29 citations · 176 across the 25 of their papers we have counts for
26 papers
Methods for Deriving Nonlinear Kinetic Equations from the Dynamics of Quantum Systems
V. I. Gerasimenko
The article outlines key topics related to deriving kinetic equations and, in general, to the relationship between the evolution equations governing quantum many-particle systems.…
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…
Kinetic equations and hierarchies of evolution equations of quantum systems
V. I. Gerasimenko
The article provides an overview of some advances in the mathematical understanding of the nature of the kinetic equations of quantum systems of many particles. The fundamental equ…
On Kinetic Equations for Collisional Dynamics of Active Soft Condensed Matter
V. I. Gerasimenko
We consider a new approach to the description of the collective behavior of complex systems of mathematical biology based on the evolution equations for observables of such systems…
On Dynamics of Correlations in Quantum Many-Particle Systems
V. I. Gerasimenko
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 solut…
On Semigroups of Large Particle Systems and their Scaling Asymptotic Behavior
V. I. Gerasimenko, Yu. Yu. Fedchun
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 hie…
Mean Field Asymptotic Behavior of Quantum Particles with Initial Correlations
V. I. Gerasimenko
In the paper we consider the problem of the rigorous description of the kinetic evolution in the presence of initial correlations of quantum large particle systems. One of the deve…
On Kinetic Equations Modeling Evolution of Systems in Mathematical Biology
Yu. Yu. Fedchun, V. I. Gerasimenko
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…
Approaches to Derivation of the Boltzmann Equation with Hard Sphere Collisions
V. I. Gerasimenko
In the paper the possible approaches to the rigorous derivation of the Boltzmann kinetic equation with hard sphere collisions from underlying dynamics are considered. In particular…
On the non-Markovian Enskog Equation for Granular Gases
M. S. Borovchenkova, V. I. Gerasimenko
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…
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…
Mean Field Asymptotics of Generalized Quantum Kinetic Equation
V. I. Gerasimenko, Zh. A. Tsvir
We construct the mean field asymptotics of a solution of initial-value problem of the generalized quantum kinetic equation and a sequence of explicitly defined unctionals of a solu…
Introduction to the Theory of Evolution Equations of Quantum Many-Particle Systems
V. I. Gerasimenko
In the paper we review some recent results of the theory of hierarchies of quantum evolution equations.
Quantum Kinetic Equations of Many-Particle Systems in Condensed States
V. I. Gerasimenko, Zh. A. Tsvir
This paper is devoted to the description of the evolution of states of quantum many-particle systems within the framework of a one-particle density operator, which enables to const…
Evolution Equations in Functional Derivatives of Many-Particle Systems
Yu. Yu. Fedchun, V. I. Gerasimenko
The hierarchies of evolution equations of classical many-particle systems are formulated as evolution equations in functional derivatives. In particular the BBGKY hierarchy for mar…
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…
On Evolution Equations for Marginal Correlation Operators
V. I. Gerasimenko, D. O. Polishchuk
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 correlat…
Quantum Kinetic Evolution of Marginal Observables
V. I. Gerasimenko
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 o…
Towards Rigorous Derivation of Quantum Kinetic Equations
V. I. Gerasimenko, Zh. A. Tsvir
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 whic…
Dynamics of Correlations of Bose and Fermi Particles
V. I. Gerasimenko, D. O. Polishchuk
We discuss the origin of the microscopic description of correlations in quantum many-particle systems obeying Fermi-Dirac and Bose-Einstein statistics. For correlation operators th…
From BBGKY Hierarchy to Non-Markovian Evolution Equations
V. I. Gerasimenko, V. O. Shtyk, A. G. Zagorodny
The problem of description of the evolution of the microscopic phase density and its generalizations is discussed. With this purpose, the sequence of marginal microscopic phase den…
On Evolution Equations of Quantum-Classical Systems
V. I. Gerasimenko
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behave…
Hydrodynamic Equations for Microscopic Phase Densities
V. I. Gerasimenko, V. O. Shtyk, A. G. Zagorodny
The evolution equations for the generalized microscopic phase densities are introduced. The evolution equations of average values of microscopic phase densities are derived and a s…
Quantum Kinetic Equations and Evolution of Many-Particle Systems
V. I. Gerasimenko
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…