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Scalar quantum kinetic theory for spin-1/2 particles: mean field theory
Umeå University, Faculty of Science and Technology, Department of Physics. (Ickelinjär fysik, Nonlinear Physics)
Umeå University, Faculty of Science and Technology, Department of Physics. (Ickelinjär fysik, Nonlinear Physics)
Umeå University, Faculty of Science and Technology, Department of Physics.
2010 (English)In: New Journal of Physics, ISSN 1367-2630, Vol. 12, 043019- p.Article in journal (Refereed) Published
Abstract [en]

Starting from the Pauli Hamiltonian operator, we derive 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 significant interest, such a scalar quantum kinetic equation makes the comparison with 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.

Place, publisher, year, edition, pages
IOP Publishing , 2010. Vol. 12, 043019- p.
Keyword [en]
Plasma kinetic equations
National Category
Physical Sciences
Research subject
URN: urn:nbn:se:umu:diva-33895DOI: 10.1088/1367-2630/12/4/043019ISI: 000276741700005OAI: diva2:318628
Available from: 2010-05-10 Created: 2010-05-10 Last updated: 2012-03-22Bibliographically approved
In thesis
1. Modelling of spin and other quantum effects in plasmas
Open this publication in new window or tab >>Modelling of spin and other quantum effects in plasmas
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The development of quantum mechanics during the 20th century gave rise to a completely new way of describing physics. The interpretation of quantum theory is inherently difficult: for example, many-body systems are described by a so called density matrix which has no straightforward analogue in classical theory. However, in the 30’s Wigner proposed an alternative way of describing many-body systems, using a quasi-probability distribution function. This made the connection between classical and quantum kinetic theory clearer.

This thesis is concerned with modelling of quantum effects in plasmas. The focus lies on describing plasmas containing spin-1/2 particles. For this purpose, new models, based on quantum kinetic theory, are derived. This is achieved by starting from the evolution equation for the density matrix and applying a combination of the Wigner transformation for the position degree of freedom and the Q-transformation for the spin. The properties of the resulting kinetic theory are then investigated and it is shown to satisfy basic necessary criteria such as energy conservation. The kinetic equation is then used to derive a fluid theory for spin-1/2 particles.

In this thesis the kinetic and fluid models are applied to different problems in quantum plasma physics. For example it will be shown that the quantum electrodynamic correction to the electron g-factor can give rise to a wave mode which lacks classical analogue, and that spin may affect the damping rate of Alfvén waves. The models will also be applied to nonlinear problems and it will be shown that they give rise to modifications of the so called spin ponderomotive force.

Place, publisher, year, edition, pages
Umeå: Umeå Universitet, 2012. 33 p.
National Category
Fusion, Plasma and Space Physics
urn:nbn:se:umu:diva-53320 (URN)978-91-7459-385-3 (ISBN)
Public defence
2012-04-13, Naturvetarhuset, N430, Umeå Universitet, Umeå, 10:00 (English)
Available from: 2012-03-23 Created: 2012-03-20 Last updated: 2012-03-22Bibliographically approved

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Zamanian, JensMarklund, MattiasBrodin, Gert
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