Particle Correlation Functions Research Articles

Towards the application of the maximum entropy method to finite temperature upsilon spectroscopy

According to the Narnhofer Thirring Theorem [1] interacting systems at finite temperature cannot be described by particles with a sharp dispersion law. It is therefore mandatory to develop new methods to extract particle masses at finite temperature. The Maximum Entropy method offers a path to obtain the spectral function of a particle correlation function directly. We have implemented the method and tested it with zero temperature ϒ correlation functions obtained from an NRQCD simulation. Results for different smearing functions are discussed.

A New Method for Determining the Detection Efficiency of Adjacent Tracks

While using a track detector located in a magnetic field to investigate the correlation of identical particles with momenta similar in value, it is necessary to know the behavior of the detector efficiency and (or) event-reconstruction program in the specific case whereby the tracks are set closely to each other throughout their lengths. With this goal in mind, we proposed to analyze the dependences of the correlation functions of particles, differing widely in mass, on their relative momenta. The method is based on the assumption that the physical and methodical singularities of the correlation function for these pairs lie in different kinematic regions.

4He Shadow Wave Function with an Inverse Seventh Power Particle–Particle Correlation Function

Many ground state studies of 4He using a shadow wave function with an inverse fifth power McMillan particle–particle correlation function have yielded radial distribution functions with misplaced peaks. It has been conjectured that this is due to the specific choice of the McMillan correlation function. However, beyond the use of fully optimized two-particle correlation functions, there has been little study of simple alternatives that can correct this defect. In this work we show that the remedy is surprisingly simple. When a shadow wave function with an inverse seventh power particle–particle correlation function is used to study 4He, it gives a correctly peaked radial distribution function, lowers the energy at all liquid and solid densities, and produces an excellent equation of state.

More efficient Brownian dynamics algorithms

We examine the relative efficiencies of three- algorithms for performing Brownian Dynamics simulations without many-body hydrodynamics. We compare the conventional Brownian Dynamics algorithm of Ermak (CBD), Smart Monte Carlo (SMC) which incorporates Boltzmann sampling into essentially a CBD procedure, and the Stochastic Runge Kutta (SRK) method. We show, using the repulsive potential φ(r) = ε(σ/r) n , where n = 36 and 72, that the SRK algorithm gives the most accurate short-time dynamics for the mean-square displacements. The SRK algorithm static and dynamical properties converge better with a reducing time step to the exact values, than those generated by the CBD algorithm; giving efficiency gains typically of a factor of 3–4. Both CBD and SMC have the incorrect sign for the first correction term to the mean square displacement in a time step, whereas the SRK algorithm gives essentially the exact solution to order Δt 2, where Δt is the simulation time step. In fact, these correction terms are almost equal and opposite in sign. Expressions for these terms were derived in terms of the average interaction energy per particle. The force, shear and bulk stress autocorrelation functions were calculated. The average energy per particle and time correlation functions at short time have values in excess of the exact values, while the corresponding quantities for SRK are below this. This difference in behaviour can be traced back to the extent of compliance of the particle trajectories with the exact expansion of the Smoluchowski equation. The accuracy, at a given value of the time step, of the stochastic algorithms can significantly depend on the form of the interaction potential between particles. It is also demonstrated that the long time limits of various correlation functions are fairly insensitive to a particular scheme (SRK or CBD) used in the simulations. All the correlation functions have a stretched exponential region at intermediate to long times, and the values of the exponents on density and force law steepness have been determined.

Linear and non-linear contributions to pairwise peculiar velocities

We write the correlation function of dark matter particles, ξ(r), as the sum of two terms — one which accounts for non-linear evolution, and dominates on small scales, and another which is essentially the term from linear theory, and dominates on large scales. We use models of the number and spatial distribution of haloes and halo density profiles to describe the non-linear term and its evolution. The result provides a good description of the evolution of ξ(r) in simulations. We then use this decomposition to provide simple and accurate models of how the single-particle velocity dispersion evolves with time, and how the first and second moments of the pairwise velocity distribution depend on scale. The key idea is to use the simple physics of linear theory on large scales, the simple physics of the virial theorem on small scales and our model for the correlation function to tell us how to weight the two types of contributions (linear and non-linear) to the pairwise velocity statistics. When incorporated into the streaming model, our results will allow a simple accurate description of redshift-space distortions over the entire range of linear to highly non-linear regimes.

