Kinetic equations for a quantum gas with bound states

The kinetic theory for dense gases is modified to take into account the existence of bound states. A molecular chaos condition is used which corresponds to the division of the two- and three-particle Hubert spaces into scattering and boundstate subspaces. A kinetic stage results from a long-time limit which converges to yield time-independent functionals for the two- and three-particle density matrices, as functionals of the density matrices for atoms and molecules. Coupled kinetic equations are obtained which describe the gas as a reacting mixture of atoms and diatomic molecules. These include the effects of scattering and rearrangement collisions between the atom and the molecule, and of molecular formation and dissociation.     

On the kinetic theory of a dense gas of rough spheres

The revised Enskog equation for a dense gas of rough spheres is considered. TheH theorem and the conservation equations are discussed.     

Monatomic gas as a singular limit of polyatomic gas in molecular extended thermodynamics with many moments

The difference in the theoretical structure between monatomic and polyatomic gases in highly nonequilibrium states is discussed from the viewpoint of molecular extended thermodynamics (MET) of rarefied gases, which is free from the local equilibrium assumption. The MET theories of these two types of gases are based on the moment balance equations with different hierarchy structures due to whether the internal degrees of freedom of a molecule are incorporated in their distribution functions or not. In particular, the number of balance equations in the MET theory of polyatomic gases is greater than the number in the corresponding theory of monatomic gases. The closure procedure for the system of balance equations of polyatomic gases obtained in a recent paper (Arima et al., 2014) is adopted. We prove that the solutions for polyatomic gases converge, in the limit where the degrees of freedom of a molecule D$D$ tend to 3, to the ones for monatomic gases provided that we impose appropriate initial conditions compatible with monatomic gases. Thus a MET theory of rarefied monatomic gases can be identified as a singular limit of the corresponding MET theory of rarefied polyatomic gases. As illustrative examples, the asymptotic behaviors when D→3$D\to 3$ in the dispersion relation of ultrasonic waves and in the shock wave structure are shown.     

Warm cascade states in a forced-dissipated Boltzmann gas of hard spheres

We study the homogeneous isotropic Boltzmann equation for an open system. For the case of a hard spheres gas, we look for nonequilibrium steady solutions in the presence of forcing and dissipation. Using the language of weak turbulence theory, we analyze the possibility of observing the Kolmogorov-Zakharov steady distributions, i.e. solutions characterized by constant fluxes of conserved quantities. We derive a differential approximation model and we find that the expected nonequilibrium steady solutions have always the form of warm cascades. We propose an analytical prediction for the relation between the forcing and dissipation and the thermodynamic quantities of the system. Specifically, we find that the temperature of the system is independent of the forcing amplitude and determined only by the forcing and dissipation scales. Finally, we perform direct numerical simulations of the Boltzmann equation finding consistent results with our theoretical predictions.     

The Boltzmann equation for a polyatomic gas

A formulation of the kinetic theory of dilute, classical polyatomic gases is given which parallels the Waldmann development for structureless molecules. In the first section the Boltzmann equation is written in terms of the specific rates of inelastic collision processes and then the properties of these rates and those of the corresponding collision cross sections are examined. The dependence of the distribution function on the dynamical variables is discussed and the equations of change for the gas are derived. Finally, a study is made of the properties of the linearized Boltzmann collision operation. In the second section the Boltzmann equation is deduced from a rigorous statistical-mechanical point of view and discussed in terms of the basic ideas of Bogoliubov. The computationally important special case of impulsive interactions is then considered.This research was supported in part by a grant from the National Science Foundation and in part by the Ames Laboratory of the U. S. Atomic Energy Commission. Contribution No. 2554.     

Boltzmann equation for a dissociating gas

The incorporation of three-body collisions for dissociation/recombination into the Boltzmann equation is discussed. Conditions are assumed such that collisions are completed in the sense of scattering theory, so the collision operator is determined by scattering and reaction cross sections. The resulting equation has anH-theorem, and the equilibrium solution requires the law of mass action in addition to the Maxwellian dependence on momentum. A brief discussion is given of the normal solution and the transport coefficients.This paper is dedicated to Prof. E. G. D. Cohen on the occasion of his 65th birthday.     

Stationary extended kinetic theory for a gas of hard spheres

Summary Analytical and numerical results for the stationary, spatially homogeneous distribution function of a gas of ?hard-sphere? particles are reported. Both removal and scattering effects are accounted for. In the case of only removal, comparison is also made with results obtained in the frame of alternative models proposed for approximating the exact ?hard-sphere? model.     

