Momentum Correlation Function Research Articles

Microscopic derivation of the Keilson–Storer master equation

We consider a classical particle bilinearly coupled to a harmonic bath. Assuming that the evolution of the particle is monitored on a timescale which is longer than the characteristic bath correlation time, we derive a Markovian master equation for the probability density of the particle. The master equation is fully specified by the time correlation function of the momenta of the particle. We find the functional form of the momentum correlation function which yields the Keilson–Storer master equation (Keilson and Storer, 1952). We show that the parameters of this master equation can directly be related to the characteristic memory time of the bath.

Pairing correlations in a trapped one-dimensional Fermi gas

We use a BCS-type variational wavefunction to study attractively-interacting quasi one-dimensional (1D) fermionic atomic gases, motivated by cold-atom experiments that access the 1D regime using an anisotropic harmonic trapping potential (with trapping frequencies $\omega_x = \omega_y \gg \omega_z$) that confines the gas to a cigar-shaped geometry. To handle the presence of the trap along the $z$-direction, we construct our variational wavefunction from the harmonic oscillator Hermite functions that are the eigenstates of the single-particle problem. Using an analytic determination of the effective interaction among harmonic oscillator states along with a numerical solution of the resulting variational equations, we make specific experimental predictions for how pairing correlations would be revealed in experimental probes like the local density and the momentum correlation function.

Correlation function intercepts for [formula omitted]-deformed Bose gas model implying effective accounting for interaction and compositeness of particles

In the recently proposed two-parameter μ˜,q-deformed Bose gas model (Gavrilik and Mishchenko, 2013) [3], aimed to take effectively into account both compositeness of particles and their interaction, the μ˜,q-deformed virial expansion of the equation of state (EOS) was obtained. In this paper we further explore the μ˜,q-deformation, namely the version of μ˜,q-Bose gas model involving deformed distributions and correlation functions. In the model, we explicitly derive the one- and two-particle deformed distribution functions and the intercept of two-particle momentum correlation function. The results are illustrated by plots, and the comparison with known experimental data on two-pion correlation function intercepts extracted in RHIC/STAR experiments is given.

Universal scaling at nonthermal fixed points of a two-component Bose gas

Quasistationary far-from-equilibrium critical states of a two-component Bose gas are studied in two spatial dimensions. After the system has undergone an initial dynamical instability it approaches a nonthermal fixed point. At this critical point the structure of the gas is characterized by ensembles of (quasi)topological defects such as vortices, skyrmions, and solitons which give rise to universal power-law behavior of momentum correlation functions. The resulting power-law spectra can be interpreted in terms of strong-wave-turbulence cascades driven by particle transport into long-wavelength excitations. Scaling exponents are determined on both sides of the miscible-immiscible transition controlled by the ratio of the intraspecies to interspecies couplings. Making use of quantum turbulence methods, we explain the specific values of the exponents from the presence of transient (quasi)topological defects.

Nucleon-nucleon momentum-correlation function as a probe of the density distribution of valence neutrons in neutron-rich nuclei

Proton-neutron, neutron-neutron, and proton-proton momentum-correlation functions (${C}_{pn},\phantom{\rule{0.28em}{0ex}}{C}_{nn}$, and ${C}_{pp}$) are systematically investigated for ${}^{15}\mathrm{C}$ and other C-isotope-induced collisions at different entrance channel conditions within the framework of the isospin-dependent quantum-molecular-dynamics model complemented by the correlation after burner (crab) computation code. ${}^{15}\mathrm{C}$ is a prime exotic nucleus candidate due to the weakly bound valence neutron coupling with closed-neutron-shell nucleus ${}^{14}\mathrm{C}$. To study density dependence of the correlation function by removing the isospin effect, the initialized ${}^{15}\mathrm{C}$ projectiles are sampled from two kinds of density distribution from the relativistic mean-field (RMF) model in which the valence neutron of ${}^{15}\mathrm{C}$ is populated in both $1d5/2$ and $2s1/2$ states, respectively. The results show that the density distributions of the valence neutron significantly influence the nucleon-nucleon momentum-correlation function at large impact parameters and high incident energies. The extended density distribution of the valence neutron largely weakens the strength of the correlation function. The size of the emission source is extracted by fitting the correlation function by using the Gaussian source method. The emission source size as well as the size of the final-state phase space are larger for projectile samplings from more extended density distributions of the valence neutron, which corresponds to the $2s1/2$ state in the RMF model. Therefore, the nucleon-nucleon momentum-correlation function can be considered as a potentially valuable tool to diagnose exotic nuclear structures, such as the skin and halo.

