Generalized Boltzmann equation for lattice gas automata

In this paper a theory is formulated that predicts velocity and spatial correlations between occupation numbers that occur in lattice gas automata violating semi-detailed balance. Starting from a coupled BBGKY hierarchy for then-particle distribution functions, cluster expansion techniques are used to derive approximate kinetic equations. In zeroth approximation the standard nonlnear Boltzmann equation is obtained; the next approximation yields the ring kinetic equation, similar to that for hard-sphere systems, describing the time evolution of pair correlations. The ring equation is solved to determine the (nonvanishing) pair correlation functions in equilibrium for two models that violate semidetailed balance. One is a model of interacting random walkers on a line, the other one is a two-dimensional fluid-type model on a triangular lattice. The numerical predictions agree very well with computer simulations.     

Alpha particle scattering in the rigid projectile approximation

We study elastic α-particle scattering offp,α-particle and¹²C targets at 17.9 GeV/c incident momentum in the rigid projectile approximation of the Glauber model. Differential and total cross-sections are computed and compared with the data. Reasonable agreement with the observed differential cross-sections is found for small momentum transfers but short-range dynamical correlations in the target will probably have to be taken into account to get better agreement at larger momentum transfers, particularly in the case of α-¹²C scattering.     

Remarks on the density functional approach to the inhomogeneous electron gas

The density functional approach is reformulated by using the most general form of the Hohenberg-Kohn theorem based on p-particle densities. Comparison with the reduced density matrix theory is made, exhibiting fully the p-particle hierarchy of both theories. Some advantages and drawbacks of the generalized density functional approach are discussed. The 1-particle spin-polarized case is presented to indicate the place of the usual DFA within the framework of the generalized theory.     

The quantum theory of nucleon correlation in finite nuclei. II. Higher order correlation effects and additive pair approximation

In the first part of this article it was shown that the variational solution of the Schroedinger equation of a finite Fermion system can be written as a finite sum of A terms (for A particles) the first of which is the Hartree-Fock energy, while the rest represent the correlation effects. In the first part explicit formulas for the 2-particle correlation energy were given. In this paper explicit formulas are given for the higher order correlation energies. It is shown that two different models can be developed depending on the orthogonality condition used. Beginning with the 4th order effects the “linked” and “unlinked” correlation terms are separated. An exact formula is given for the case in which only the 2-particle effects, linked and unlinked are taken into account. The “additive pair approximation” in which the correlation energy is given as the sum of 2-particle energies is investigated and it is shown to be related to the exact formula by a clearly defined set of approximations. Various possible applications of the model are discussed.     

Quantum Dynamics with Mean Field Interactions: a New Approach

We propose a new approach for the study of the time evolution of a factorized N-particle bosonic wave function with respect to a mean-field dynamics with a bounded interaction potential. The new technique, which is based on the control of the growth of the correlations among the particles, leads to quantitative bounds on the difference between the many-particle Schrödinger dynamics and the one-particle nonlinear Hartree dynamics. In particular the one-particle density matrix associated with the solution to the N-particle Schrödinger equation is shown to converge to the projection onto the one-dimensional subspace spanned by the solution to the Hartree equation with a speed of convergence of order 1/N for all fixed times.     

Coulomb wave function corrections for n-particle Bose–Einstein correlations

The effect of multi-particle Coulomb final state interactions on higher-order intensity correlations is determined in general, based on a scattering wave function which is a solution of the n-body Coulomb Schr?dinger equation in (a large part of) the asymptotic region of n-body configuration space. In particular, we study Coulomb effects on the n-particle Bose–Einstein correlation functions of similarly charged particles and remove a systematic error as big as 100% from higher-order multi-particle Bose–Einstein correlation functions. Received: 24 November 1999 / Published online: 17 March 2000     

Out-of-plane correlations of α-particles and heavy ions in the reaction of 373 MeV32S with gold

Out-of-plane correlations between α-particles and projectile-like heavy ions have been measured for the system³²S+¹⁹⁷Au at E_LAB=373 MeV. The angular widths of the correlations range from 24° to 40° (FWHM) depending on theZ of the heavy ion. In the framework of a model calculation these widths are shown to be very sensitive to the outof-plane momentum of the α-particle at emission. It is concluded that only little heating of the reaction partners occurs prior to α-particle emission.     

