单一多体不可逆聚集方程的解

本文研究的是单一多体不可逆聚集方程的解,从广义Smoluchovski方程出发,分别讨论凝结核为K(i₁,i₂,…,i_n)=const和凝结核为K(i₁,i₂,…,i_n)=sumfrom i=1 to n(i_l)的精确解,求出集团的体积分布C_m(t)。并且还讨论它们的长时行为。 关键词：     

Gravitational and inertial mass of bodies of interacting electrical charges

Starting from the equations of motion of particles interacting with both electromagnetic and gravitational fields, the (passive) gravitational mass (M _g) and the inertial mass (M _i) of the total system of interacting charges is calculated. It is found that in both Einstein's General Relativity and the scalar-tensor gravitational theory of Brans and Dicke,M _g andM _i are both equal to the Special Relativistic energy of the system of interacting charged particles. Therefore, both theories are compatible with the high accuracy measurements of theM _g/M _i ratio of laboratory objects. This work was supported by National Aeronautics and Space Administration grant NGR 27-001-035.     

Yang–Baxter equation-based potential model for a one-dimensional fermion system

We propose a velocity-dependent δ-function potential model for a one-dimensional fermion system, under which the two-particle interchange operators in the Bethe hypothesis satisfy the Yang–Baxter equation. This model, proportional to the product of the momenta of two interacting particles, is not translation invariant. It is found that the ground-state particle distribution densities become negative in the low momentum region. To resolve the controversy, we apply an overall momentum shift to the system, and obtain reasonable solutions. The dependence of the ground-state distributions on the momentum shift is discussed.     

The N-mode squeezed state with enhanced squeezing

It is known that exp [iλ (Q1P1i/2)] is a unitary single-mode squeezing operator,where Q1,P1 are the coordinate and momentum operators,respectively.In this paper we employ Dirac’s coordinate representation to prove that the exponential operator S n ≡ exp [iλ sum((QiPi+1+Qi+1Pi))) from i=1 to n ],(Qn+1=Q1,Pn+1=P1),is an n-mode squeezing operator which enhances the standard squeezing.By virtue of the technique of integration within an ordered product of operators we derive S n ’s normally ordered expansion and obtain new n-mode squeezed vacuum states,its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.     

Linear quantum enskog equation II. Inhomogeneous quantum fluids

This is the second part of a work concerned with the quantum-statistical generalization of classical Enskog theory, whereby the first part is extended to spatially inhomogeneous fluids. In particular, working with Liouville operators and using cluster expansions and projection operators, we derive the inhomogeneous linear quantum Enskog equation and express the dynamic structure factor and the nonlocal mobility tensor in terms of the corresponding quantum Enskog collision operator. Thereby static correlations due to excluded volume effects and quantum-statistical correlations due to the fermionic (bosonic) character of the pairwise strongly interacting particles are treated exactly. When static correlations are neglected, this Enskog equation reduces to the inhomogeneous linear quantum Boltzmann equation (containing an exchange-modifiedt-matrix). In the classical limit, the well-known linear revised Enskog theory is recovered for hard spheres.     

n体聚集过程和联合聚集过程的集团尺寸分布

本文研究n体聚集过程和联合聚集过程的集团分布演化。从广义Smoluchovki方程出发,给出聚集核K(i₁,i₂,…,i_n)=A sumfrom i=1 to n i₁+B(A,B均为常数)的显解;利用聚集核K(i₁,i₂,…,i_n)=(Ai₁+B)(Ai₂+B)…(Ai_n+B)和核K(i₁,i₂,…,i_n)=A sumfrom i=1 to n i₁+B的方程之间的联系,得出核K(i₁,i₂,…,i_n)=S_(i1)S_(i2)…S_(in)(S_K=AK+B)的凝前解。而且,根据联合聚集动力学方程,讨论了聚集和型核分别为K₂(i,j)=i+j,K₃(i,j,k)=i+j+k的集团尺寸分布C_m(t)的长时行为,并将结论推广到一般的联合聚集过程。 关键词：     

Eigenvalues of the Faddeev equation kernel for a system of three spinless particles

For a system of three spinless particles interacting via separable Yamaguchi potential the possibility of the existence of three-particle resonances is studied. To this end, the eigenvaluesλ _i ^L (E ₃) of the Faddeev equation kernel have been calculated in the c.m.-energy region ?30 MeV≦E ₃≦15 MeV for total momentum statesL=0 andL=1. It is shown that in the investigated energy range there are no resonances.     

