Particle Correlation Functions Research Articles

Component Particle Structure in Heterogeneous Disordered Ensembles Extracted from High-Throughput Fluctuation X-Ray Scattering

The ring angular correlation function is a characteristic feature determined by the particle structure. Averaging over a large number of ring angular correlation functions calculated from x-ray diffraction patterns will cancel out the cross correlations between different particles and converge to the autocorrelation functions of single particles. Applied on heterogeneous disordered ensembles, the retrieved function is a linear combination of a single-particle autocorrelation function multiplied by the molar ratios in a heterogeneous system. Using this relation, the ring angular correlation functions of the individual component particles in the heterogeneous system can be retrieved through the high throughput fluctuation x-ray scattering technique. This method is demonstrated with a simulated heterogeneous system composed of nanorods, nanoprism, and nanorice.

On the viscosity-modifying method for activating the Brownian motion of magnetic particles in lattice Boltzmann simulations

In order to apply the lattice Boltzmann method to a flow problem of magnetic suspensions, we have investigated the feasibility of the viscosity-modifying method that is expected to be a technique for sophisticating the activating method of the particle Brownian motion based on fluctuation hydrodynamics. We have addressed a magnetic suspension in thermodynamic equilibrium to clarify the influences of various factors such as the roughness of a lattice system and the volumetric fraction of magnetic particles on the scaling coefficient of viscosity. From the snapshots and pair correlation functions of magnetic particles, it is seen that the viscosity-modifying method can show good agreement with the results of Monte Carlo method in both quantitative and qualitative aspects. This good agreement is almost independent of the roughness of a lattice system if a relatively fine lattice system is used. The scaling coefficient of viscosity is almost constant and independent of the strengths of magnetic particle–field and particle–particle interactions, and also is almost constant for the variation of the volumetric fraction and the number of particles for a given lattice system unless a coarse lattice system is used. We may conclude from these results that the lattice Boltzmann method with the viscosity-modifying procedure is quite a possible technique for simulating a flow problem of magnetic particles under a non-uniform applied magnetic field.

Tagged Particle Diffusion in One-Dimensional Gas with Hamiltonian Dynamics

We consider a one-dimensional gas of hard point particles in a finite box that are in thermal equilibrium and evolving under Hamiltonian dynamics. Tagged particle correlation functions of the middle particle are studied. For the special case where all particles have the same mass, we obtain analytic results for the velocity auto-correlation function in the short time diffusive regime and the long time approach to the saturation value when finite-size effects become relevant. In the case where the masses are unequal, numerical simulations indicate sub-diffusive behaviour with mean square displacement of the tagged particle growing as t/ln(t) with time t. Also various correlation functions, involving the velocity and position of the tagged particle, show damped oscillations at long times that are absent for the equal mass case.

The HBOM method for unfolding detector effects

We present the Hit Backspace Once More (HBOM) method for correcting a measurement for the effect of an imperfect detector. The HBOM method is a model-independent and potentially data-driven technique that repeatedly applies a parameterisation of the detector effects to observed data. The correction is determined, after applying the detector parameterisation, by extrapolating the data to a detector effect of zero. We demonstrate this technique using the two particle correlation function, which is an observable that can otherwise be difficult to correct for systematic shifts introduced by the detector.

Correlations in excited states of local Hamiltonians

Physical properties of the ground and excited states of a $k$-local Hamiltonian are largely determined by the $k$-particle reduced density matrices ($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least enough for the calculation of the ground state and excited state energies. Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even the state itself is completely determined by its $k$-RDMs, and therefore contains no genuine ${>}k$-particle correlations, as they can be inferred from $k$-particle correlation functions. It is natural to ask whether a similar result holds for non-degenerate excited states. In fact, for fermionic systems, it has been conjectured that any non-degenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any non-degenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure $n$-particle states. We construct explicit counterexamples to show that both conjectures are false. It means that correlations in excited states of local Hamiltonians could be dramatically different from those in ground states. We further show that any non-degenerate excited state of a $k$-local Hamiltonian is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely determined by its $2k$-RDMs (or $2k$-matrix).

