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

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

2009-10-27

arxiv.org/abs/0910.5165v1

New J. Phys. 12 043019 (2010)

Physics

Condensed Matter

Quantum Gases

21 pages, 2 figures

Scientific paper

10.1088/1367-2630/12/4/043019

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.

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