Quantum Current Algebra Symmetry and Description of Boltzmann Type Kinetic Equations in Statistical Physics
| Autor: | Yarema A. Prykarpatsky, Anatolij K. Prykarpatski, Valeriy H. Samoilenko, Lev I. Ivankiv |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
Physics and Astronomy (miscellaneous) Dynamical systems theory General Mathematics functional equations Current algebra multi-particle distribution function kinetic equations Bogolubov chain Symmetry (physics) Hamiltonian system Correlation function (statistical mechanics) symbols.namesake Distribution function Chemistry (miscellaneous) Boltzmann constant Computer Science (miscellaneous) symbols current algebra QA1-939 Invariant (mathematics) Wigner representation Mathematics Mathematical physics |
| Zdroj: | Symmetry, Vol 13, Iss 1452, p 1452 (2021) |
| ISSN: | 2073-8994 |
| Popis: | We review a non-relativistic current algebra symmetry approach to constructing the Bogolubov generating functional of many-particle distribution functions and apply it to description of invariantly reduced Hamiltonian systems of the Boltzmann type kinetic equations, related to naturally imposed constraints on many-particle correlation functions. As an interesting example of deriving Vlasov type kinetic equations, we considered a quantum-mechanical model of spinless particles with delta-type interaction, having applications for describing so called Benney-type hydrodynamical praticle flows. We also review new results on a special class of dynamical systems of Boltzmann–Bogolubov and Boltzmann–Vlasov type on infinite dimensional functional manifolds modeling kinetic processes in many-particle media. Based on algebraic properties of the canonical quantum symmetry current algebra and its functional representations, we succeeded in dual analysis of the infinite Bogolubov hierarchy of many-particle distribution functions and their Hamiltonian structure. Moreover, we proposed a new approach to invariant reduction of the Bogolubov hierarchy on a suitably chosen correlation function constraint and deduction of the related modified Boltzmann–Bogolubov kinetic equations on a finite set of multi-particle distribution functions. There are also presented results of application of devised methods to describing kinetic properties of a many-particle system with an adsorbent surface, in particular, the corresponding kinetic equation for the occupation density distribution function is derived. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|