Spin-adapted density matrix renormalization group algorithms for quantum chemistry

We extend the spin-adapted density matrix renormalization group (DMRG) algorithm of McCulloch and Gulacsi [Europhys. Lett. 57, 852 (2002)] to quantum chemical Hamiltonians. This involves using a quasi-density matrix, to ensure that the renormalized DMRG states are eigenfunctions of Ŝ(2), and the Wigner-Eckart theorem, to reduce overall storage and computational costs. We argue that the spin-adapted DMRG algorithm is most advantageous for low spin states. Consequently, we also implement a singlet-embedding strategy due to Tatsuaki [Phys. Rev. E 61, 3199 (2000)] where we target high spin states as a component of a larger fictitious singlet system. Finally, we present an efficient algorithm to calculate one- and two-body reduced density matrices from the spin-adapted wavefunctions. We evaluate our developments with benchmark calculations on transition metal system active space models. These include the Fe(2)S(2), [Fe(2)S(2)(SCH(3))(4)](2-), and Cr(2) systems. In the case of Fe(2)S(2), the spin-ladder spacing is on the microHartree scale, and here we show that we can target such very closely spaced states. In [Fe(2)S(2)(SCH(3))(4)](2-), we calculate particle and spin correlation functions, to examine the role of sulfur bridging orbitals in the electronic structure. In Cr(2) we demonstrate that spin-adaptation with the Wigner-Eckart theorem and using singlet embedding can yield up to an order of magnitude increase in computational efficiency. Overall, these calculations demonstrate the potential of using spin-adaptation to extend the range of DMRG calculations in complex transition metal problems.

Optical and kinetic properties of the dusty plasma in radiofrequency discharge

Dependence of diffusion coefficient of dusty particles in dusty plasma was experimentally obtained. A proportional increase of diffusion of the dust particles with the increase of the discharge power was experimentally found. The pair correlation functions of dusty particles were also obtained from the experiments and the change of dust cloud structure with the increase of the discharge power was observed. The influence of the dust particles on the spectrum of plasma glow was investigated using spatial spectrometer. It was shown that upon introduction of dust particles into the plasma bulk the overall intensity of the plasma glow decreases.

Energy momentum conservation effects on two-particle correlation functions

Two particle correlations are used to extract information about the characteristic size of the system in proton-proton and heavy ion collisions. The size of the system can be extracted from the Bose-Einstein quantum mechanical effect for identical particles. However there are also long range correlations that shift the baseline of the correlation function from the expected flat behavior. A possible source of these correlations is the conservation of energy and momentum, especially for small systems, where the energy available for particle production is limited. A new technique, first used by the STAR collaboration, of quantifying these long range correlations using energy-momentum conservation considerations is presented in this talk. Using Monte Carlo simulations of proton-proton collisions at 900 GeV, it is shown that the baseline of the two particle correlation function can be described using this technique.

Effect of ionic size on the structure of spherical double layers: a Monte Carlo simulation and density functional theory study

The effect of ionic size on the diffuse layer characteristics of a spherical double layer is studied using Monte Carlo simulation and density functional theory within the restricted primitive model. The macroion is modelled as an impenetrable charged hard sphere carrying a uniform surface charge density, surrounded by the small ions represented as charged hard spheres and the solvent is taken as a dielectric continuum. The density functional theory uses a partially perturbative scheme, where the hard sphere contribution to the one particle correlation function is evaluated using weighted density approximation and the ionic interactions are calculated using a second-order functional Taylor expansion with respect to a bulk electrolyte. The Monte Carlo simulations have been performed in the canonical ensemble. The detailed comparison is made in terms of zeta potentials for a wide range of physical conditions including different ionic diameters. The zeta potentials show a maximum or a minimum with respect to the polyion surface charge density for a divalent counterion. The ionic distribution profiles show considerable variations with the concentration of the electrolyte, the valency of the ions constituting the electrolyte, and the ionic size. This model study shows clear manipulations of ionic size and charge correlations in dictating the overall structure of the diffuse layer.

Femtoscopy and energy-momentum conservation effects in proton-proton collisions at 900 GeV in ALICE

Two particle correlations are used to extract information about the characteristic size of the system for proton-proton collisions at =900 GeV measured by the ALICE (A Large Ion Collider Experiment) detector at CERN. The correlation functions obtained show the expected Bose-Einstein effect for identical particles, but there are also long range correlations present that shift the baseline from the expected flat behavior. A possible source of these correlations is the conservation of energy and momentum, especially for small systems, where the energy available for particle production is limited. A new technique, first introduced by the STAR collaboration, of quantifying these long range correlations using energy-momentum conservation considerations is presented here. It is shown that the baseline of the two particle correlation function can be described using this technique.