Two-body momentum correlations in a weakly interacting one-dimensional Bose gas

We analyze the two-body momentum correlation function for a uniform weakly interacting one-dimensional Bose gas. We show that the strong positive correlation between opposite momenta, expected in a Bose-Einstein condensate with a true long-range order, almost vanishes in a phase-fluctuating quasicondensate where the long-range order is destroyed. Using the Luttinger liquid approach, we derive an analytic expression for the momentum correlation function in the quasicondensate regime, showing (i) the reduction and broadening of the opposite-momentum correlations (compared to the singular behavior in a true condensate) and (ii) an emergence of anticorrelations at small momenta. We also numerically investigate the momentum correlations in the crossover between the quasicondensate and the ideal Bose-gas regimes using a classical field approach and show how the anticorrelations gradually disappear in the ideal-gas limit.

Quantum Coherence and Bose-Einstein Correlations for Time-Dependent Source

Bose-Einstein correlation (BEC) is appropriate conditions quantum coherence which is between two or more bosons. In this paper, we study the coherence of two-boson in accelerating and decelerating expansion source. The two-boson momentum correlation function is given by quantum statistics methods. The conclusion is that the momentum correlation function is a sensitive function of several parameters which includes particles’ momentum, the temperatures and evolution time of system.

Exact expressions for the intercepts of r-particle momentum correlation functions in μ-Bose gas model

Recently, the deformed μ-Bose gas model based on so-called μ-deformed oscillators was proposed. For that model, the intercepts of r-particle momentum correlation functions (correlation functions at coinciding momenta of particles) were treated for r=2,3, within certain order of approximation in μ. In this work, we derive for μ-Bose gas model the exact expressions for r-particle correlation function intercepts, for all r, through Lerch transcendent and find their asymptotics (as functions of μ). For 2-, 3-particle intercepts and deformed distribution function 〈ak†ak〉 the dependence on particles momentum is presented graphically.

Galactic angular momenta and angular momentum couplings in the large-scale structure

In this paper, we revisit the aquisition of angular momentum of galaxies by tidal shearing and compute the angular momentum variance sigma_L^2 as well as the angular momentum correlation function C_L(r) from a peak-restricted Gaussian random process. This stochastic process describing the initial conditions treats both the tidal shear as well as the inertia as dynamical fields and explicitly accounts for the discreteness of the inertia field. We describe the way in which the correlations in angular momentum result from an interplay of long-ranged correlations in the tidal shear, and short ranged correlations in the inertia field and which reflects the correlation between the eigensystems of these two symmetric tensors. We propose a new form of the angular momentum correlation function which is able to distinguish between parallel and antiparallel alignment of angular momentum vectors, and comment on implications of intrinsic alignments for weak lensing measurements. We confirm the scaling L/M propto. M^{2/3} and find the angular momentum distribution of Milky Way-sized haloes to be correlated on scales of ~1 Mpc/h. The correlation function can be well fitted by an empirical relation of the form C_L(r) propto. exp(-[r/r_0]^beta).

Hard-photon flow and photon-photon correlation in intermediate-energy heavy-ion collisions

Hard photons emitted from energetic heavy-ion collisions are very interesting since they do not experience nuclear interaction, and therefore they are useful to explore properties of nuclear matter. We investigated hard-photon production and its properties in intermediate-energy heavy-ion collisions with the help of the Blotzmann-Uehling-Ulenbeck model. Two components of hard photons are discussed: direct and thermal. The positive directed flow parameter and negative elliptic flow parameter of direct photons are demonstrated and they are anticorrelated to the flows of free protons. The dependencies of hard-photon production and anisotropic parameters on impact parameter, beam energy, nuclear equation of state, and symmetry energy are also discussed. Furthermore, we investigated the two-photon momentum correlation function, from which the space-time structure information of the photon source could be extracted, as well as the two-photon azimuthal correlation, which could provide another good method to determine the elliptic flow parameter ${v}_{2}$ of direct hard photons.

