Scalar quantum kinetic theory for spin-1/2 particles: mean field theory

Understand

Starting from the Pauli Hamiltonian operator, we derive a scalar quantum kinetic equations for spin-1/2 systems.

• Here the regular Wigner two-state matrix is replaced by a scalar distribution function in extended phase space.
• Apart from being a formulation of principal interest, such scalar quantum kinetic equation makes the comparison to classical kinetic theory straightforward, and lends itself naturally to currently available numerical Vlasov and Boltzmann schemes.
• Moreover, while the quasi-distribution is a Wigner function in regular phase space, it is given by a Q-function in spin space.