G050091 格子ボルツマン・シミュレーションにおける磁性粒子のブラウン運動誘起のための粘度修正法([G05009]流体工学部門一般セッション(9):数値解)

In order to apply the lattice Boltzmann method to a flow problem of magnetic suspensions, we have investigated the feasibility of the viscosity-modifying method that is expected to be a technique for sophisticating the activating method of the particle Brownian motion based on fluctuation hydrodynamics. We have addressed a magnetic suspension in thermodynamic equilibrium to clarify the influences of various factors such as the roughness of a lattice system and the volumetric fraction of magnetic particles on the scaling coefficient of viscosity. From the snapshots and pair correlation functions of magnetic particles, it is seen that the viscosity-modifying method can show good agreement with the results of Monte Carlo method in both quantitative and qualitative points. This good agreement is almost independent of the roughness of a lattice system if a relatively fine lattice system is used. The scaling coefficient of viscosity is almost constant and independent of the strengths of magnetic particle-field and particle-particle interactions, and also is almost constant for the variation of the volumetric fraction and the number of particles for a given lattice system unless a coarse lattice system is used. We may conclude from these results that the lattice Boltzmann method with the viscosity-scaling procedure is quite a possible technique for simulating a flow problem of magnetic particles under a non-uniform applied magnetic field.

格子ボルツマン・シミュレーションにおける磁性粒子のブラウン運動誘起のための粘度修正法

In order to apply the lattice Boltzmann method to a flow problem of magnetic suspensions, we have investigated the feasibility of the viscosity-modifying method that is expected to be a technique for sophisticating the activating method of the particle Brownian motion based on fluctuation hydrodynamics. We have addressed a magnetic suspension in thermodynamic equilibrium to clarify the influences of various factors such as the roughness of a lattice system and the volumetric fraction of magnetic particles on the scaling coefficient of viscosity. From the snapshots and pair correlation functions of magnetic particles, it is seen that the viscosity-modifying method can show good agreement with the results of Monte Carlo method in both quantitative and qualitative points. This good agreement is almost independent of the roughness of a lattice system if a relatively fine lattice system is used. The scaling coefficient of viscosity is almost constant and independent of the strengths of magnetic particle-field and particle-particle interactions, and also is almost constant for the variation of the volumetric fraction and the number of particles for a given lattice system unless a coarse lattice system is used. We may conclude from these results that the lattice Boltzmann method with the viscosity-scaling procedure is quite a possible technique for simulating a flow problem of magnetic particles under a non-uniform applied magnetic field.

Velocity correlation functions of charged particles derived from the Fokker–Planck equation

An important ingredient in theories for diffusion of charged particles across a mean magnetic field are velocity correlation functions along and across that field. In the current article we present an analytical study of these functions by investigating the two-dimensional Fokker–Planck equation. We show that for an isotropic pitch-angle Fokker–Planck coefficient, the parallel velocity correlation function is an exponential function in agreement with the standard model used previously. For other forms of the pitch-angle diffusion coefficient, however, we find non-exponential forms. Also a new, velocity correlation function based, approach for deriving the so-called Earl-relation is presented. This new derivation is more systematic and simpler than previous derivations. We also discuss higher-order velocity correlations and the applicability of the quasi-normal hypothesis in particle diffusion theory. Furthermore, we compute velocity correlation functions across the mean field and develop an alternative theory for perpendicular diffusion.

SqueezedK+K−correlations in high energy heavy ion collisions

The hot and dense medium formed in high energy heavy ion collisions may modify some hadronic properties. In particular, if hadron masses are shifted in-medium, it was demonstrated that this could lead to back-to-back squeezed correlations (BBC) of particle-antiparticle pairs. Although well-established theoretically, the squeezed correlations have not yet been discovered experimentally. A method has been suggested for the empirical search of this effect, which was previously illustrated for $\ensuremath{\phi}\ensuremath{\phi}$ pairs. We apply here the formalism and the suggested method to the case of ${K}^{+}{K}^{\ensuremath{-}}$ pairs, since they may be easier to identify experimentally. The time distribution of the emission process plays a crucial role in the survival of the BBC's. We analyze the cases where the emission is supposed to occur suddenly or via a Lorentzian distribution, and compare with the case of a L\'evy distribution in time. Effects of squeezing on the correlation function of identical particles are also analyzed.

Two-body recombination in a quantum-mechanical lattice gas: Entropy generation and probing of short-range magnetic correlations

We study entropy generation in a one-dimensional (1D) model of bosons in an optical lattice experiencing two-particle losses. Such heating is a major impediment to observing exotic low temperature states, and "simulating" condensed matter systems. Developing intuition through numerical simulations, we present a simple empirical model for the entropy produced in this 1D setting. We also explore the time evolution of one and two particle correlation functions, showing that they are robust against two-particle loss. Because of this robustness, induced two-body losses can be used as a probe of short range magnetic correlations.

