Quantum-relativistic hydrodynamic model for a spin-polarized electron gas interacting with light

Area of Science:

• Quantum fluid dynamics
• Relativistic quantum mechanics
• Plasma physics

Background:

• The Dirac Hamiltonian describes relativistic electrons.
• Quantum fluid theories simplify complex quantum systems.
• Understanding electron spin dynamics is crucial for plasma phenomena.

Purpose of the Study:

• To develop a semirelativistic quantum fluid theory.
• To investigate quantum-relativistic spin effects on Faraday rotation.
• To model dense, weakly relativistic electron plasmas.

Main Methods:

• Expanding the Dirac Hamiltonian to second order in 1/c.
• Utilizing the Madelung representation for the wave function.
• Deriving hydrodynamic equations (continuity, Euler, spin density evolution).

Main Results:

• A novel set of hydrodynamic equations was derived.
• The model captures quantum-relativistic spin effects.
• The impact on Faraday rotation in a plasma slab was analyzed.

Conclusions:

• The developed theory provides a framework for studying relativistic quantum plasmas.
• Quantum-relativistic spin effects significantly impact Faraday rotation.
• This model is applicable to phenomena like x-ray laser-plasma interactions.