Nonperturbative renormalization group for the Kardar-Parisi-Zhang equation: General framework and first applications

We present an analytical method, rooted in the nonperturbative renormalization group, that allows one to calculate the critical exponents and the correlation and response functions of the Kardar-Parisi-Zhang (KPZ) growth equation in all its different regimes, including the strong-coupling one. We analyze the symmetries of the KPZ problem and derive an approximation scheme that satisfies the linearly realized ones. We implement this scheme at the minimal order in the response field, and show that it yields a complete, qualitatively correct phase diagram in all dimensions, with reasonable values for the critical exponents in physical dimensions. We also compute in one dimension the full (momentum and frequency dependent) correlation function, and the associated universal scaling function. We find a very satisfactory quantitative agreement with the exact result from Prähofer and Spohn [J. Stat. Phys. 115, 255 (2004)]. In particular, we obtain for the universal amplitude ratio g_{0}≃1.149(18), to be compared with the exact value g_{0}=1.1504... (the Baik and Rain [J. Stat. Phys. 100, 523 (2000)] constant). We emphasize that all these results, which can be systematically improved, are obtained with sole input the bare action and its symmetries, without further assumptions on the existence of scaling or on the form of the scaling function.

Evolution of the differential transverse momentum correlation function with centrality in Au + Au collisions at [formula omitted

We present first measurements of the evolution of the differential transverse momentum correlation function, C, with collision centrality in Au+Au interactions at sNN=200 GeV. This observable exhibits a strong dependence on collision centrality that is qualitatively similar to that of number correlations previously reported. We use the observed longitudinal broadening of the near-side peak of C with increasing centrality to estimate the ratio of the shear viscosity to entropy density, η/s, of the matter formed in central Au+Au interactions. We obtain an upper limit estimate of η/s that suggests that the produced medium has a small viscosity per unit entropy.

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

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

Self-consistent equations governing the dynamics of nonequilibrium colloidal systems

A self-consistent theoretical procedure is proposed to derive the governing equations for the dynamic properties of nonequilibrium colloidal systems within the framework of the probability theory. Unlike alternative methods in the literature, the self-consistent procedure completely decouples dynamic variables from thermodynamic functions introduced for equilibrium systems. The intrinsic characteristics of a nonequilibrium system is described by the one-body temporal- and spatial-dependent dynamic variables, including the particle density profile, the local momentum, the kinetic energy or dynamic temperature, and by various forms of the two-body position and momentum correlation functions. Within appropriate constraints related to the initial/boundary conditions of a nonequilibrium system, the governing equations for the time evolution of these dynamic functions are obtained by maximizing the information entropy, i.e., the time-evolution equations for the dynamic variables correspond to a probability distribution in the reduced phase space that best represents the known information. It is shown that the dynamic equations are in parallel to and fully consistent with the statistical description of equilibrium systems. With certain assumptions, the self-consistent procedure can be reduced to various conventional theories of nonequilibrium processes.

DYNAMICAL SPATIALLY RESOLVED RESPONSE FUNCTION OF FINITE 1-D NANO PLASMAS

The dynamical response of one dimensional chains containing 55 till 309 atoms is investigated using a restricted molecular dynamics simulation scheme. The total momentum correlation function of an electron cloud shows resonances that are related to different collective excitation modes of the nano plasma. Spatially resolved cross correlation functions are calculated to deduce the spatial structure and strength of these resonance modes. The dependence of the corresponding resonance frequencies on temperature, density and chain size is investigated. The width of the resonances is analyzed in terms of a mode dependent collision frequency.

MEASUREMENT OF THE PROTON-PROTON CORRELATION FUNCTION FROM THE BREAK-UP OF 22Mg AND 20Ne

An experiment of 22 Mg and 20 Ne beams bombarding on a 12 C target at an energy of 60~70 A MeV has been performed at the RIKEN projectile fragment separator (RIPS) in the RIKEN Ring Cyclotron Facility to study the two-proton correlated emission from 22 Mg and 20 Ne excited states. The two-protons momentum correlation functions have been obtained for 22 Mg and 20 Ne , respectively. The trajectories of the 22 Mg decayed products (20 Ne + p + p ) were also measured to get the angular correlations between the two protons in Center of Mass of decaying system by relativistic-kinematics reconstruction. The results exhibit that 22 Mg has the features of 2 He cluster decay mechanism.