Inclusion of Final-State-Interaction Effects at Higher Energies in the Photodisintegration of the α-Particle

Final-state-interaction (FSI) effects are included in the treatment of the photodisintegration of the α-particle via the K-matrix approximation. These are applied to the exact AGS-type integral equation for this process at photon energies 50–100 MeV. Direct comparison with the plane-wave (Born) approximation indicates that these effects are small, which explains the good fit to the data we found previously. The FSI in the integro-differential equation treatment of the problem in configuration space are included by means of effective nucleon-trinucleon potentials constructed via an exact inverse scattering method and by using the phase shifts obtained from the K-matrix approach to the 3 + 1 → 3 + 1 scattering. Comparison between this approach and the integral-equation approach confirms the validity of this model previously employed at low energies using experimental phase shifts. Finally we show that the photonuclear cross sections are sensitive to the details of the boundstate wave functions of the ³He and ⁴He as calculated exactly via the AGS equations and in the integro-differential-equation approach, which for the ⁴He neglects higher-order correlations. Received April 18, 1994; revised September 12, 1994; accepted for publication October 12, 1994     

Generalized enskog theory for homogeneous systems

We propose a generalization of the Enskog equation for homogeneous dense systems including the complete three-particle dynamics. To this end the time derivative of the one-particle distribution is represented in the thermodynamic limit as the sum of three terms describing the effect of the initials-particle correlations, collisions withins-particle clusters, and coupling ofs-particle clusters to the surrounding gaseous medium, respectively. The analysis of casess=2 ands=3 is performed both for hard spheres and for a smooth, repulsive interaction. On assuming the equilibrium structure and spatial dependence of terms reflecting the effect of the medium, we obtain fors=2 the Enskog equation, and fors=3 a new equation, going beyond the Enskog theory. Apart from the Enskog collision term it contains additional contributions, and can be shown to reduce to the Choh-Uhlenbeck equation in the long-time, low-density limit.     

Multiparticle correlations from momentum conservation

Using a generating-function formalism, we compute the contribution of momentum conservation to multiparticle correlations between the emitted particles in high-energy collisions. In particular, we derive a compact expression of the genuine M-particle correlation, for arbitrary M.Received: 17 February 2003, Published online: 5 September 2003     

Non-equilibrium statistical mechanics in the general theory of relativity: II. Linear fields in a kinetic approximation

The first paper in this series introduced a new, manifestly covariant approach to non-equilibrium statistical mechanics in classical general relativity. The object of this second paper is to apply that formalism to the evolution of a collection of particles that interact via linear fields in a fixed curved background spacetime. Given the viewpoint adopted here, the fundamental objects of the theory are a many-particle distribution function, which lives in a many-particle phase space, and a many-particle conservation equation which this distribution satisfies. By viewing a composite N-particle system as interacting one- and (N ? 1)-particle subsystems, one can derive exact coupled equations for appropriately defined reduced one- and (N ? 1)-particle distribution functions. Alternatively, by treating all the particles on an identical footing, one can extract an exact closed equation involving only the one-particle distribution. The implementation of plausible assumptions, which constitute straightforward generalizations of standard non-relativistic “kinetic approximations”, then permits the formulation of an approximate kinetic equation for the one-particle distribution function. In the obvious non-relativistic limit, one recovers the well-known Vlasov-Landau equation. The explicit form for the relativistic expression is obtained for three concrete examples, namely, interactions via an electromagnetic field, a massive scalar field, and a symmetric second rank tensor field. For a large class of interactions, of which these three examples are representative, the kinetic equation will admit a relativistic Maxwellian distribution as an exact stationary solution; and, for these interactions, an H-theorem may be proved.     

Integral equations for N-particle scattering

Integral equations are derived for the N-particle transition operators. The equations couple together only transition operators between two-body channels. The kernel of the equations becomes connected after a single iteration. Transition operators involving channels with three or more particles can be obtained by quadratures from the solution of the equations. It is also shown that the N-particle equations can be reduced to multichannel two-body equations by the use of the quasiparticle method.     

Duality relations for asymmetric exclusion processes

We derive duality relations for a class ofU _q [SU(2)]-symmetric stochastic processes, including among others the asymmetric exclusion process in one dimension. Like the known duality relations for symmetric hopping processes, these relations express certainm-point correlation functions inN-particle systems (Nm) in terms of sums of correlation functions of the same system but with onlym particles. For the totally asymmetric case we obtain exact expressions for some boundary density correlation functions. The dynamical exponent for these correlators isz=2, which is different from the dynamical exponent for bulk density correlations, which is known to bez=3/2.     

