Kinetic equations and hierarchies of evolution equations of quantum systems

Publication date: 22 July 2021

Abstract: The article provides an overview of some advances in the mathematical understanding of the nature of the kinetic equations of quantum systems of many particles. The fundamental equations of modern mathematical physics are studied, in particular, the hierarchies of evolution equations of quantum systems and their asymptotic behavior described by kinetic nonlinear equations.

Mathematics Subject Classification ID

Other elementary particle theory in quantum theory (81V25) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics (82C44) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05) Nonlinear evolution equations (47J35) Boltzmann equations (35Q20) Applications of functional analysis in statistical physics (46N55)

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