On Semigroups of Large Particle Systems and their Scaling Asymptotic Behavior
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 that the generating operators of the expansions for one-paramet...
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| description | 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 that the generating operators of the expansions for one-parametric families of operators of these hierarchies are the corresponding order cumulants (semi-invariants) of semigroups for the Liouville equations. We also apply constructed semigroups to the description of the kinetic evolution of interacting stochastic Markovian processes, modeling the microscopic evolution of soft active matter. For this purpose we consider the mean field asymptotic behavior of the semigroup generated by the dual BBGKY hierarchy for marginal observables. The constructed scaling limit is governed by the set of recurrence evolution equations, namely, by the Vlasov-type dual hierarchy. Moreover, the relationships of this hierarchy of evolution equations with the Vlasov-type kinetic equation with initial correlations are established. |
| doi_str_mv | 10.48550/arxiv.1408.1781 |
| format | Article |
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We establish that the generating operators of the expansions for one-parametric families of operators of these hierarchies are the corresponding order cumulants (semi-invariants) of semigroups for the Liouville equations. We also apply constructed semigroups to the description of the kinetic evolution of interacting stochastic Markovian processes, modeling the microscopic evolution of soft active matter. For this purpose we consider the mean field asymptotic behavior of the semigroup generated by the dual BBGKY hierarchy for marginal observables. The constructed scaling limit is governed by the set of recurrence evolution equations, namely, by the Vlasov-type dual hierarchy. 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| source | World Web Journals; arXiv.org |
| subjects | Asymptotic properties BBGKY hierarchy Distribution functions Evolution Hierarchies Kinetic equations Liouville equations Markov chains Mathematics - Mathematical Physics Operators Physics - Mathematical Physics Physics - Soft Condensed Matter Physics - Statistical Mechanics Quantum theory Scaling |
| title | On Semigroups of Large Particle Systems and their Scaling Asymptotic Behavior |
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