Spin kinetic theory - quantum kinetic theory in extended phase space

Abstract

The concept of phase space distribution functions and their evolution is used in the case of en enlarged phase space. In particular, we include the intrinsic spin of particles and present a quantum kinetic evolution equation for a scalar quasi-distribution function. In contrast to the proper Wigner transformation technique, for which we expect the corresponding quasi-distribution function to be a complex matrix, we introduce a spin projection operator for the density matrix in order to obtain the aforementioned scalar quasi-distribution function. There is a close correspondence between this projection operator and the Husimi (or Q) function used extensively in quantum optics. Such a function is based on a Gaussian smearing of a Wigner function, giving a positive definite distribution function. Thus, our approach gives a Wigner-Husimi quasi-distribution function in extended phase space, for which the reduced distribution function on the Bloch sphere is strictly positive. We also discuss the gauge issue and the fluid moment hierarchy based on such a quantum kinetic theory.

10 pages, to appear in Transport Theory and Statistical Physics, proceedings of Vlasovia III, 2009

References in corpus (12)

• Dynamics of spin 1/2 quantum plasmas
• Spin magnetohydrodynamics
• Quantum plasma effects in the classical regime
• New Quantum Limits in Plasmonic Devices
• Autoresonant control of the many-electron dynamics in nonparabolic quantum wells
• Effects of the $g$-factor in semi-classical kinetic plasma theory
• Spin solitons in magnetized pair plasmas
• Scalar quantum kinetic theory for spin-1/2 particles: mean field theory
• Nonlinear wave interactions in quantum magnetoplasmas
• Ferromagnetic behavior in magnetized plasmas
• Fluid moment hierarchy equations derived from quantum kinetic theory
• Fluid moment hierarchy equations derived from gauge invariant quantum kinetic theory

Cited by in corpus (5)

• Exchange effects in Coulomb quantum plasmas: Dispersion of waves in 2D and 3D mediums
• Balance equations in semi-relativistic quantum hydrodynamics
• Energy conserving particle-in-cell methods for relativistic Vlasov--Maxwell equations of laser-plasma interaction
• Ultrafast dynamics of a spin-polarized electron plasma with magnetic ions
• Analytical Properties of Linear Electrostatic Waves in Two-Component Quantum and Classical Plasmas