Collapse transitions of a supersized neutral chain due to irreversibly adsorbed small colloidal particles

We performed Monte Carlo simulations to study the destabilization processes of large neutral and flexible polymer chains due to irreversibly adsorbed colloidal particles attached to the chains like beads on a necklace. The particles are modeled as charged spherical units which interact with each other via repulsive electrostatic and attractive van der Waals (vdW) potentials. The usual Monte Carlo search procedure is extended and carefully checked to completely sample the chain conformational space and achieve dense conformations in the limit of both strong attractive and repulsive interaction potentials. Configurational properties, such as the radius of gyration, the end-to-end length, and the Kuhn length, are calculated as a function of the intensity of the vdW interactions and ionic strength values. It is observed that chains exhibit a new range of possible conformations compared to the classical random walk and self avoiding walk chains or polyelectrolytes. In the limit of low salt concentration, by gradually increasing vdW interactions, chains undergo a cascade of transitions from extended structures to dumbbells, from dumbbells to pearl necklaces, and from pearl necklaces to collapsed coils. Because of strong competition between the vdW and electrostatic forces, the distance along the chain between the interacting particles, and the sampling limitations, these transitions are found to sample metastable domains and to depend on the initial conformations. To gain insight into the spatial organization of the collapsed conformations, the pair correlation functions of both monomers and particles are calculated. It is shown that collapsed conformations which are the result of strong particle–particle interactions exhibit two distinct parts: a hard core mainly composed of particles and a surrounding polymeric shell composed of loops and tails. Possible effects of such a collapsed transition on the kinetics of flocculation of a mixture containing large flexible chains and small adsorbing colloidal particles are discussed.

Analytical solution to the equation for pair correlation function of particles formed in the course of phase separation in a glass

The problem of determining the pair correlation function of phase-separated particles from the experimental data obtained for the plane section of a sample has already been consul and in the literature. The integral equation relating the pair correlation function of monodisperse spherical particulers and the pair correlation function of their traces on the secant plane was obtained, and the method of numerical solution of this equation was elaborated with the aim of determining the pair correlation function of places. The present paper describes the analytical solution to this equation.

Optimization of Multiparticle Correlations in Bose Fluids

We study a variational multiparticle correlation theory for the ground state of inhomogeneous Bose fluids at zerotemperature. The ground state wave function of a many-boson system is written as a generalized Jastrow–Feenberg function including multiparticle correlation functions. Euler–Lagrange equations for the one, two, three and four particle correlation functions are derived using a systematic functional theoretical approach within the framework of the generalized hypernetted chain theory (HNC2 equations). The Euler–Lagrange equations for the optimal one and two particle correlation functions are analyzed including the infinite series of the elementary diagrams summed by integral equations. For the determination of the optimal triplet correlation factor we propose a novel iterative procedure in which the HNC2 equation is used to calculate the triplet distribution function.

Directed random walk in adsorbed monolayer

We study the dynamics of a tracer particle, which performs a totally directed random walk in an adsorbed monolayer composed of mobile hard-core particles undergoing continuous exchanges with a vapour phase. In terms of a mean-field-type approach, based on the decoupling of the tracer–particle–particle correlation functions into the product of pairwise, tracer–particle correlations, we determine the density profiles of the monolayer particles, as seen from the stationary moving tracer, and calculate its terminal velocity, V tr . In the general case the latter is determined implicitly, as the solution of a certain transcendental equation. In two extreme limits of slow and fast monolayer particles diffusion, we obtain explicit asymptotic forms of V tr . We show next that the density profile in the monolayer is strongly inhomogeneous: in front of the stationary moving tracer the local density is higher than the average value, ρ L , and approaches ρ L as an exponential function of the distance from the tracer; past the tracer the local density is lower than ρ L and the approach to ρ L may proceed differently depending on whether the particle number in the monolayer is explicitly conserved or not. In the former case the approach is described by an exponential dependence with a different characteristic length, compared with the behaviour in front of the tracer; in the latter case, the density tends to ρ L algebraically. The characteristic lengths and the amplitudes of the density relaxation functions are also determined explicitly.

