29 citations · 56 across the 8 of their papers we have counts for
8 papers
Cumulant expansions of operator groups of quantum many-particle systems
V. I. Gerasimenko, I. V. Gapyak
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, aimin…
Advances in theory of evolution equations of many colliding particles
V. I. Gerasimenko, I. V. Gapyak
The review presents rigorous results of the theory of fundamental equations of evolution of many-particle systems with collisions and also considers their connection with nonlinear…
Non-perturbative solutions of hierarchies of evolution equations for colliding particles
V. I. Gerasimenko, I. V. Gapyak
The article deals with the challenge of the construction of solutions to hierarchies of fundamental evolution equations for many colliding particles. The method of cluster expansio…
Propagation processes of correlations of hard spheres
V. I. Gerasimenko, I. V. Gapyak
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 probab…
Dynamics of correlations in a system of hard spheres
V. I. Gerasimenko, I. V. Gapyak
The possible ways to describe the states of a system of many hard spheres are considered, in particular by means of functions describing correlations of states. It is stated an app…
The Boltzmann-Grad asymptotic behavior of collisional dynamics: a brief survey
V. I. Gerasimenko, I. V. Gapyak
The article discusses some of the latest advances in the mathematical understanding of the nature of kinetic equations that describe the collective behavior of many-particle system…
On Microscopic Origin of the Fokker - Planck Kinetic Evolution of Hard Spheres
I. V. Gapyak, V. I. Gerasimenko
The rigorous approach to the description of the kinetic evolution of a many-particle system composed of a trace hard sphere and an environment of finitely many hard spheres is deve…
On Rigorous Derivation of the Enskog Kinetic Equation
I. V. Gapyak, V. I. Gerasimenko
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…