multiplicity Dependence of Partially Coherent Pion Production in Relativistic Heavy Ion Collisions

We investigate two- and three-particle intensity correlation functions of pions in relativistic heavy ion collisions for different colliding energies. Based on three models of particle production, we analyze the degree to which the pion sources are chaotic in the SPS S+Pb, Pb+Pb and the RHIC Au+Au collisions. The “chaoticity”, λ, of the two-particle correlation functions is corrected for long-lived resonance decays. The effect of the partial Coulomb correction is also examined. Although the partially coherent model gives a result which is consistent with that of STAR, the chaotic fraction does not exhibit clear multiplicity dependence if we take into account both the corrected chaoticity and the weight factor of the three-pion correlation function. The result of the partially-multicoherent model indicates an increasing number of coherent sources in higher multiplicity events.

Fitted Hanbury-Brown–Twiss radii versus space-time variances in flow-dominated models

The inability of otherwise successful dynamical models to reproduce the Hanbury-Brown--Twiss (HBT) radii extracted from two-particle correlations measured at the Relativistic Heavy Ion Collider (RHIC) is known as the RHIC HBT Puzzle. Most comparisons between models and experiment exploit the fact that for Gaussian sources the HBT radii agree with certain combinations of the space-time widths of the source that can be directly computed from the emission function without having to evaluate, at significant expense, the two-particle correlation function. We here study the validity of this approach for realistic emission function models, some of which exhibit significant deviations from simple Gaussian behavior. By Fourier transforming the emission function, we compute the two-particle correlation function, and fit it with a Gaussian to partially mimic the procedure used for measured correlation functions. We describe a novel algorithm to perform this Gaussian fit analytically. We find that for realistic hydrodynamic models the HBT radii extracted from this procedure agree better with the data than the values previously extracted from the space-time widths of the emission function. Although serious discrepancies between the calculated and the measured HBT radii remain, we show that a more apples-to-apples comparison of models with data can play an important role in any eventually successful theoretical description of RHIC HBT data.

Structure and decay width of the [formula omitted] in a one-gluon exchange model

The mass and decay width of the Θ + ( 1540 ) with isospin 0 are calculated in a constituent quark model comprising u u d d s ¯ quarks. A correlated basis is used in a non-relativistic five-particle model, and the Θ + is identified with a resonance state described as a solution stable against changes in the basis. With the use of a one-gluon exchange quark–quark interaction, the mass is found to be larger than 2 GeV, in a sequence of spin-parity 1 2 − , 3 2 − , 1 2 + ( 3 2 + ) , and only the 3 2 − state has a small width to the n K ∗ + decay. By shifting the calculated mass to around 100 MeV above the N + K threshold, the level to be identified with the Θ + ( 1540 ) has spin-parity 1 2 + ( 3 2 + ) or 3 2 − , though in the latter case it cannot decay to the n K + channel. In addition it is conjectured that other pentaquark states with different spin-parities exist below the Θ + ( 1540 ) . The structure of the pentaquark states is discussed in terms of the densities and two-particle correlation functions of the quarks and in terms of the wave function decompositions into a baryon–meson model and into a diquark-pair model.

Detecting Correlation Functions of Ultracold Atoms through Fourier Sampling of Time-of-Flight Images

We propose a detection method for ultracold atoms which allows reconstruction of the full one-particle and two-particle correlation functions from the measurements. The method is based on Fourier sampling of the time-of-flight images through two consecutive impulsive Raman pulses. For applications of this method, we discuss a few examples, including detection of phase separation between superfluid and Mott insulators, various types of spin or superfluid orders, entanglement, exotic or fluctuating orders.

