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Phase-space methods for the spin dynamics in condensed matter systems.

Jérôme Hurst1, Paul-Antoine Hervieux2, Giovanni Manfredi1

  • 1Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, 67000 Strasbourg, France.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|March 22, 2017
PubMed
Summary
This summary is machine-generated.

We derived a quantum mechanical model for spin-fermions, incorporating Zeeman and spin-orbit effects. This model yields semiclassical and hydrodynamic equations for studying complex quantum dynamics.

Keywords:
Wigner quasi-probability distributionnanostructuresquantum phase spacespin and charge dynamicsultrafast phenomena

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Theoretical physics

Background:

  • Phase-space formulation of quantum mechanics provides a powerful framework for describing quantum systems.
  • Understanding quantum dynamics in systems with spin is crucial for many areas of physics.

Purpose of the Study:

  • To derive a quantum mechanical model for spin-fermions including Zeeman and spin-orbit coupling.
  • To obtain semiclassical and hydrodynamic equations from the full quantum model.

Main Methods:

  • Utilizing the phase-space formulation of quantum mechanics.
  • Coupling the Wigner equation with Maxwell equations for a self-consistent mean-field model.
  • Expanding the quantum model to first order in Planck's constant to derive Vlasov equations.
  • Taking velocity moments to obtain hydrodynamic equations.

Main Results:

  • A four-component Wigner equation for spin-fermions was derived.
  • A self-consistent mean-field model was established by coupling the Wigner and Maxwell equations.
  • Semiclassical Vlasov equations with spin effects and corresponding hydrodynamic equations were obtained.

Conclusions:

  • The derived model provides a framework for studying non-equilibrium dynamics of spin-fermions.
  • The proposed closure relation allows for a closed set of hydrodynamic equations.
  • This work contributes to theoretical and computational studies of quantum dynamics.