Momentum Correlation Function Research Articles

Chaoticity parameter λ in Hanbury-Brown–Twiss interferometry

In Hanbury-Brown--Twiss interferometry measurements using identical bosons, the chaoticity parameter \ensuremath{\lambda} has been introduced phenomenologically to represent the momentum correlation function at zero relative momentum. It is useful to study an exactly solvable problem in which the \ensuremath{\lambda} parameter and its dependence on the coherence properties of the boson system can be worked out in great detail. We are therefore motivated to study the state of a gas of noninteracting identical bosons at various temperatures held together in a harmonic oscillator potential that arises either externally or from bosons' own mean fields. We determine the degree of Bose-Einstein condensation and its momentum correlation function as a function of the attributes of the boson environment. The parameter \ensuremath{\lambda} can then be evaluated from the momentum correlation function. We find that the $\ensuremath{\lambda}(p,T)$ parameter is a sensitive function of both the average pair momentum $p$ and the temperature $T$, and the occurrence of $\ensuremath{\lambda}=1$ is not a consistent measure of the absence of a coherent condensate fraction. In particular, for large values of $p$, the \ensuremath{\lambda} parameter attains the value of unity even for significantly coherent systems with large condensate fractions. We find that if a pion system maintains a static equilibrium within its mean field, and if it contains a root-mean-squared radius, a pion number, and a temperature typical of those in high-energy heavy-ion collisions, then it will contain a large fraction of the Bose-Einstein pion condensate.

Momentum and Velocity Autocorrelation Functions of a Diatomic Molecule Are Not Necessarily Proportional to Each Other

We present a computation of the classical momentum and velocity correlation functions of Br2 considered as an idealized molecular wire connecting dissipated lead atoms at each end of the dimer. It is demonstrated that coupling of the diatomic relative momentum to the leads may result in momenta that are not equal to the mass-weighted velocity. These differences show up in numerical simulations of both the average value and time correlations of the bond momentum and velocity. These observations are supported by analytical predictions for the average temperature of the diatomic. They imply that the "standard recipes" for modeling the system with a generalized Langevin equation are insufficient.

Selected results on strong and coulomb-induced correlations from the STAR experiment

Using recent high-statistics STAR data from Au+Au and Cu+Cu collisions at full RHIC energy I discuss strong and Coulomb-induced final state interaction effects on identical ($\pi-\pi$) and non-identical ($\pi-\Xi$) particle correlations. Analysis of $\pi-\Xi$ correlations reveals the strong and Coulomb-induced FSI effects allowing for the first time to estimate space extension of $\pi$ and $\Xi$ sources and average shift between them. Source imaging technique providing clean separation of these effects from effects due to the source function itself is applied to one-dimensional relative momentum correlation function of identical pions. For low momentum pions and/or non-central collisions large departure from a single-Gaussian shape is observed.

On the UV behavior of cascading gauge theories

In this note we consider the high energy behavior of cascading gauge theories. We discuss their holographic renormalization and high momentum correlation functions. These indicate that the cascading gauge theories are renormalizable (meaning one may obtain sensible correlation functions) and that they may be interpreted as gauge theories where the effective number of degrees of freedom runs with the renormalization group scale.

Nucleon-nucleon momentum correlation function for light nuclei

Nucleon-nucleon momentum correlation function have been presented for nuclear reactions with neutron-rich or proton-rich projectiles using a nuclear transport theory, namely Isospin-Dependent Quantum Molecular Dynamics model. The relationship between the binding energy of projectiles and the strength of proton-neutron correlation function at small relative momentum has been explored, while proton-proton correlation function shows its sensitivity to the proton density distribution. Those results show that nucleon-nucleon correlation function is useful to reflect some features of the neutron- or proton-halo nuclei and therefore provide a potential tool for the studies of radioactive beam physics.

A multiscale modeling demonstration based on the pair correlation function

For systems with interatomic interactions that are well described by pairwise potentials, the pair correlation function provides a vehicle for passing information from the molecular-level to the macroscopic level of description. In this work, we present a complete demonstration of the use of the pair correlation function to simulate a fluid at the molecular and macroscopic levels. At the molecular-level, we describe a monatomic fluid using the Ornstein–Zernike integral equation theory closed with the Percus–Yevick approximation. At the macroscopic level, we perform a multiscale simulation with macroscopic evolution equations for the mass, momentum, temperature, and pair correlation function, using molecular-level simulation to provide the boundary conditions. We perform a self-consistency check by comparing the pair correlation function that evolved from the multiscale simulation with the one evaluated at the molecular-level; excellent agreement is achieved.

