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Short-scale quantum kinetic theory including spin-orbit interactions
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We present a quantum kinetic theory for spin-1/2 particles, including the spin-orbit interaction, retaining particle dispersive effects to all orders in ℏ, based on a gauge-invariant Wigner transformation. Compared to previous works, the spin-orbit interaction leads to a new term in the kinetic equation, containing both the electric and magnetic fields. Like other models with spin-orbit interactions, our model features "hidden momentum". As an example application, we calculate the dispersion relation for linear electrostatic waves in a magnetized plasma, and electromagnetic waves in a unmagnetized plasma. In the former case, we compare the Landau damping due to spin-orbit interactions to that due to the free current. We also discuss our model in relation to previously published works. 

National Category
Fusion, Plasma and Space Physics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:umu:diva-162462OAI: oai:DiVA.org:umu-162462DiVA, id: diva2:1344425
Available from: 2019-08-20 Created: 2019-08-20 Last updated: 2019-08-21
In thesis
1. Quantum Kinetic Theory for Plasmas: spin, exchange, and particle dispersive effects
Open this publication in new window or tab >>Quantum Kinetic Theory for Plasmas: spin, exchange, and particle dispersive effects
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is about developing and studying quantum mechanical models of plasmas. Quantum effects can be important at high densities, at low temperatures, and in strong electromagnetic fields, in various laboratory and astrophysical systems. The focus is on the electron spin, the intrinsic magnetic moment; exchange interactions, a purely quantum mechanical effect arising from particles being indistinguishable; and particle dispersive effects, essentially the Heisenberg uncertainty principle. The focus is on using phase-space formulations of quantum mechanics, namely Wigner and -functions. These methods allow carrying over techniques from classical plasma physics and identifying quantum as opposed to classical behavior.

Two new kinetic models including the spin are presented, one fully relativistic and to first order in ħ, and one semi-relativistic but to all orders in ħ. Among other example calculations, for the former, conservation laws for energy, momentum, and angular momentum are derived and related to “hidden momentum” and the Abraham-Minkowski dilemma. Both models are discussed in the context of the existing literature.

A kinetic model of exchange interactions, formally similar to a collision operator, is compared to a widely used fluid description based on density functional theory, for the case of electrostatic waves. The models are found to disagree significantly.

A new, non-linear, wave damping mechanism is shown to arise from particle dispersive effects. It can be interpreted as the simultaneous absorption or emission of multiple wave quanta. This multi-plasmon damping is of particular interest for highly degenerate electrons, where it can occur on time scales comparable to or shorter than that of linear Landau damping.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2019. p. 47
National Category
Fusion, Plasma and Space Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:umu:diva-162465 (URN)978-91-7855-102-6 (ISBN)
Public defence
2019-09-13, N 420, Naturvetarhuset, Umeå, 10:00 (English)
Opponent
Supervisors
Available from: 2019-08-23 Created: 2019-08-20 Last updated: 2019-08-21Bibliographically approved

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Other links

https://arxiv.org/abs/1908.05131

Authority records BETA

Ekman, RobinAl-Naseri, HaidarZamanian, JensBrodin, Gert

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