Abstract
This article discusses the structure of expansions that represent non-perturbative solutions of the Cauchy problem for the evolution equation hierarchies for the state and observables of many-particle systems with topological nearest-neighbor interaction. The generating operators for these expansions are derived using a proposed cluster expansion
method applied to the groups of operators in the Liouville equations for both states and observables, respectively. The article also introduced the concept of a cumulant representation for distribution functions that describe the state of many particles with topological interactions and constructs a non-perturbative solution to the Cauchy problem for the hierarchy of nonlinear evolution equations for the cumulants of distribution functions. Furthermore, a relationship is established between the constructed solution and the series expansion structures
for reduced distribution and correlation functions.
Key words: Topological interaction, cluster expansion, cumulant expansion,
semigroup of operators, hierarchy of evolution equations.
Full Text
Article Information
| Title | Cumulant Expansions of Groups of Operators for Particle Systems with Topological Nearest-neighbor Interaction |
| Source | Methods Funct. Anal. Topology, Vol. 31 (2025), no. 1, 11-29 |
| DOI | 10.31392/MFAT-npu26_1.2025.02 |
| MathSciNet |
MR5007511 |
| Milestones | Received 15/03/2025; Revised 18/04/2025 |
| Copyright | The Author(s) 2025 (CC BY-SA) |
Authors Information
Viktor Gerasimenko
Institute of Mathematics of NAS of Ukra¨ıne, 3, Tereshchenkivs’ka Str., 01601, Kyıv-4, Ukraine
Igor Gapyak
Taras Shevchenko National University of Kyiv, Department of Mechanics and Mathematics, 2, Academician Glushkov Av., 03187, Kyiv, Ukraine
Citation Example
Viktor Gerasimenko and Igor Gapyak, Cumulant Expansions of Groups of Operators for Particle Systems with Topological Nearest-neighbor Interaction, Methods Funct. Anal. Topology 31
(2025), no. 1, 11-29.
BibTex
@article {MFAT2095,
AUTHOR = {Viktor Gerasimenko and Igor Gapyak},
TITLE = {Cumulant Expansions of Groups of Operators for Particle Systems with Topological Nearest-neighbor Interaction},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {31},
YEAR = {2025},
NUMBER = {1},
PAGES = {11-29},
ISSN = {1029-3531},
MRNUMBER = {MR5007511},
DOI = {10.31392/MFAT-npu26_1.2025.02},
URL = {https://mfat.imath.kiev.ua/article/?id=2095},
}
