Resolution of B-B-G-K-Y Hierarchy and Transport Coefficients

Abstract

It has been known for many years that the Boltzmann equation provides a good description of the transport coefficients for a dilute gas of particles interacting with short-range forces. While this equation for the phase space (or Wigner) distribution function f(r, p, t) is closed, the rigorous mechanical evolution equation for f is not according to the investigation of Bogoliubov, Born and Green, Kirkwood, Yvon and others.D, 2 l Recently many efforts have been made to derive and generalize the former equation from the latter by introducing approximations.ll,3J Unfortunately. most of the approximations previously proposed by various authors seem to be motivated by mathematical tractability rather than by physical reasoning. To this category of approximations belong e. g. Bogoliubov's ffunctional dependence assumption on the many-body distribution functions,ll the factorizability of the initial many-body density into one-body densities, 3 l,<l and the random phase approximation. slIn the pre~ent letter we point out that(1) the evolution equation for f which is rigorous in the bulk limit IS non-linear but closed aside from the term R representing the contribution of the initial particle correla-*l This research was supported by the Office of Naval Research, United States Navy.tions, and (2) 'the solution of the asymptotic evolution equation with the neglect of R provides a description of transport coefficients equivalent to the (rigorous) description in terms of correlation function formulas.6l The combination of these two implies complete resolution of the B-B-G-K-Y hierarchy for the practical purpose of calculating transport coefficients. None of these assumptions quoted above are used in the present theory. We consider a quantum system of distinguishable particles characterized by the Hamiltonian H= L;hfiJl + .<L;v<iJJ,(1) 1 i<j where, the upper indices denote particles. The one-body density matrix is defined by n (111, 112, t) =n (1, 2, t) = Tr{nt2P(t)}, (2) n12 = .Q-1 L; j l11fJl > <11fJ) I,where p(t) is a many-particle density operator, .Q the volume; I11CJl > and <11<JJ I are orthonormalized ket and bra vectors corresponding to the state 11 of the j-th particle.According to the connected-diagram analysis reported earlier,7l the evolution equation for n(t) can be written in the thermodynamic limit as [reference 7) (3 · 11)] 8tn(t) +i [ho, n(t)] =G(t, n) + R(t), (4) where the first term G defined in [reference 7), (3 · 9)] on the r. h. s. (right-hand side) is that part which can be expressed in terms of n with time arguments in general different from t. and the second term R [reference 7), (3 ·10)] the rest which cannot, and which represents the effect of the initial particle correlations described by p(O) on 8tn. Equation ( 4) is expected to be valid for normal systems in which the main at

Hyperon single-particle potentials calculated from quark-model baryon–baryon interactions

“…Since the whole interaction acting between the baryons is determined by a strong cancellation between this repulsion at the short-range and the intermediate-range attraction, it is natural to expect that these two models predict quite different results for some observables whose experimental data are still not yet available. In fact, we have shown in the previous papers [7][8][9] that, in some Y N observables and also in certain partial waves, the quark-model potential gives predictions different from that of the one-boson exchange model such as the Nijmegen model [10][11][12][13] and the Jülich model [14,15]. Since available experimental data are still scarce in the strangeness sector, it is useful to elucidate further the characteristics of the quark-model potential and to pursue its implications to hypernuclear physics.…”

“…The SU 6 quark-model provides a unified framework to describe baryonbaryon interactions including hyperons [1,2]. Recently the Kyoto-Niigata group has developed a modern quark-model baryon-baryon interaction [3][4][5][6][7][8][9], which reproduces essential features of the nucleon-nucleon (NN) and hyperon-nucleon (Y N) scattering data below 300 MeV. In this model, the quark-quark interaction is assumed to consist of a phenomenological quark-confining potential, the Fermi-Breit interaction coming from the one-gluon exchange mechanism and effective meson-exchange potentials of scalar and pseudo-scalar meson nonets directly coupled to quarks.…”

Lippmann-Schwinger Resonating-Group Formalism for NN and YN Interactions in an SU6 Quark Model

“…As mentioned in the Introduction, FSS 5), 6), 7) , RGM-H 6), 7) and their preceding version RGM-F 3), 4) are formulated in the (3q)-(3q) RGM applied to the system of two (0s) 3 clusters. The qq interaction is composed of the full FB interaction with explicit quark-mass dependence, a simple confinement potential of quadratic power law and EMEP acting between quarks.…”

“…3), 4), 5), 6), 7), 8), 9), 10) We have recently achieved a simultaneous description of the N N and Y N interactions in the RGM formulation of the spin-flavor SU 6 quark model. 3), 4), 5), 6), 7) In this model the meson-exchange effect of scalar (S) and pseudo-scalar (PS) meson nonets is incorporated in the quark Hamiltonian in the form of effective mesonexchange potentials (EMEP) acting between quarks. The flavor symmetry breaking for the Y N system is explicitly introduced through the quark-mass dependence of the Hamiltonian, as well as the flavor dependence of the exchanged meson masses.…”

Theory of Hindered Gamow-Teller Matrix Elements

“…The relation ~ G"~O can be obtained, if the approximate quantum numbers for the initial and final states are Ai = T 0 and A 1 = T 0 -1, respectively. In such a case the projection operator 20 ) projecting the state with a definite A out of a mixed state is useful just as in the isospin case. The explicit expression for the projection operator is given in Appendix B.…”