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

TL;DR

This paper derives a scalar quantum kinetic equation for spin-1/2 particles from the Pauli Hamiltonian, simplifying the comparison to classical kinetic theory and enabling numerical simulations of quantum plasma phenomena.

Contribution

It introduces a scalar distribution function in extended phase space for spin-1/2 systems, replacing the Wigner two-state matrix, and discusses gauge invariance and applications.

Findings

Formulation of scalar quantum kinetic equations from the Pauli Hamiltonian

Facilitates comparison with classical kinetic theory and numerical schemes

Applicable to quantum plasma problems like laser compressed targets

Abstract

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. As such, nonlinear and dynamical quantum plasma problems are readily handled. Moreover, the issue of gauge invariance is treated. Applications (e.g. ultra-dense laser compressed targets and their diagnostics), possible extensions, and future improvements of the presented quantum statistical model are discussed.