Relaxation of rotational angular momentum of polar diatomic molecules in simple liquids

The relaxation processes of rotational angular momentum of polar diatomic molecules diluted in simple liquids are analyzed by applying a non-Markovian relaxation theory to the study of the binary time autocorrelation function of the angular momentum. This non-Markovian theory was previously applied to the study of the infrared and Raman spectroscopy, and also to the analysis of the rotational energy relaxation processes. We have obtained non-Markovian evolution equations for the two-time $j$-level angular momentum correlation components involved in the angular momentum correlation function. In these equations, the time-dependent angular momentum transfer rates and the pure orientational angular transfer rates are given in terms of the binary time autocorrelation function of the diatomic-solvent anisotropic interaction. The non-Markovian evolution equations converge to Markovian ones in the long time limit, reaching the angular momentum transfer rates in the usual time-independent form. Alternative time scales for the angular relaxation processes, relative to the individual rotational processes as well as to the global decay correlations, are introduced and analyzed. The theory is applied to the study of the angular momentum relaxation processes of HCl diluted in liquid $\mathrm{S}{\mathrm{F}}_{6}$, a system for which rotational energy relaxation and infrared and Raman spectroscopy was previously analyzed in the scope of the same theory.

Surveying the nucleon-nucleon momentum correlation function in the framework of quantum molecular dynamics model

Momentum correlation functions of nucleon-nucleon pairs are presented for reactions with C isotopes bombarding a ${}^{12}C$ target within the framework of the isospin-dependent quantum molecular dynamics model. The binding-energy dependence of the momentum correlation functions is also explored, and other factors that have an influence on momentum correlation functions are investigated. These factors include momentum-dependent nuclear equations of state, in-medium nucleon-nucleon cross sections, impact parameters, total pair momenta, and beam energy. In particular, the rise and the fall of the strength of momentum correlation functions at lower relative momentum are shown with an increase in beam energy.

Systematic studies of binding energy dependence of neutron–proton momentum correlation function

Hanbury Brown–Twiss (HBT) results of the neutron–proton correlation function have been systematically investigated for a series of nuclear reactions with light projectiles with the help of the isospin-dependent quantum molecular dynamics model. The relationship between the binding energy per nucleon of the projectiles and the strength of the neutron–proton HBT at small relative momentum has been obtained. Results show that neutron–proton HBT results are sensitive to the binding energy per nucleon.

Earl Robert Callen

Earl Robert Callen

Momentum distribution and correlation function of quasicondensates in elongated traps

We calculate the spatial correlation function and momentum distribution of a phase-fluctuating, elongated three-dimensional condensate, in a trap and in free expansion. We take the inhomogeneous density profile into account {\it{via}} a local density approximation. We find an almost Lorentzian momentum distribution, in stark contrast with a Heisenberg-limited Thomas-Fermi condensate.

Electronic transport in a one-dimensional random array of scatterers

The quantum dynamics of an ensemble of interacting electrons in an array of random scatterers is treated using a new numerical approach for the calculation of average values of quantum operators and time correlation functions in the Wigner representation. This approach combines both molecular dynamics and Monte Carlo methods and computes numerical traces and spectra of the relevant dynamical quantities such as momentum–momentum correlation functions and spatial dispersions. Considering, as an application, a system with fixed scatterers, the results clearly demonstrate that the many-particle interaction between the electrons can lead to an enhancement of the conductivity at intermediate densities.

Molecular dynamics simulations of the orientational motion of liquid chloroform at 298 K and 220K

Molecular dynamics simulations of liquid chloroform at 298 K and 220 K, using established optimized potential parameters and run on single-processor workstations, are employed to compute the first- and second-order Legendre polynomial, single-molecule orientational correlation functions describing the tumbling motion of the carbon-hydrogen bond direction. The results of the simulated Raman correlation functions compare well with their experimental counterparts from previously reported Fourier-transformed band contours of two totally symmetric vibration-rotation modes of the liquid. Simulated angular momentum, angular velocity, and intermolecular torque correlation functions are shown, and helped to characterize the insignificance of free orientational mobility within the system. Perturbation effects from rotation-vibration interaction and collision-induced intensities are present, but their effects on the correlation results are not sufficiently high to be of major significance.

Non-extensive statistics effects in quark–gluon plasma and in relativistic heavy-ion collisions

The presence of memory effects and color long-range forces among the many-parton system in the early stage of heavy-ion collisions can affect the particle statistical behavior at the freeze-out temperature. In this context, we calculate, in the framework of the equilibrium generalized non-extensive thermostatistics, the shape of pion transverse mass spectrum and the value of the transverse momentum correlation function of the pions emitted during the central Pb+Pb collisions and we show that the experimental results is well reproduced assuming very small deviations from the standard statistics.

