Related papers: On Evolution Equations for Marginal Correlation Op…
A statistical approach to a self-consistent description of kinetic and hydrodynamic processes in systems of interacting particles is formulated on the basis of the nonequilibrium statistical operator method by D.N.Zubarev. It is shown how…
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…
Theoretical methods based on the density matrix are powerful tools to describe open quantum systems. However, such methods are complicated and intricate to be used analytically. Here we present an object-oriented framework for constructing…
We develop a rigorous formalism for the description of the kinetic evolution of interacting entities modeling systems in mathematical biology within the framework of the evolution of marginal observables. For this purpose we construct the…
We derived state probability equations describing the queue M(t)|M[k, B]|1 and formulated as an abstract Cauchy problem to investigate by means of the semi-group theory of bounded linear operators in functional analysis. For the abstract…
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 many-particle systems with the dissipative interaction. The relationships of the evolution of a hard sphere system with inelastic collisions described within…
The Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy provides a time-reversal-symmetric framework for describing the nonequilibrium evolution of many-body systems. Despite the success of Boltzmann-based numerical approaches,…
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. We construct the multiscale representation for hierarchy of reduced distribution functions in the…
This paper develops a non-asymptotic approach to mean field approximations for systems of $n$ diffusive particles interacting pairwise. The interaction strengths are not identical, making the particle system non-exchangeable. The marginal…
We construct a regularized cumulant (semi-invariant) representation of a solution of the initial value problem for the BBGKY hierarchy for a one-dimensional infinite system of hard spheres interacting via a short-range potential. An…
We introduce a well-defined and unbiased measure of the strength of correlations in quantum many-particle systems which is based on the relative von Neumann entropy computed from the density operator of correlated and uncorrelated states.…
A chain of kinetic equations for non-equilibrium one-particle, two-particle and $ s $-particle distribution functions of particles which take into account nonlinear hydrodynamic fluctuations is proposed. The method of Zubarev…
The derivation of the Nordheim-Boltzmann transport equation for weakly interacting quantum fluids is a longstanding problem in mathematical physics. Inspired by the method developed to handle classical dilute gases, a conventional approach…
We present a family of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be applied. We…
In this paper, we prove that in macroscopic times of order one, the solutions to the truncated BBGKY hierarchy (to second order) converge in the weak coupling limit to the solution of the nonlinear spatially homogeneous Landau equation. The…
We study the growth of correlations in systems with weak long-range interactions. Starting from the BBGKY hierarchy, we determine the evolution of the two-body correlation function by using an expansion of the solutions of the hierarchy in…
The paper develops an approach to the description of the evolution of correlations for many hard spheres based on a hierarchy of evolution equations for the cumulants of the probability distribution function governed by the Liouville…
Time-resolved measurement techniques are opening a window on nonequilibrium quantum phenomena that is radically different from the traditional picture in the frequency domain. The simulation and interpretation of nonequilibrium dynamics is…