New interpretations of a physical theory significantly enrich that theory. A good example is quantum mechanics with three equivalent interpretations: Schrödinger’s interpretation based on the Schrödinger equation, Heisenberg’s interpretation based on the Heisenberg equation, and Feynman’s interpretation based on the path integral.
The idea of the project is to further expand the interpretation of the kinetic theory using the two-particle kinetic equation previously proposed by us, as well as the concepts of “quasiparticle” and “quasi-collision” based on the exact transformation of the scattering operator into a divergence form, and with the usage of the renormalization group method to transform the equations.
Two-particle collisions are the main factor in Boltzmann gas dynamics, and therefore the two-particle kinetic equation written in Boltzmann’s assumptions is structurally even simpler than the one-particle one.
The term “renormalization group” is used in physics in different senses. We will use the idea of applying the renormalization group of transformations in its original sense, as was done by Kadanov and Wilson (1982 Nobel Prize) within the Ising lattice model. Acting by analogy, we will use a group of transformations in Hilbert space, which includes distribution function smoothing, stretching, translation and rotation transformations. We will consider the transformation of the two-particle Boltzmann equation under gauge renormalization group transformations, and from that we will analyze the connection between the hydrodynamic and kinetic descriptions. We will show how the Lagrangian “liquid particles” in hydrodynamics are related to the “quasiparticles” introduced by us in the kinetic theory. We will propose the description of turbulence based on the transformed kinetic equation.
We will construct algorithms and numerically simulate the dynamics of rarefied gas using the two-particle equation. “Quasiparticles” move along smooth trajectories. By “quasi-collision” we mean the recalculation of small changes in the velocity of “quasiparticles” at a fractional time step with the exact conservation of energy and momentum for each pair of interacting “quasiparticles”.
The methods of kinetic theory are used in stellar dynamics to treat the evolution of collisional systems, i.e. groups of stars where the effect of pair interactions cannot be neglected on time scales shorter than the lifetime of the systems. These are compact star clusters in the centers of galaxies, open star clusters and inner parts of globular clusters. We plan to apply the “quasiparticle” approach to describe these systems and to compare results with those obtained within standard methods (e.g., following from the Vlasov-Landau-Fokker-Planck equation).
