Quantum Current Algebra Symmetry and Description of Boltzmann Type Kinetic Equations in Statistical Physics
Abstract
:1. Introduction
2. Kinetic Equations: Introductory Quantum-Mechanical Example
2.1. The Quantum Many-Particle Hamiltonian and the Related Quasi-Classical Averaging
2.2. Boltzmann Equation, the Associated Momentum Problem and Related Hydrodynamic Type Particle Flow
3. The Bogolubov Generating Functional in Non-Equilibrium Statistical Mechanics and Its Wigner Quasi-Classical Representation
3.1. The Current Lie Algebra Representation
3.2. The Bogolubov’s Functional Equations in Non-Equilibrium Statistical Mechanics
4. Kinetic Boltzmann Equation in Non-Equilibrium Statistical Mechanics within Bogolubov’s Approach
4.1. Main Bogolubov Functional Equation and Its Solutions
4.2. Bogolubov–Boltzmann Kinetic Equation in the Frame of Functional Hypothesis
5. Kinetic Equations, Their Algebraic Structure and Invariant Reductions
5.1. Lie-Algebraic Setting
5.2. The Lie–Poisson–Vlasov Bracket
5.3. The Boltzmann–Vlasov Equation, Its Microscopic Exact Solutions and Functional Properties
5.4. The Invariant Reduction of the Bogolubov Distribution Functions Chain
6. Kinetic Theory of the Many-Particle Systems and Adsorption Phenomenon
6.1. Boltzmann–Bogolubov Equation, Surface Peculiarities, and Collision Integral
6.2. The Interactive Surface and Boundary Conditions
6.3. Adsorption Kinetics Equations
6.4. Kernels of the Collision Integrals and Their Structure
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Ivankiv, L.I.; Prykarpatsky, Y.A.; Samoilenko, V.H.; Prykarpatski, A.K. Quantum Current Algebra Symmetry and Description of Boltzmann Type Kinetic Equations in Statistical Physics. Symmetry 2021, 13, 1452. https://doi.org/10.3390/sym13081452
Ivankiv LI, Prykarpatsky YA, Samoilenko VH, Prykarpatski AK. Quantum Current Algebra Symmetry and Description of Boltzmann Type Kinetic Equations in Statistical Physics. Symmetry. 2021; 13(8):1452. https://doi.org/10.3390/sym13081452
Chicago/Turabian StyleIvankiv, Lev I., Yarema A. Prykarpatsky, Valeriy H. Samoilenko, and Anatolij K. Prykarpatski. 2021. "Quantum Current Algebra Symmetry and Description of Boltzmann Type Kinetic Equations in Statistical Physics" Symmetry 13, no. 8: 1452. https://doi.org/10.3390/sym13081452
APA StyleIvankiv, L. I., Prykarpatsky, Y. A., Samoilenko, V. H., & Prykarpatski, A. K. (2021). Quantum Current Algebra Symmetry and Description of Boltzmann Type Kinetic Equations in Statistical Physics. Symmetry, 13(8), 1452. https://doi.org/10.3390/sym13081452