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math-ph2025
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…
math-ph2025
Cluster expansions of particle system state with topological nearest-neighbor interaction
V. I. Gerasimenko, I. V. Gapyak
The article presents the concept of a cumulant representation for distribution functions describing the states of many-particle systems with topological nearest-neighbor interactio…
math-ph2024
Towards kinetic equations of open systems of active soft matter
V. I. Gerasimenko
The chapter presents some new approaches to describing the collective behavior of complex systems of mathematical biology based on the evolution equations of observables such as op…