supplementary from Phase-space methods for the spin dynamics in condensed matter systems
Jérôme Hurst
Paul-Antoine Hervieux
Giovanni Manfredi
10.6084/m9.figshare.4630090.v2
https://rs.figshare.com/articles/supplementary_from_Phase-space_methods_for_the_spin_dynamics_in_condensed_matter_systems/4630090
Using the phase-space formulation of quantum mechanics, we derive a four-component Wigner equation for a system composed of spin-½ fermions (typically, electrons) including the Zeeman effect and the spin–orbit coupling. This Wigner equation is coupled to the appropriate Maxwell equations to form a self-consistent mean-field model. A set of semiclassical Vlasov equations with spin effects is obtained by expanding the full quantum model to first order in the Planck constant. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. A simple closure relation is proposed to obtain a closed set of hydrodynamic equations.
2017-02-22 06:10:21
spin and charge dynamics
ultrafast phenomena
nanostructures
Wigner quasi-probabilitydistribution
quantum phase space