scholarly journals Low-Density Asymptotic Behavior of Observables of Hard Sphere Fluids

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Viktor Gerasimenko ◽  
Igor Gapyak
Keyword(s):  
Asymptotic Behavior ◽  
Hard Sphere ◽  
Particle Distribution ◽  
Scaling Limit ◽  
Bbgky Hierarchy ◽  
Boltzmann Kinetic Equation ◽  
Low Density ◽  
Nonperturbative Solution ◽  
Rigorous Description ◽  
The Cauchy Problem

The paper deals with a rigorous description of the kinetic evolution of a hard sphere system in the low-density (Boltzmann–Grad) scaling limit within the framework of marginal observables governed by the dual BBGKY (Bogolyubov–Born–Green–Kirkwood–Yvon) hierarchy. For initial states specified by means of a one-particle distribution function, the link between the Boltzmann–Grad asymptotic behavior of a nonperturbative solution of the Cauchy problem of the dual BBGKY hierarchy for marginal observables and a solution of the Boltzmann kinetic equation for hard sphere fluids is established. One of the advantages of such an approach to the derivation of the Boltzmann equation is an opportunity to describe the process of the propagation of initial correlations in scaling limits.

scholarly journals Evolution of Correlations of Many-Particle Quantum Systems in Condensed States

2018 ◽  
Author(s):  
Viktor Gerasimenko
Keyword(s):  
Evolution Equations ◽  
Bbgky Hierarchy ◽  
Quantum Systems ◽  
Nonlinear Evolution Equations ◽  
Von Neumann ◽  
Correlation Operator ◽  
Nonperturbative Solution ◽  
Rigorous Description ◽  
The Cauchy Problem ◽  
Dynamics Of Correlations

We review some new approaches to the description of the evolution of states of many-particle quantum systems by means of the correlation operators. Using the denition of marginal correlation operators within the framework of dynamics of correlations governed by the von Neumann hierarchy, we establish that a sequence of such operators is governed by the nonlinear quantum BBGKY hierarchy. The constructed nonperturbative solution of the Cauchy problem to this hierarchy of nonlinear evolution equations describes the processes of the creation and the propagation of correlations in many-particle quantum systems. Moreover, we consider the problem of the rigorous description of collective behavior of many-particle quantum systems by means of a one-particle (marginal) correlation operator that is a solution of the generalized quantum kinetic equation with initial correlations, in particular, correlations characterizing the condensed states of systems.

The relativistic Enskog equation near the vacuum in the Robertson–Walker space-time

2019 ◽  
Vol 10 (3) ◽  
pp. 273-284
Author(s):  
Fidele Lavenir Ciake Ciake ◽  
Etienne Takou
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Hard Sphere ◽  
Weighted Space ◽  
Space Time ◽  
Uniqueness Result ◽  
Enskog Equation ◽  
The Cauchy Problem

Abstract In this paper, we consider the Cauchy problem for the relativistic Enskog equation with near vacuum data for a hard sphere gas in the Robertson–Walker space-time. We prove an existence and uniqueness result of the global (in time) mild solution in a suitable weighted space. We also study the asymptotic behavior of the solution as well as the {L^{\infty}} -stability.

STATIC STRUCTURE FACTOR OF HARD-SPHERE YUKAWA SYSTEMS

1996 ◽  
Vol 10 (30) ◽  
pp. 1507-1515 ◽  
Author(s):  
JOSÉ-PEDRO RINO ◽  
NELSON STUDART
Keyword(s):  
Distribution Function ◽  
Computer Simulations ◽  
Structure Factor ◽  
Hard Sphere ◽  
Particle Distribution ◽  
Bbgky Hierarchy ◽  
Static Structure Factor ◽  
Static Structure ◽  
Theory Of Liquids ◽  
Hierarchy Equations

We have applied the Singwi, Tosi, Land and Sjölander approximation for the two-particle distribution function in the BBGKY hierarchy equations to investigate the properties of the hard-sphere Yukawa systems. The static structure factor and the radial distribution function are evaluated and compared with other approximations of the theory of liquids and computer simulations.

scholarly journals Comparison between the Cauchy problem and the scattering problem for the Landau damping in the Vlasov-HMF equation

2021 ◽  
pp. 1-24
Author(s):  
Dario Benedetto ◽  
Emanuele Caglioti ◽  
Stefano Rossi
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Scattering Problem ◽  
New Method ◽  
Landau Damping ◽  
The Cauchy Problem ◽  
The One ◽  
Perturbative Result

We analyze the analytic Landau damping problem for the Vlasov-HMF equation, by fixing the asymptotic behavior of the solution. We use a new method for this “scattering problem”, closer to the one used for the Cauchy problem. In this way we are able to compare the two results, emphasizing the different influence of the plasma echoes in the two approaches. In particular, we prove a non-perturbative result for the scattering problem.

scholarly journals Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Yu-Zhu Wang
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Hyperbolic Equation ◽  
Contraction Mapping ◽  
Dimensional Space ◽  
Contraction Mapping Principle ◽  
Nonlinear Hyperbolic Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Initial Value ◽  
The Cauchy Problem

We consider the Cauchy problem for the damped nonlinear hyperbolic equation inn-dimensional space. Under small condition on the initial value, the global existence and asymptotic behavior of the solution in the corresponding Sobolev spaces are obtained by the contraction mapping principle.

The Cauchy problem for BBGKY hierarchy of quantum kinetic equations with coulomb potential

2009 ◽  
Author(s):  
M. Brokate ◽  
M. Yu. Rasulova ◽  
A. H. Siddiqi ◽  
M. Brokate ◽  
A. K. Gupta
Keyword(s):  
Cauchy Problem ◽  
Coulomb Potential ◽  
Kinetic Equations ◽  
Bbgky Hierarchy ◽  
The Cauchy Problem
Sign in / Sign up

Export Citation Format

Share Document