Abstract: The Pauli-Poisson equation is a semi-relativistic description of electrons under the influence of a given linear (strong) magnetic field and a self-consistent electric potential computed from the Poisson equation in 3 space dimensions. It is a system of two magnetic Schrödinger type equations for the two components of the spinor, coupled by the additional Stern-Gerlach term of magnetic field and spin represented by the Pauli matrices.
We introduce the equation and study its semiclassical limit towards a semi-relativistic Vlasov equation with Lorentz force coupled to the Poisson equation.
We use Wigner transform methods and a mixed state formulation, extending the work of Lions-Paul and Markowich-Mauser on the semiclassical limit of the Schrödinger-Poisson equation.
The Pauli-Poisson equation and its semiclassical limit
23.03.2022 14:30 - 15:00
Organiser:
SFB 65, DK
Location:
Zoom Meeting
Related Files
- pde_afternoon_2022-03-23.pdf 603 KB