Nonequilibrium ultrashort laser pulse phenomena described by Fermion coherent states

Generating functionals for time-dependent many particle systems in a semiconductor are derived with Fermion coherent states. In the case of noninteracting electrons and holes the one particle correlation functions follow from the inverse of a matrix, containing the kinetic energy and the time-dependent driving electric field. It is important to reorder the Grassmann fields of the holes to obtain proper generating functionals. In the case of interacting electrons and holes a Hubbard Stratonovich transformation has to be performed with auxiliary commuting fields. A saddle point approximation is considered in terms of these new fields.

Partial coherence in the core–halo picture of Bose–Einstein n-particle correlations

We study the influence of a possible coherent component in the boson source on the two-, three- and $n$-particle correlation functions in a generalized core/halo type of boson-emitting source. In particular, a simple formula is presented for the strengh of the $n$-particle correlation functions for such systems. Graph rules are obtained to evaluate the correlation functions of arbitrary high order. The importance of experimental determination of the 4-th and 5-th order Bose-Einstein correlation function is emphasized.

Au+Au reactions at the AGS: Experiments E866 and E917

Particle production and correlation functions from Au+Au reactions have been measured as a function of both beam energy (2-10.7AGeV) and impact parameter. These results are used to probe the dynamics of heavy-ion reactions, confront hadronic models over a wide range of conditions and to search for the onset of new phenomena.

Optimized discretization of sources imaged in heavy-ion reactions

We develop a new method of optimized discretization for imaging the relative source from two particle correlation functions. In this method, the source resolution depends on the relative particle separation and is adjusted to available data and their errors. We test the method by restoring assumed $\mathrm{pp}$ sources and then apply the method to $\mathrm{pp}$ and IMF data. In reactions below 100 MeV/nucleon, significant portions of the sources extend to large distances $(r>20 \mathrm{fm}).$ The results from the imaging show the inadequacy of common Gaussian source parametrizations. We establish a simple relation between the height of the $\mathrm{pp}$ correlation function and the source value at short distances, and between the height and the proton freeze-out phase-space density.

Hydrodynamic waves and correlation functions in dusty plasmas

A hydrodynamic description of strongly coupled dusty plasmas is given when physical quantities vary slowly in space and time and the system can be assumed to be in local thermodynamic equilibrium. The linear waves in such a system are analyzed. In particular, a dispersion equation is derived for low-frequency dust acoustic waves, including collisional damping effects, and compared with experimental results. The linear response of the system is calculated from the fluctuation-dissipation theorem and the hydrodynamic equations. The requirement that these two calculations coincide constrains the particle correlation function for slowly varying perturbations. It is shown that in the presence of weakly damped, long-wavelength dust-acoustic waves, the dust autocorrelation function is of the Debye–Hückel form and the characteristic shielding distance is the dust Debye length.