Nonequilibrium structure of primary particles in colloidal bidispersion

The nonequilibrium aggregation structure of primary particles in colloidal bidispersions is investigated at high volume fractions by Brownian dynamics simulations. It is found that introducing limited different sized particles in the monodispersion can obviously affect the short-range structures of primary particles. In a bidispersion, fractal dimension of aggregates, only consisting of primary particles, increases with increasing the size difference in the long-range scale. The structure factor S(q) of aggregates, obtained from the particle correlation function g(r), suggests that fractal structure disappears when the primary particles become not “primary” in volume fraction.

Controlled expansion for certain non-Fermi-liquid metals

The destruction of Fermi liquid behavior when a gapless Fermi surface is coupled to a fluctuating gapless boson field is studied theoretically. This problem arises in a number of different contexts in quantum many body physics. Examples include fermions coupled to a fluctuating transverse gauge field pertinent to quantum spin liquid Mott insulators, and quantum critical metals near a Pomeranchuk transition. We develop a new controlled theoretical approach to determining the low energy physics. Our approach relies on combining an expansion in the inverse number (N) of fermion species with a further expansion in the parameter \epsilon = z_b -2 where z_b is the dynamical critical exponent of the boson field. We show how this limit allows a systematic calculation of the universal low energy physics of these problems. The method is illustrated by studying spinon fermi surface spin liquids, and a quantum critical metal at a second order electronic nematic phase transition. We calculate the low energy single particle spectra, and various interesting two particle correlation functions. In some cases deviations from the popular Random Phase Approximation results are found. Some of the same universal singularities are also calculated to leading non-vanishing order using a perturbative renormalization group calculation at small N extending previous results of Nayak and Wilczek. Implications for quantum spin liquids, and for Pomeranchuk transitions are discussed. For quantum critical metals at a nematic transition we show that the tunneling density of states has a power law suppression at low energies.

Correlated initial condition for an embedded process by time partitioning

Study of transients in the electron quantum transport by nonequilibrium Green's function often requires an explicit inclusion of correlations at a finite initial time. For processes embedded in a host process, a universal treatment of the correlated initial conditions based on the formalism of partitioning in time allows to express their self-energy including the ``irregular'' correlation part in terms of the known properties of the host process. This unified formalism also yields the renormalized semigroup property for propagators and the reconstruction equations for the particle correlation function. The Bogolyubov principle of the decay of correlations then permits to buildup a theory of quantum transport equations with finite-time initial conditions.

Phase diagram of superconductivity and antiferromagnetism in high- Tc hole-doped cuprates

A phase diagram of superconductivity (SC) and antiferromagnetism (AFM) for hole-doped cuprate superconductors in presence of chemical potential ( μ) by using a model Hamiltonian is reported here. The Hamiltonian of the system is a mean field one and has been solved by writing equations of motion for the single particle Green functions. The expressions for appropriate single particle correlation function are derived. It is assumed that SC arises due to BCS pairing mechanism and AFM order is simulated by staggered magnetic field in lattices of Cu–O planes. The expressions for SC order parameter, AFM order parameter and dopant concentration are calculated analytically by using Green function technique of D.N. Zubarev. The value of SC gap ( z), AFM gap ( h) and chemical potential ( μ) are solved self consistently for different dopant concentrations ( x) by changing model parameters. It is found that a disordered phase appears after antiferromagnetism is destroyed in the range of very small doping. On further increase of the doping, the SC critical temperature first increases, attains a maximum value (≃39 K) and then decreases which agrees well with experimental observations for hole-doped cuprates. Our theoretical findings suggest that the AFM coupling plays the vital role of the glue for the Cooper pairs.

Molecular Solvent Model of Spherical Electric Double Layers: A Systematic Study by Monte Carlo Simulations and Density Functional Theory

The structure of spherical electric double layers is studied using Monte Carlo simulation and density functional theory by considering solvent as the third component. In this molecular solvent model (MSM), ions and solvent molecules are considered as charged and neutral hard spheres, respectively, having equal diameter. The macroion is considered as an isolated hard sphere having uniform surface charge density surrounded by the electrolyte and the solvent. The theory is partially perturbative as the hard-sphere contribution to the one particle correlation function is evaluated using suitably averaged weighted density, and the ionic part is obtained through a second-order functional Taylor expansion around the bulk electrolyte. The Monte Carlo simulations have been performed in a canonical ensemble. The system is studied at varying concentrations of electrolytes, and the solvent molecules, at different valences of the electrolyte, at different macroion radii, and at varying surface charge densities. The theory is found to be in good agreement with the simulation results over a wide range of parametric conditions. The excluded volume effects due to the molecular nature of the solvent are shown to have much richer features in diffuse layer phenomena like layering and charge inversion.