Quantum kinetics derivation as generalization of the quantum hydrodynamics method

TL;DR

This paper introduces a generalized quantum kinetic equation derivation method extending quantum hydrodynamics, applicable to various particles including spins, dipoles, and graphene carriers, incorporating quantum correlations and self-consistent fields.

Contribution

It presents a novel derivation of quantum kinetic equations as a natural extension of quantum hydrodynamics, including spin, dipole, and graphene systems, with a focus on quantum correlations.

Findings

Derived kinetic equations for spinning particles with spin-distribution functions.

Formulated kinetic equations for particles with electric dipole moments.

Applied the method to graphene carriers near Dirac points.

Abstract

We present a new way of quantum kinetic equation derivation. This method appears as a natural generalization of the many-particle quantum hydrodynamic method. Kinetic equations are derived for different system of particles. First of all we consider quantum plasma and pay special attention to the spin evolution. We show that we need a set of two kinetic equations for description of spinning particles. One of these equations is the equation for distribution function, however this equation contains new function, even in the self-consistent field approximation. This is a spin-distribution function introduced in the paper. Therefore we have to derive kinetic equation for spin distribution function evolution, which is presented here and used to construct a closed set of kinetic equations. We also present kinetic equation for system of neutral particles with a short-range interaction in the first order by the interaction radius approximation. We derive a set of kinetic equations for particles having electric dipole moment, this set analogous to the equations set for spinning particles, but it has some differences. As a special topic we find kinetic equations for graphene carriers in the vicinity of the Dirac points. Derived equations, in general case, contain two-particle distribution functions, which take into account contribution of the quantum correlations including the exchange interaction, but we restrict ourself by the self-consistent field approximation to obtain closed kinetic description, in the system of particles with the short-range interaction.