Molecular dynamics simulations of polyampholyte solutions: osmotic coefficient

Polyampholytes are charged polymers containing both positively and negatively charged monomers widely used in colloid stabilization, wetting, adhesion, lubrication, etc. Due to the randomly distributed positive and negative charges on polymer backbone, polyampholyte chains have both the contraction tendency by counter charges and the stretch tendency by similar charges, which causes difficulty to develop a reliable molecular thermodynamic model. In this work, osmotic coefficients of solutions containing neutral or non-neutral polyampholyte chains with different segment sizes and charged sequences were obtained by molecular dynamics (MD) simulation, in which the Langevin equation considering both the viscous force from solvent and the stochastic force from heat-bath is used. A molecular thermodynamic model based on chemical association theory was developed where the polyampholyte molecules are modeled as positively and negatively charged hard-sphere chains with a chain length l. Those chains and counter-ions are embedded in a continuum medium. The l-particle cavity correlation function for a polyion chain is linearly approximated by a product of nearest-neighbor two-particle cavity correlation functions, density dependence of which is analytically expressed as a function of a scaling parameter from the mean-spherical approximation (MSA). It is shown that the predicted osmotic coefficients by the model agree satisfactorily with those obtained from MD simulation for neutral polyampholytes.

Correlation functions of light charged particles from projectile-like fragment source in [formula omitted] and 77 MeV 40Ar + 27Al collisions

Two-particle correlation functions, involving protons, deuterons, tritons, and α-particles, have been measured at very forward angles ( 0.7 ° ⩽ θ lab ⩽ 7 ° ), in order to study projectile-like fragment (PLF) emission in E / A = 44 and 77 MeV 40Ar + 27Al collisions. The observed correlations are similar for the two reactions at E / A = 44 and 77 MeV, except for peaks originating from resonance decays, which are larger at the lower bombarding energy. Particle-velocity gated correlation functions are presented, and possible implications on the time sequence of the light charged particles, emitted from the PLF, are discussed.

Polymer density functional approach to efficient evaluation of path integrals

A polymer density functional theory (P-DFT) has been extended to the case of quantum statistics within the framework of Feynman path integrals. We start with the exact P-DFT formalism for an ideal open chain and adapt its efficient numerical solution to the case of a ring. We show that, similarly, the path integral problem can, in principle, be solved exactly by making use of the two-particle pair correlation function (2p-PCF) for the ends of an open polymer, half of the original. This way the exact data for one-dimensional quantum harmonic oscillator are reproduced in a wide range of temperatures. The exact solution is not, though, reachable in three dimensions (3D) because of a vast amount of storage required for 2p-PCF. In order to treat closed paths in 3D, we introduce a so-called "open ring" approximation which proves to be rather accurate in the limit of long chains. We also employ a simple self-consistent iteration so as to correctly account for the interparticle interactions. The algorithm is speeded up by taking convolutions with the aid of fast Fourier transforms. We apply this approximate path integral DFT (PI-DFT) method to systems within spherical symmetry: 3D harmonic oscillator, atoms of hydrogen and helium, and ions of He and Li. Our results compare rather well to the known data, while the computational effort (some seconds or minutes) is about 100 times less than that with Monte Carlo simulations. Moreover, the well-known "sign problem" is expected to be considerably reduced within the reported PI-DFT, since it allows for a direct estimate of the corresponding partition functions.

XY-spin fluids in an external magnetic field: An integral equation approach

We develop an integral equation approach to study anisotropic fluids with planar spins in the presence of an external field. As a result, the integral equation calculations for these systems appear to be no more difficult than those for ordinary isotropic liquids. The method presented is applied to the investigation of phase coexistence properties of ferromagnetic XY-spin fluids in a magnetic field. The soft mean spherical approximation is used for the closure relation connecting the orientationally dependent two-particle direct and total correlation functions. The Lovett-Mou-Buff-Wertheim and Born-Green-Yvon equations are employed to describe the one-particle orientational distribution. The phase diagrams are obtained in the whole range of varying the external field for a wide class of XY-spin fluid models with various ratios of the strengths of magnetic to nonmagnetic Yukawa-like interactions. The influence of changing the screening radii of the interaction potentials is also considered. Different types of the phase diagram topology are identified. They are characterized by the existence of critical, tricritical, critical end, and triple points related to transitions between gas, liquid, and para- and ferromagnetic states, accompanied by different external field dependencies of critical temperatures and densities corresponding to the gas-liquid and liquid-liquid transitions. As is demonstrated, the integral equation approach leads to accurate predictions of the complicated phase diagram behavior which coincide well with those evaluated by the cumbersome Gibbs ensemble simulation and multiple-histogram reweighting techniques.