Magnetism in the single-band Hubbard model

A self-consistent spectral density approach (SDA) is applied to the Hubbard model to investigate the possibility of spontaneous ferro- and antiferromagnetism. The starting point is a two-pole ansatz for the single-electron spectral density, the free parameter of which can be interpreted as energies and spectral weights of respective quasiparticle excitations. They are determined by fitting exactly calculated spectral moments. The resulting self-energy consists of a local and a non-local part. The higher correlation functions entering the spin-dependent local part can be expressed as functionals of the single-electron spectral density. Under certain conditions for the decisive model parameters (Coulomb interaction U, Bloch bandwidth W, band occupation n, temperature T) the local part of the self-energy gives rise to a spin-dependent band shift, thus allowing for spontaneous band magnetism. As a function of temperature, second-order phase transitions are found away from half-filling, but close to half-filling, the system exhibits a tendency towards first-order transitions. The non-local self-energy part is determined by use of proper two-particle spectral densities. Its main influence concerns a (possibly spin-dependent) narrowing of the quasiparticle bands with the tendency to stabilize magnetic solutions. The non-local self-energy part disappears in the limit of infinite dimensions. We present a full evaluation of the Hubbard model in terms of quasiparticle densities of states, quasiparticle dispersions, magnetic phase diagram, critical temperatures ( T c, T N) as well as spin and particle correlation functions. Special attention is focused on the non-locality of the electronic self-energy, for which some rigorous limiting cases are worked out.

Structure and energetics of small helium clusters: Quantum simulations using a recent perturbational pair potential

We report accurate ground state energies and structural properties for small clusters of 4He computed with the diffusion quantum Monte Carlo (DMC) method combined with high quality trial wave functions and using the recent analytical pair potential of Tang, Toennies, and Yiu [Phys. Rev. Lett. 74, 1546 (1995)]. Calculations based on the older HFD-B(He) potential are reported for comparison. The clusters are found to be extremely floppy and to be characterized by very diffuse wave functions. The DMC results for 4He2 and 4He3 are in excellent agreement with other calculations using conventional methods. 4He3 is found to have a noticeable contribution from nearly linear geometries. The internal structure of the clusters is described by a three particle correlation function which reveals a significantly non-spherical internal cluster structure. The energies for all cluster sizes are found to be slightly higher than those obtained with the HFD-B(He) pair potential. Exploratory calculations on the helium trimer indicate that the effects of three body interactions do not exceed the uncertainty margin provided by different state of the art pair potentials.

Forward depolarized light scattering: heterodyne versus homodyne detection

The rotational correlation function of anisotropic colloidal particles can be measured by observing the fluctuations of the depolarized intensity scattered in the forward direction. In this work we present a theoretical treatment of forward depolarized light scattering. Our calculations show the importance of the insertion of a quarter-wave plate between the scattering cell and the analyzer. The role of the quarter-wave plate is to generate a heterodyne signal between the transmitted beam and the depolarized forward scattered field. In order to illustrate the theoretical calculations, we present experimental results obtained with dispersions of fluorinated polymer colloids and with solutions of tobacco mosaic virus.

Equivalences between stochastic systems

Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are calculated. This is achieved by similarity transformations between different stochastic models and between stochastic and soluble {\em non-stochastic} models. The results agree with experiments on one-dimensional annihilation-coagulation processes.

Correlations in two-component log-gas systems

A systematic study of the properties of particle and charge correlation functions in the two-dimensional Coulomb gas confined to a one-dimensional domain is undertaken. Two versions of this system are considered: one in which the positive and negative charges are constrained to alternate in sign along the line, and the other where there is no charge ordering constraint. Both systems undergo a zero-density Kosterlitz-Thouless type transition as the dimensionless coupling $\Gamma := q^2 / kT$ is varied through $\Gamma = 2$. In the charge ordered system we use a perturbation technique to establish an $O(1/r^4)$ decay of the two-body correlations in the high temperature limit. For $\Gamma \rightarrow 2^+$, the low-fugacity expansion of the asymptotic charge-charge correlation can be resummed to all orders in the fugacity. The resummation leads to the Kosterlitz renormalization equations.

Long-range correlations in nonequilibrium Lorentz gases.

Spatial correlation functions in Lorentz gases maintained in nonequilibrium steady states are studied. The correlation function of microscopic number densities of the moving particle and scatterer is found to have long range spatial correlations that decay as 1/${\mathit{r}}^{2}$ in three dimensions in the presenece of either a concentration gradient, a temperature gradient, or an electric field. Stronger correlations are found at higher order in the electric field. Our analysis is based on a derived kinetic equation for the two particle correlation function. Possible extensions of our work are discussed.