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Quantum Current Algebra Symmetry and Description of Boltzmann Type Kinetic Equations in Statistical Physics
- Source :
- Symmetry, Vol 13, Iss 1452, p 1452 (2021)
- Publication Year :
- 2021
- Publisher :
- MDPI AG, 2021.
-
Abstract
- 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.
- Subjects :
- 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
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 13
- Issue :
- 1452
- Database :
- OpenAIRE
- Journal :
- Symmetry
- Accession number :
- edsair.doi.dedup.....eac074e6a58a6f5ae7f3bd50f020e192