We develop a semirelativistic quantum fluid theory based on the expansion of the Dirac Hamiltonian to second order in 1/c. By making use of the Madelung representation of the wave function, we derive a set of hydrodynamic equations that comprises a continuity equation, an Euler equation for the mean velocity, and an evolution equation for the electron spin density. This hydrodynamic model is then applied to study the dynamics of a dense and weakly relativistic electron plasma. In particular, we investigate the impact of the quantum-relativistic spin effects on the Faraday rotation in a one-dimensional plasma slab irradiated by an x-ray laser source.
Quantum-relativistic hydrodynamic model for a spin-polarized electron gas interacting with light / Morandi, Omar; Zamanian, Jens; Manfredi, Giovanni; Hervieux, Paul-Antoine. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - STAMPA. - 90:(2014), pp. 013103-013113. [10.1103/PhysRevE.90.013103]
Quantum-relativistic hydrodynamic model for a spin-polarized electron gas interacting with light
MORANDI, OMAR;
2014
Abstract
We develop a semirelativistic quantum fluid theory based on the expansion of the Dirac Hamiltonian to second order in 1/c. By making use of the Madelung representation of the wave function, we derive a set of hydrodynamic equations that comprises a continuity equation, an Euler equation for the mean velocity, and an evolution equation for the electron spin density. This hydrodynamic model is then applied to study the dynamics of a dense and weakly relativistic electron plasma. In particular, we investigate the impact of the quantum-relativistic spin effects on the Faraday rotation in a one-dimensional plasma slab irradiated by an x-ray laser source.File | Dimensione | Formato | |
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