The Maxwell-Pauli equations

Mathematical physics;The analysis of partial differential equations

Kieffer, Thomas Forrest ; Loss, Michael Mathematics Kennedy, Brian Harrell, Evans Bonetto, Federico Zeng, Chongchun ; Loss, Michael

University:Georgia Institute of Technology

Department:Mathematics

关键词: Mathematical physics;    The analysis of partial differential equations;   

Others  :  https://smartech.gatech.edu/bitstream/1853/62787/1/KIEFFER-DISSERTATION-2020.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

We study the quantum mechanical many-body problem of N ≥ 1 non-relativistic electrons with spin interacting with their self-generated classical electromagnetic field and K ≥ 0 static nuclei. We model the dynamics of the electronsand their self-generated electromagnetic field using the so-called many-body Maxwell-Pauli equations. The main result of this thesis is to construct timeglobal, finite-energy, weak solutions to the many-body Maxwell-Pauli equations under the assumption that the fine structure constant α and the nuclear charges are not too large. The assumptions on the size of α and the nuclear charges ensure that we have energetic stability for this system, i.e., the absolute ground state energy exists. The work in this thesis serves as an initial step towards understanding the connection between the energetic stability of matter in quantum mechanics and the well-posedness of the corresponding dynamical equations.