The Pauli-Poisson equation and its semiclassical limit

The Pauli-Poisson equation is a semi-relativistic model for charged spin-1∕2-par-ticles in a strong external magnetic field and a self-consistent electric potential computed from the Poisson equation in three space dimensions. It is a system of two magnetic Schrödinger equations for the two componen...

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Published inCommunications in partial differential equations Vol. 50; no. 1-2; pp. 130 - 161
Main Author Möller, Jakob
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 01.02.2025
Taylor & Francis Ltd
Subjects
Asymptotic Analysis
Fermions
Lorentz force
Magnetic fields
magnetic Schrödinger equation
Pauli equation
Poisson equation
Relativistic effects
Schrodinger equation
Vlasov equations
Vlasov-Poisson equation
Wigner measures
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ISSN0360-5302
1532-4133
DOI10.1080/03605302.2024.2439358

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Abstract The Pauli-Poisson equation is a semi-relativistic model for charged spin-1∕2-par-ticles in a strong external magnetic field and a self-consistent electric potential computed from the Poisson equation in three space dimensions. It is a system of two magnetic Schrödinger equations for the two components of the Pauli 2-spinor, representing the two spin states of a fermion, coupled by the additional Stern-Gerlach term representing the interaction of magnetic field and spin. We study the global well-posedness in the energy space and the semiclassical limit of the Pauli-Poisson to the magnetic Vlasov-Poisson equation with Lorentz force and the semiclassical limit of the linear Pauli equation to the magnetic Vlasov equation with Lorentz force. We use Wigner transforms and a density matrix formulation for mixed states, extending the work of P. L. Lions & T. Paul as well as P. Markowich & N.J. Mauser on the semiclassical limit of the non-relativistic Schrödinger-Poisson equation.
AbstractList The Pauli-Poisson equation is a semi-relativistic model for charged spin-1∕2-par-ticles in a strong external magnetic field and a self-consistent electric potential computed from the Poisson equation in three space dimensions. It is a system of two magnetic Schrödinger equations for the two components of the Pauli 2-spinor, representing the two spin states of a fermion, coupled by the additional Stern-Gerlach term representing the interaction of magnetic field and spin. We study the global well-posedness in the energy space and the semiclassical limit of the Pauli-Poisson to the magnetic Vlasov-Poisson equation with Lorentz force and the semiclassical limit of the linear Pauli equation to the magnetic Vlasov equation with Lorentz force. We use Wigner transforms and a density matrix formulation for mixed states, extending the work of P. L. Lions & T. Paul as well as P. Markowich & N.J. Mauser on the semiclassical limit of the non-relativistic Schrödinger-Poisson equation.
Author Möller, Jakob
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Snippet The Pauli-Poisson equation is a semi-relativistic model for charged spin-1∕2-par-ticles in a strong external magnetic field and a self-consistent electric...
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SubjectTerms Asymptotic Analysis
Fermions
Lorentz force
Magnetic fields
magnetic Schrödinger equation
Pauli equation
Poisson equation
Relativistic effects
Schrodinger equation
Vlasov equations
Vlasov-Poisson equation
Wigner measures
Title The Pauli-Poisson equation and its semiclassical limit
URI https://www.tandfonline.com/doi/abs/10.1080/03605302.2024.2439358
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