On the H-theorem for polyatomic gases

The H-theorem for a classical gas of polyatomic molecules of arbitrarily complex structure is examined. A simple use of time reversal invariance of the equations of dynamics is used to circumvent the objections which were raised by Lorentz against Boltzmann's proof (nonexistence of inverse collisions).     

An imaginary potential with universal normalization for dissipative processes in heavy-ion reactions

In this work we present new coupled channel calculations with the São Paulo potential (SPP) as the bare interaction, and an imaginary potential with system and energy independent normalization that has been developed to take into account dissipative processes in heavy-ion reactions. This imaginary potential is based on high-energy nucleon interaction in nuclear medium. Our theoretical predictions for energies up to ≈100 MeV/nucleon agree very well with the experimental data for the p,n+nucleus, ¹⁶O + ²⁷Al, ¹⁶O + ⁶⁰Ni, ⁵⁸Ni + ¹²⁴Sn, and weakly bound projectile ⁷Li + ¹²⁰Sn systems.     

Matrix-product states for a one-dimensional lattice gas with parallel dynamics

The hopping motion of classical particles on a chain coupled to reservoirs at both ends is studied for parallel dynamics with arbitrary probabilities. The stationary state is obtained in the form of an alternating matrix product. The properties of one- and two-dimensional representations are studied in detail and a general relation of the matrix algebra to that of the sequential limit is found. In this way the general phase diagram of the model is obtained. The mechanism of the sequential limit, the formulation as a vertex model, and other aspects are discussed.     

Free Transport Limit for <Emphasis Type=Italic>N</Emphasis>-particles Dynamics with Singular and Short Range Potential

We study the limit of systems of interacting particles, when the number of particle becomes very large. The support of the interaction vanishes as the number of particles goes to infinity, so that the natural limit is just free transport, but no limitation is assumed about the strength of the interaction. We obtain explicit estimates for the number of particles effectively interacting and describe the way they do it.     

Classical and quantum kinetic equations with exact conservation laws

Stationary and dynamic properties of reduced density matrices can be determined from formal or approximate closures of an infinite hierarchy of equations. The local macroscopic conservation laws place weak but important constraints on the reduced density matrices which should be respected by any closure. For pairwise additive forces conditions on the closure of the one- and two-particle equations are obtained that preserve the exact functional dependence of the conserved densities and their fluxes on the reduced density matrices. To illustrate the nature of these conditions, a closure approximation suitable for a quantum gas is given, yielding an extension of the time-dependent Hartree-Fock equations for the dynamics of a nuclear fluid to include collisions.     

Maximum entropy principle for rarefied polyatomic gases

The aim of this paper is to show that the procedure of maximum entropy principle for the closure of the moments equations for rarefied monatomic gases can be extended also to polyatomic gases. The main difference with respect to the usual procedure is the existence of two hierarchies of macroscopic equations for moments of suitable distribution function, in which the internal energy of a molecule is taken into account. The field equations for 14 moments of the distribution function, which include dynamic pressure, are derived. The entropy and the entropy flux are shown to be a generalization of the ones for classical Grad’s distribution. The results are in perfect agreement with the recent macroscopic approach of extended thermodynamics for real gases.     

Exact solutions for a semilinear hyperbolic system with general quadratic interactions

Summary The approximate conservation laws for a binary gas mixture with quadratic interactions can be written as a system of two semilinear hyperbolic equations. By using the method of characteristics the study of this system is reduced to the study of a system of nonlinear ordinary differential equations, for which we find several classes of exact solutions. Exact integrability conditions are found for ODE systems of generalized Lotka-Volterra type. Some situations are also considered, in which the characteristic method cannot be applied and exact solutions are obtained via an operator method.     

Analytical solutions for the energy distribution of charged particles in a weak electric field

The paper deals with the stationary distribution of charged particles moving in a material medium, having scattering and absorption properties, in which a uniform electric field is present. The purpose of the work is finding analytical solutions in simplified but physically significant situations and comparing different approximations based on a spherical-harmonics expansion of the velocity distribution. Received: 28 July 1998     

Fusion reactions in plasmas as probe of the high-momentum tail of particle distributions

In fusion reactions, the Coulomb barrier selects particles from the high-momentum part of the distribution. Therefore, small variations of the high-momentum tail of the velocity distribution can produce strong effects on fusion rates. In plasmas several potential mechanisms exist that can produce deviations from the standard Maxwell-Boltzmann distribution. Quantum broadening of the energy-momentum dispersion relation of the plasma quasi-particles modifies the high-momentum tail and could explain the fusion-rate enhancement observed in low-energy nuclear reaction experiments.