Superposition approximations from a variation principle

A variation principle is introduced involving then-particle molecular distribution function (where 1 n N) for a fluid containingN molecules. An integral involving any approximaten-particle distribution function proves to define aleast upper bound to the true system free energy. This integral can, therefore, be minimized with respect to the form of a trial distribution function to provide a best estimate to the exact distribution function. When no other constraints, save the requirement of normalization, are applied to the trial function, the extremum corresponds to the exact function. Using this variation principle, it is possible to demonstrate that the optimum triplet superposition approximation is the Krikwood approximation, and that the optimum quadruplet approximation is the form suggested by Fisher and Kopeliovich. Furthermore, all higher-order optimum superposition approximations are specified.Research supported under NSF Grant GP-20884.     

Growth, percolation, and correlations in disordered fiber networks

This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameterp which controls the degree of clustering. Forp=1 the deposited network is uniformly random, while forp=0 only a single connected cluster can grow. Forp=0 we first derive the growth law for the average size of the cluster as well as a formula for its mass density profile. Forp>0 we carry out extensive simulations on fibers, and also needles and disks, to study the dependence of the percolation threshold onp. We also derive a mean-field theory for the threshold nearp=0 andp=1 and find good qualitative agreement with the simulations. The fiber networks produced by the model display nontrivial density correlations forp<1. We study these by deriving an approximate expression for the pair distribution function of the model that reduces to the exactly known case of a uniformly random network. We also show that the two-point mass density correlation function of the model has a nontrivial form, and discuss our results in view of recent experimental data on mss density correlations in paper sheets.     

Theorems on n-representability in finite dimensions

The subject of the paper is the n-representability problem of p-particle density operators, and, in general, of p-particle positive operators in the case when the 1-particle reference space is of finite dimension r.     

Cumulative production of nucleons and extremely light nuclei in 4Hep interactions at an incident momentum of 5 GeV/c

The invariant cross sections for the cumulative production of protons, neutrons, and extremely light nuclei (d, ³H, and ³He) are determined on the basis of experimental data obtained by exposing the 2-m liquid-hydrogen bubble chamber of the Institute of Theoretical and Experimental Physics (ITEP, Moscow) to a 5-GeV/c α-particle beam, the kinetic energy of primary protons in the rest frame of the nucleus involved being T _p = 620 MeV. The results obtained in this way are compared with the predictions of the Frankfurt-Strikman model, which takes into account short-range few-nucleon correlations, and with the predictions of the nuclear coalescence model.     

Relationship between experimental pKa values in aqueous solution and a gas phase bond length in bicyclo[2.2.2]octane and cubane carboxylic acids

Linear correlations were established between the calculated bond lengths and the pK_a or σ_I values for a series of 4‐substituted bicyclo[2.2.2]octane‐1‐carboxylic acid and 4‐cubane‐1‐carboxylic acid derivatives. The bond lengths have been calculated at a modest computational level, HF/6‐31G(d), both in the gas phase and with the continuum solvation model, polarisable continuum model (PCM). In general, the best correlations are obtained when the PCM model is taken into account, especially when neutral and charged molecules are considered together. The best models in each case show square correlation coefficients (R²) larger than 0.9 and indicate that they can be used as predictive tools. These results expand previous results that indicate the possibility of a relationship between gas phase bond length and pK_a values in aqueous solution and indicate that such relationships are more general than hitherto expected. Copyright © 2013 John Wiley & Sons, Ltd.     

Frustration signatures in the anisotropic model of a nine-spin <Emphasis Type="Italic">s</Emphasis> = 3/2 ring with bond defect

Effects of magnetic frustration in the model of nine-membered antiferromagnetic s = 3/2 molecular spin ring are investigated. We use a Heisenberg spin model with nearest-neighbor interactions, single-ion anisotropy and with tunable bond defect leading to continuously varying topology: from closed to open ring. In order to identify a frustrated phase we calculate the full energy spectrum of the model and a number of thermodynamic quantities at low temperature. The calculations are performed by means of numerically exact methods: quantum transfer matrix and exact diagonalization. It is shown that total and local magnetizations, nearest-neighbor spin correlations and spin fluctuations can serve as consistent frustration signatures. Magnetizations and spin-spin correlations are reduced in the frustrated phase whereas fluctuations and correlations of fluctuations increase. The ground state in a frustrated phase is a m = 1/2 doublet and in the non-frustrated phase a m = 3/2 doublet. In the system studied bipartiteness is not opposite to frustration as there are regions in the parameter space for which the system is neither bipartite nor frustrated.