Quantum kinetics of spinning neutral particles: General theory and Spin wave dispersion

TL;DR

This paper develops a general quantum kinetic theory for neutral spinning particles with anisotropic long-range interactions, deriving equations for spin and particle distributions, and analyzes spin wave dispersion in 2D and 3D systems.

Contribution

It introduces a novel method to derive coupled kinetic equations for spinning particles, extending quantum hydrodynamics to anisotropic interactions and various dimensions.

Findings

Derived kinetic and spin-distribution equations for neutral spinning particles.

Analyzed spin wave dispersion in 2D and 3D systems.

Provided a framework for studying anisotropic long-range interactions.

Abstract

Plasma physics give an example of physical system of particles with the long range interaction. At small velocity of particles we can consider the plasma approximately as a system of particles with the Coulomb interaction. The Coulomb interaction is isotropic. Systems of spinning neutral particles have long-range anisotropic interparticle interaction. So, they can reveal more reach properties than plasma. Furthermore for studying of systems of spinning particles we can develop kinetic and hydrodynamic methods analogous to used for the plasma. We derive kinetic equations by a new method, which is the generalization of the many-particle quantum hydrodynamics. Obtained set of kinetic equations is truncated, so we have closed set of two equations. One of them is the kinetic equation for quantum distribution function. The second equation is the equation for the spin-distribution. Which describes the spin kinetic evolution and gives contribution in time evolution of the distribution function. Our method allows to obtain equations as for three dimensional system of particles and for low dimensional systems. So, we consider spin waves in three- and two dimensional systems of neutral spinning particles.