Phase-space methods for the spin dynamics in condensed matter systems. (28th April 2017)

• Record Type: Journal Article
• Authors: Hurst, Jérôme; Hervieux, Paul-Antoine; Manfredi, Giovanni
• Is Part Of: Philosophical transactions. Volume 375:Number 2092(2017)
• Publication Date: 2017-04-28
• Subjects: spin and charge dynamics -- ultrafast phenomena -- nanostructures -- Wigner quasi-probability distribution -- quantum phase space; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rsta.2016.0199
• Languages: English
• ISSNs: 1364-503X

Abstract

Abstract : Using the phase-space formulation of quantum mechanics, we derive a four-component Wigner equation for a system composed of spin- fermions (typically, electrons) including the Zeeman effect and the spin–orbit coupling. This Wigner equation is coupled to the appropriate Maxwell equations to form a self-consistent mean-field model. A set of semiclassical Vlasov equations with spin effects is obtained by expanding the full quantum model to first order in the Planck constant. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. A simple closure relation is proposed to obtain a closed set of hydrodynamic equations. This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.