Toward classification of conformal theories

By studying the representations of the mapping class groups which arise in 2D conformal theories we derive some restrictions on the value of the conformal dimension h_i of operators and the central charge c of the Virasoro algebra. As a simple application we show that when there are a finite number of operators in the conformal algebra, the h_i and c are all rational.     

2D LOCUS CONFIGURATIONS AND THE TRIGONOMETRIC CALOGERO–MOSER SYSTEM

A central hyperplane arrangement in ?² with multiplicity is called a "locus configuration" if it satisfies a series of "locus equations" on each hyperplane. Following [4], we demonstrate that the first locus equation for each hyperplane corresponds to a force-balancing equation on a related interacting particle system on ?*: the charged trigonometric Calogero-Moser system. When the particles lie on S¹ ? ?*, there is a unique equilibrium for this system. For certain classes of particle weight, this is enough to show that all the locus equations are satisfied, producing explicit examples of real locus configurations. This in turn produces new examples of Schrödinger operators with Baker–Akhiezer functions.     

Ursell operators in statistical physics of dense systems: the role of high order operators and of exchange cycles

The purpose of this article is to discuss cluster expansions in dense quantum systems, as well as their interconnection with exchange cycles. We show in general how the Ursell operators of order l≥ 3 contribute to an exponential which corresponds to a mean-field energy involving the second operator U₂, instead of the potential itself as usual - in other words, the mean-field correction is expressed in terms of a modification of a local Boltzmann equilibrium. In a first part, we consider classical statistical mechanics and recall the relation between the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles) and show that each Ursell operator U_n with n≥ 3 contains a “tree-reducible part”, which groups naturally with U₂ through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles, and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach, in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum statistics and dynamics. Received 18 October 2001     

Rotational diffusion of a tracer colloid particle: I. Short time orientational correlations

We extend the generalized Smoluchowski equation to descrbe the diffusional relaxation of position and orientation in a suspension of interacting spherical colloid particles. Considering a tracer particle which interacts with other particles through spherically symmetric pair potentials and with an external field we obtain a cluster expansion representation of the orientational time correlation functions for the tracer. The one and two body cluster contributions are studied explicitly at short times. Working to first order in volume fraction φ we show that the initial slope of the time correlation functions is described by a modified diffusion coefficient D^r = D^r₀(1 −C^rφ) where C^r is a number determined by hydrodynamic and potential interactions. We evaluate C^r numerically for spheres with slip-stick hydrodynamic boundary conditions and also for permeable spheres.     

Mouvement brownien dans une assemblée de bâtonnets minces dans la phase isotrope

Using the kinetic methods of the Brussels School, we establish the equation (to the 2nd order in the perturbation) for the return to equilibrium of the one particle energy distribution function in an isotropic fluid made of thin slabs interacting through a P₂-type potential. We show that for a very heavy brownian particle in a bath of identical light particles in equilibrium, this equation reduces to a Fokker-Planck equation, the coefficients of which are explicitly calculated. In the same manner we study the return to equilibrium of an angular excitation.     

Kinetic analysis of the ionization ratio effects on a three‐species plasma

In partially ionized plasmas, the energy transferred to electrically charged species by the electromagnetic field can be partly channelized to the population of neutrals, due to interspecies collisional processes. Depending on the relative density of neutrals, these effects may govern the collective plasma dynamics by drastically modifying particle dynamics and energy‐transport processes with respect to the fully ionized plasma‐approximation models. In this work, the influence of the ionization ratio r_i on a partially ionized plasma is analysed by means of a three‐species one‐dimensional kinetic model to compute transient and steady state velocity‐dependent distribution functions. The conservative collision operators accounting for charge–charge and charge–neutral interactions allow studying several plasma scenarios with the same entire number of particles per unit of volume but for an increasing r_i parameter, in the presence of a modulated signal‐like electric field. For a sequence of plasma scenarios of fixed r_i, ranging from typical weakly ionized to highly ionized plasma values r_i ～ 10^?7–10^?4, the mass species flows are examined. These flows behave linearly with respect to r_i up to a value r_i ? 10^?5 from which the quasi‐linear dependence is critically altered. The convection–diffusion equations are solved with the semianalytical Propagator Integral Method, which behaves well to deal with conservative operators, density, and field discontinuities, allowing for the use of collision terms of disparate time and spatial characteristic scales. The results can be relevant to a wide class of plasma systems and to analyse the ionization ratio effects on transport coefficients.     