Mapping Out Electron-Electron Interactions at Surfaces

Using a high resolution coincidence technique, we measured for the first time the angular and energy correlation of an electron pair emitted from the valence band of a single crystal upon the impact of an electron with a specified momentum. We observe a hole in the measured two-particle correlation function when the two excited electrons have comparable momentum vectors, a fact traced back to exchange and repulsion among the electrons. We find the hole is not isotropic, has a finite extension, and is strongly suppressed when decoherence is operating.

Decomposition of harmonic and jet contributions to particle-pair correlations at ultrarelativistic energies

Methodology is presented for analysis of two-particle azimuthal angle correlation functions obtained in collisions at ultra-relativistic energies. We show that harmonic and di-jet contributions to these correlation functions can be reliably decomposed by two techniques to give an accurate measurement of the jet-pair distribution. Results from detailed Monte Carlo simulations are used to demonstrate the efficacy of these techniques in the study of possible modifications to jet topologies in heavy ion reactions.

Isospin effects in two-particle correlation functions: A probe for the isospin dependence of the nuclear equation of state

Small-angle two-particle correlation functions, involving neutrons and protons, have been measured for E/A = 61 MeV Ar + Sn-112,Sn-124 collisions, i.e. systems similar in size but with different isospin asymmetry. The correlation strength of neutron-proton (np) and proton-proton (pp) pairs is stronger for the more neutron-rich system, indicating a shorter average emission time for this system. Comparisons with isospin-dependent BUU transport model simulations are presented, and their implications for the density dependence of the nuclear symmetry energy are discussed.

Modification of jet properties at the Relativistic Heavy Ion Collider

The two-particle azimuthal correlation function in p+p and Au+Au at is studied. It is shown that the away-side correlation width is a measure of the product of parton mean transverse momentum ⟨kT⟩ and the average momentum fraction of the trigger particle ⟨ztrig⟩. The phenomenological parametrization of the parton final-state spectrum is used for the estimation of the slope of the fragmentation function. Using the knowledge of the fragmentation function the ⟨kT⟩ values in p+p collisions are deduced. The broadening of the away-side peak in Au+Au collisions is discussed.

Nonrelativistic rescattering effects on two-particle correlation

We derive a general formula for the two-particle correlation function when the produced particles are allowed to elastically rescatter in the medium. We then specialize to rescattering centres that are localized static potentials. With a Gaussian source distribution, we calculate the corrections for Rout and Rside. The ratio Rout/Rside increases with momentum from below to above unity. An example for kaon interferometry is given with some specific numbers.

Photon tagged correlations in heavy ion collisions

A detailed study of various two-particle correlation functions involving photons and neutral pions is presented in proton-proton and lead-lead collisions at the LHC energy. The aim is to use these correlation functions to quantify the effect of the medium (in lead-lead collisions) on the jet decay properties. The calculations are carried out at the leading order in QCD but the next-to-leading order corrections are also discussed. The competition between different production mechanisms makes the connection between the jet energy loss spectrum and the gamma-pi correlations somewhat indirect while the gamma-gamma correlations have a clearer relation to the jet fragmentation properties.

Isospin effects on particle emission time sequence inE∕A=61MeVAr36+Sn112,124reactions

The emission time sequence of neutrons, protons, and deuterons is deduced from velocity-gated two-particle correlation functions in E/A = 61 MeV 36Ar+112,124Sn reactions. A dependence of the emission sequence on the isospin of the emitting source is observed.

The Bose Molecule in One Dimension

We give the Green function, momentum distribution, two-particle correlation function, and structure factor for the bound state of N indistinguishable bosons with an attractive delta-function interaction in one dimension, and an argument showing that this boson “molecule” has no excited states other than dissociation into separated pieces.