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

• Kinetic equations derived in terms of many-particle quantum hydrodynamic method.
• The long-range spin–spin interaction is the main mechanism of wave propagation.
• Dispersion and collisionless damping of spin waves are calculated.
• Dispersion of three- and two-dimensional spin waves is calculated.

Plasma physics gives an example of physical system of particles with the long-range interaction. At the small velocities of particles we can consider the plasmas approximately as the systems of particles with the Coulomb interaction. The Coulomb interaction is an isotropic interaction. Systems of spinning neutral particles are involved in the spin–spin interaction, which is a long-range anisotropic interparticle interaction. Therefore they can reveal more rich properties than the Coulomb plasmas. Furthermore, to study the systems of spinning particles we can develop the kinetic and hydrodynamic methods similar to the methods applying in the plasma physics. We derive the kinetic equations by a new method, which is the generalization of the many-particle quantum hydrodynamics. Obtained set of the kinetic equations is truncated, so we have a closed set of two equations. First of them is the kinetic equation for the quantum distribution function. The second equation is the equation for the spin-distribution function, which describes the spin kinetic evolution and contributes to the time evolution of the distribution function. Our method allows one to obtain equations for both the three dimensional systems of particles and the low dimensional systems. Hence we consider the spin waves in the three- and the two-dimensional systems of neutral spinning particles.