Overcomplete Free Energy Functional for D = 1 Particle Systems with Next Neighbor Interactions

We deduce an overcomplete free energy functional for D=1 particle systems with next neighbor interactions, where the set of redundant variables are the local block densities _i of i interacting particles. The idea is to analyze the decomposition of a given pure system into blocks of i interacting particles by means of a mapping onto a hard rod mixture. This mapping uses the local activity of component i of the mixture to control the local association of i particles of the pure system. Thus it identifies the local particle density of component i of the mixture with the local block density _i of the given system. Consequently, our overcomplete free energy functional takes on the hard rod mixture form with the set of block densities _i representing the sequence of partition functions of the local aggregates of particle numbers i. The system of equations for the local particle density of the original system is closed via a subsidiary condition for the block densities in terms of . Analoguous to the uniform isothermal-isobaric technique, all our results are expressible in terms of effective pressures. We illustrate the theory with two standard examples, the adhesive interaction and the square-well potential. For the uniform case, our proof of such an overcomplete format is based on the exponential boundedness of the number of partitions of a positive integer (Hardy-Ramanujan formula) and on Varadhan's theorem on the asymptotics of a class of integrals.     

Glueball spectrum from N_f=2 lattice QCD study on anisotropic lattices

The lowest-lying glueballs are investigated in lattice QCD using N_f = 2 clover Wilson fermions on anisotropic lattices. We simulate at two different and relatively heavy quark masses, corresponding to physical pion masses of mπ～938 MeV and 650 MeV. The quark mass dependence of the glueball masses has not been investigated in the present study. Only the gluonic operators built from Wilson loops are utilized in calculating the corresponding correlation functions. In the tensor channel, we obtain the ground state mass to be 2.363(39) GeV and 2.384(67)GeV at mπ～938 MeV and 650 MeV, respectively. In the pseudoscalar channel, when using the gluonic operator whose continuum limit has the form of ∈_ijkTrB_iD_jB_k, we obtain the ground state mass to be 2.573(55) GeV and 2.585(65) GeV at the two pion masses. These results are compatible with the corresponding results in the quenched approximation. In contrast, if we use the topological charge density as field operators for the pseudoscalar, the masses of the lowest state are much lighter(around 1 GeV) and compatible with the expected masses of the flavor singlet qq meson. This indicates that the operator ∈ijk TrBiDjBk and the topological charge density couple rather differently to the glueball states and qq mesons. The observation of the light flavor singlet pseudoscalar meson can be viewed as the manifestation of effects of dynamical quarks. In the scalar channel, the ground state masses extracted from the correlation functions of gluonic operators are determined to be around 1.4-1.5 GeV, which is close to the ground state masses from the correlation functions of the quark bilinear operators. In all cases, the mixing between glueballs and conventional mesons remains to be further clarified in the future.     

The ground state energy per particle for infinite particle quantum systems

We give a simple proof that the ground state energy per particle for several interacting particle systems is monotone and bounded as the number of particles increases. Some of the systems for which the proof holds are anharmonic oscillator approximations to || _d ^/4 quantum fields, many body Schrödinger operators with nearest and next to nearest neighbor couplings, and systems whose energy is given by operators which are not restricted to being differential operators.Research partially supported by the National Science Foundation under grant No. MCS-77-03568     

Interacting generalized Chaplygin gas model in non-flat universe

We employ the generalized Chaplygin gas of interacting dark energy to obtain the equation of state for the generalized Chaplygin gas energy density in a non-flat universe. By choosing a negative value for B we see that w_Λ ^eff<-1, which corresponds to a universe dominated by phantom dark energy.     

Fock space representations of affine lie algebras and integral representations in the Wess-Zumino-Witten models

Fock space representations of affine Lie algebras are studied. Explicit forms of correction terms adding to the currentsF _i (z) are determined. It is proved that the Sugawara energy-momentum tensor on the Fock spaces is quadratic in free bosons. Furthermore, screening operators are constructed. This implies the existence of generalized hypergeometric integrals satisfying the Knizhnik-Zamolodchikov equation.     

Theory of light scattering from a system of interacting Brownian particles

Starting from a N-particle diffusion equation for a system of N interacting spherical Brownian particles, a non-linear transport equation for concentration fluctuations δc(r, t) of the particles is derived. This dynamic equation is transformed into a hierarchy of equations for retarded propagators of increasing numbers of concentration fluctuations. A cluster expansion to lowest order in the average concentration results in a set of two coupled equations. The spectrum of light scattered by the interacting particles is in general not a Lorentzian, due to the non-linear term in the transport equation. For small scattering wave vectors k the width is D(ω)k², where ω is the transferred frequency. It is shown that D(0) = D_e, the effective diffusion coefficient. For a hardcore interaction potential the spectrum is Lorentzian and it is found that D_e = D₀(1 + φ), where D₀ is the diffusion constant for independent particles and φ the volume concentration of Brownian particles.