Quantum current algebra symmetry and description of Boltzmann type kinetic equations in statistical physics / Lev I. Ivankiv, Yarema A. Prykarpatsky, Valeriy H. Samoilenko, Anatolij K. Prykarpatski // ... więcej

Quantum current algebra symmetry and description of Boltzmann type kinetic equations in statistical physics / Lev I. Ivankiv, Yarema A. Prykarpatsky, Valeriy H. Samoilenko, Anatolij K. Prykarpatski // Symmetry [Dokument elektroniczny]. – 2021, Vol. 13, Iss. 8, Spec. Iss., 35 s. – Tryb dostępu: https://www.mdpi.com/2073-8994/13/8/1452/htm. – Oznaczenie ref./art.: 1452. – Bibliogr. 59 poz., Abstr. – Special Issue: Symmetry with Quantum Statistical Field Theory. – doi: 10.3390/sym13081452. – ISSN 2073-8994

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 ... więcej

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.