Molecular dynamics study of the dynamical behavior in ionic liquids through interionic interactions

We have focused on the interionic dynamics of an IL, 1-butyl-3-methylimidazolium cation with the anion, [PF 6] −, [BMIm][PF 6], and have investigated the interionic interaction in the IL and the polarization effects on the system. Molecular dynamics simulations have been carried out to pursue the understanding of interionic properties in ILs at molecular level. The analyses of velocity cross-correlation functions have been performed to study the interionic interactions. We have computed the momentum correlation functions between ionic species. From simulation results, it is suggested that, at the short time region up to 1 ps, the velocity cross-correlation is predominantly governed by the longitudinal contribution. It is found out that, compared with the longitudinal correlation in the nonpolarizable model, the longitudinal motions are further influenced in the polarizable model. It is indicated that the behavior of mean-squared displacement of the cation at a long-time region is not influenced by polarization effects, while the anion shows important difference. Also, it is concluded that the cage effect in ILs could be reduced by many-body polarization effects.

Estimation of shear viscosity based on transverse momentum correlations

Event anisotropy measurements at RHIC suggest the strongly interacting matter created in heavy ion collisions flows with very little shear viscosity. Precise determination of “shear viscosity-to-entropy” ratio is currently a subject of extensive study [S. Gavin and M. Abdel-Aziz, Phys. Rev. Lett. 97 (2006) 162302]. We present preliminary results of measurements of the evolution of transverse momentum correlation function with collision centrality of A u + A u interactions at s N N = 200 GeV . We compare two differential correlation functions, namely inclusive [J. Adams et al. (STAR Collaboration), Phys. Rev. C 72 (2005) 044902] and a differential version of the correlation measure C̃ introduced by Gavin et al. [S. Gavin and M. Abdel-Aziz, Phys. Rev. Lett. 97 (2006) 162302; M. Sharma and C. A. Pruneau, Phys. Rev. C 79 (2009) 024905.]. These observables can be used for the experimental study of the shear viscosity per unit entropy.

Thermodynamic properties and electrical conductivity of strongly correlated plasma media

We study thermodynamic properties and the electrical conductivity of dense hydrogen and deuterium using three methods: classical reactive Monte Carlo, direct path integral Monte Carlo (PIMC) and a quantum dynamics method in the Wigner representation of quantum mechanics. We report the calculation of the deuterium compression quasi-isentrope in good agreement with experiments. We also solve the Wigner–Liouville equation of dense degenerate hydrogen calculating the initial equilibrium state by the PIMC method. The obtained particle trajectories determine the momentum–momentum correlation functions and the electrical conductivity and are compared with available theories and simulations.

Empirical relaxation function and spectral density for underdamped vibrations at low temperatures

A new relaxation function which accounts for electronic dephasing (electronic phase loss and excited state lifetime) is presented, whose applicability for underdamped motion at low temperatures is examined in detail. This new empirical relaxation function phi(t) yields linear and nonlinear spectral/temporal profiles that render accurate dephasing time in the underdamped regime. The relaxation function phi(t) is normally expressed in terms of the coupling functions M(j) (') and M(j) (") on which the time evolution of the vibrational modes in question depends. The corresponding spectral density, which is a central quantity in probing dynamics, is derived and compared to that of the multimode Brownian oscillator model. Derivation and discussion of the new position and momentum autocorrelation functions in terms of our new spectral density are presented. While the position autocorrelation function plays a key role in representing solvation structure in polar or nonpolar medium, the momentum correlation function projects out the molecular vibrational motion. The Liouville space generating function (LGF) for harmonic and anharmonic systems is expressed in terms of our new empirical phi(t) and spectral density, leading to more physical observation. Several statistical quantities are derived from the position and momentum correlation function, which in turn contribute to LGF. Model calculations reflecting the infinite population decay in the low temperature limit in linear and nonlinear spectroscopic signals are presented. The herein quantum dipole moment correlation function is compared to that derived in [M. Toutounji, J. Chem. Phys. 118, 5319 (2003)] using mixed quantum-classical dynamics framework, yielding reasonable results, in fact identical at higher temperatures. The results herein are found to be informative, useful, and consistent with experiments.