Related papers: Non-perturbative solutions of hierarchies of evolu…
The hierarchies of evolution equations of classical many-particle systems are formulated as evolution equations in functional derivatives. In particular the BBGKY hierarchy for marginal distribution functions, the dual BBGKY hierarchy for…
The article presents a method of cluster expansions for groups of operators associated with the von Neumann equations for states and the Heisenberg equations for observables, aiming to construct generating operators for nonperturbative…
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…
We investigate the initial-value problem of the non-linear Liouville hierarchy. For the general form of the interaction potential we construct an explicit solution in terms of an expansion over particle clusters whose evolution is described…
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…
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…
The Cauchy problem for the von Neumann hierarchy of nonlinear equations is investigated. One describes the evolution of all possible states of quantum many-particle systems by the correlation operators. A solution of such nonlinear…
We consider semigroups of operators for hierarchies of evolution equations of large particle systems, namely, of the dual BBGKY hierarchy for marginal observables and the BBGKY hierarchy for marginal distribution functions. We establish…
The aim of this work is to study the properties of groups of operators for evolution equations of quantum many-particle systems, namely, the von Neumann hierarchy for correlation operators, the BBGKY hierarchy for marginal density operators…
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…
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…
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,…
The paper deals with the problem of the rigorous description of the evolution of states of large particle quantum systems by means of correlation operators. A nonperturbative solution of the Cauchy problem of the hierarchy of nonlinear…
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…
We present a Hamiltonian method of constructing BBGKY-like hierarchies for quantum field theories. With suitable choices, our method creates a hierarchical system of evolution equations for the k-th order reduced density matrices. These…
In the paper we discuss possible approaches to the problem of the rigorous derivation of quantum kinetic equations from underlying many-particle dynamics. For the description of a many-particle evolution we construct solutions of the Cauchy…
A BBGKY-like hierarchy is derived from the non-equilibrium Redfield equation. Two further approximations are introduced and each can be used to truncate and solve the hierarchy. In the first approximation such a truncation is performed by…
We develop a rigorous formalism for the description of the evolution of states of quantum many-particle systems in terms of a one-particle density operator. For initial states which are specified in terms of a one-particle density operator…
We consider solutions of the Cauchy problem for semilinear equations with (possibly) different L\'evy operators. We provide various results on their convergence under the assumption that symbols of the involved operators converge to the…
We derive the BBGKY hierarchy for the Fermi and Bose many-particle systems, using the von Neumann hierarchy for the correlation operators. The solution of the Cauchy problem of the formulated hierarchy for the case of a n-body interaction…