Related papers: On Regularized Solution for BBGKY Hierarchy of One…
We develop a rigorous formalism for the description of the evolution of observables in quantum systems of particles. We construct a solution of the initial-value problem to the quantum dual BBGKY hierarchy of equations as an expansion over…
A new direct integration method is established to construct the solutions of the stationary BBGKY hierarchy, assuming the usual form of the equilibrium correlation functions, for infinite classical systems of particles interacting via a…
We develop a rigorous formalism for the description of the kinetic evolution of infinitely many hard spheres. On the basis of the kinetic cluster expansions of cumulants of groups of operators of finitely many hard spheres the nonlinear…
On the basis of the sequence of marginal observables the evolution equations of the microscopic phase density and its generalizations is discussed. We introduced dual BBGKY hierarchy for these microscopic observables and their average…
In classical kinetic theory, the BBGKY hierarchy is an infinite chain of integro-differential equations that describes the full time-reversal-invariant (Liouville) system of interacting (quasi)-particles in terms of $N$-particle…
The aim of this work is to study the existence of mean values of observables for infinite-particle systems. Using solutions of the initial value problems to the BBGKY hierarchy and to its dual, we prove the local, in time, existence of the…
A fast and efficient numerical-analytical approach is proposed for modeling complex behaviour in the BBGKY hierarchy of kinetic equations. We construct the multiscale representation for hierarchy of reduced distribution functions in the…
A solution to the BBGKY hierarchy for nonequilibrium distribution functions is obtained within modified boundary conditions. The boundary conditions take into account explicitly both the nonequilibrium one-particle distribution function as…
This paper is devoted to the problem of the description of nonequilibrium correlations in quantum many-particle systems. The nonlinear quantum BBGKY hierarchy for marginal correlation operators is rigorously derived from the von Neumann…
We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics of a solution of the initial-value problem of the dual…
We establish a theoretical framework for exploring the quantum dynamics of finite ultracold bosonic ensembles based on the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations of motion for few-particle reduced density…
A fast and efficient numerical-analytical approach is proposed for modeling complex behaviour in the BBGKY--hierarchy of kinetic equations. Our calculations are based on variational and multiresolution approaches in the basis of polynomial…
We prove that the evolution of marginals associated to the empirical measure of a finite system of hard spheres is driven by the BBGKY hierarchical expansion. The usual hierarchy of equations for $L^1$ measures is obtained as a corollary.…
The present article proposes a rigorous derivation of the Boltzmann equation in the half-space. We show an analog of the Lanford's theorem in this domain, with specular reflection boundary condition, stating the convergence in the low…
We complete the existing literature on the kinetic theory of systems with long-range interactions. Starting from the BBGKY hierarchy, or using projection operator technics or a quasilinear theory, a general kinetic equation can be derived…
We consider the motion of interacting particles governed by a coupled system of ODEs with random initial conditions. Direct computations for such systems are prohibitively expensive due to a very large number of particles and randomness…
For elliptic systems with block structure in the upper half-space and t-independent coefficients, we settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal…
We present a derivation of the kinetic equation describing the secular evolution of spatially inhomogeneous systems with long-range interactions, the so-called inhomogeneous Landau equation, by relying on a functional integral formalism. We…
The kinetic theory description of a low density gas of hard spheres or disks, confined between two parallel plates separated a distance smaller than twice the diameter of the particles, is addressed starting from the Liouville equation of…
The article presents the concept of a cumulant representation for distribution functions describing the states of many-particle systems with topological nearest-neighbor interaction. A solution to the Cauchy problem for the hierarchy of…