Effect of collisions on the orientational relaxation of photofragments

Effect of collisions is investigated on the photofragment anisotropy decay. We restrict ourselves to studying linear fragments, and no rotational predissociation is assumed. Photoproducts are produced with a nonequilibrium rotational distribution, basically due to the applied torque and the parent molecule rotation. A kinetic equation, describing rotational relaxation of linear fragments under nonequilibrium conditions, is derived and solved for angular momentum correlation functions (CFs), rotational energy CFs, and also orientational CFs (OCFs). The characteristic decay times for the angular momentum and rotational energy CFs are shown to be insensitive to the mechanism of the photofragmentation. On the contrary, OCF of the second rank, that completely determines anisotropy of the photoproduct emission, is demonstrated to be very sensitive to peculiarities of the dissociation process and collision dynamics. This is confirmed by comparison of the calculated photoproduct anisotropies with experimental [M. Volk, S. Gnanakaran, E. Gooding, Y. Kholodenko, N. Pugliano, R.M. Hochstrasser, J. Phys. Chem. A 101 (1997) 638] and simulated [I. Benjamin, U. Banin, S. Ruhman, J. Chem. Phys. 98 (1993) 8337] ones. The fragment ensemble is proved to retain some memory about its initial nonequilibrium distribution. This pertains not only to the short time behavior for the anisotropy, but also for its long time decay. Therefore, the study of the polarization response of the ensemble of photoproducts allows one to know about features of the photofragmentation dynamics, and also to get information about peculiarities of collisions of fragments with buffer medium species.

Non-extensive statistics, fluctuations and correlations in high-energy nuclear collisions

Starting from the experimental evidence that high-energy nucleus-nucleus collisions cannot be described in terms of superpositions of elementary nucleon-nucleon interactions, we analyze the possibility that memory effects and long-range forces imply a nonextensive statistical regime during high energy heavy ion collisions. The relevance of these statistical effects and their compatibility with the available experimental data are discussed. In particular we show that theoretical estimates, obtained in the framework of the generalized nonextensive thermostatistics, can reproduce the shape of the pion transverse mass spectrum and explain the different physical origin of the transverse momentum correlation function of the pions emitted during the central Pb+Pb and during the p+p collisions at 158 A GeV.

The Coulomb interaction betweenpion wavepackets: the puzzle

The time-dependent Schrödinger equation for pairs, which are emitted from the interaction zone in relativistic nuclear collisions, is solved using wavepacket states. It is shown that the Coulomb enhancement in the momentum correlation function of such pairs is smaller than obtained in earlier calculations based on Coulomb distorted plane waves. These results suggest that the experimentally observed positive correlation signal cannot be caused by the Coulomb interaction between pions emitted from the interaction zone. But other processes which involve long-living resonances and pions emitted with a large coherence length could provide a possible explanation for the observed signal.

The role of the quantum dispersion in the Coulomb correction of Bose-Einstein correlations

The time dependent Schrödinger equation for two identical and charged pions is solved using wavepacket states. It is shown that the expected Coulomb distortion in the momentum correlation function is obliterated by the dispersion of the localized states, and therefore becomes unobservable.

A stochastic cage model for linear solutes

A stochastic cage model describing a linear solute reorienting under the action of a librational potential due to neighboring solvent molecules is presented. The fluctuations of the cage structure are taken into account by means of a suitable distribution of the librational frequency. Moreover, a detailed description of the cage dynamics is introduced by considering both the cage rotation and its restructuring through randomizations of the librational frequency and of the equilibrium orientation of the solute. With a suitable choice of the basis functions for the representation of the time evolution operator, the cage model can be solved numerically in order to compute different types of dynamical observables: angular momentum and orientational correlation functions, frequency dependent dielectric permittivity, and far-infrared spectra. Typical behavior of such observables in normal liquids is recovered from the cage model, thus demonstrating its capability of describing experimental observations at quite different time scales.

Quantum statistical correlations and single-particle distributions for slowly expanding systems with temperature profile

Competition among particle evaporation, temperature gradient and flow is investigated in a phenomenological manner, based on a simultaneous analysis of quantum statistical correlations and momentum distributions for a non-relativistic, spherically symmetric, three-dimensionally expanding, finite source. The parameters of the model emission function are constrained by fits to neutron and proton momentum distributions and correlation functions in intermediate energy heavy-ion collisions. The temperature gradient is related to the momentum dependence of the radius parameters of the two-particle correlation function, as well as to the momentum-dependent temperature parameter of the single particle spectrum, while a long duration of particle evaporation is found to be responsible for the low relative momentum behavior of the two-particle correlations.