Quantum-classical motion of charged particles interacting with scalar fields
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929351353696256 |
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| author | Farhat, Shahnaz |
| author_facet | Farhat, Shahnaz |
| contents | The goal of this article is to investigate the dynamics of semi-relativistic or non-relativistic charged particles in interaction with a scalar meson field. Our main contribution is the derivation of the classical dynamics of a particle-field system as an effective equation of the quantum microscopic Nelson model, in the classical limit where the value of the Planck constant approaches zero ($\hbar\to 0$). Thus, we prove the validity of Bohr's correspondence principle, that is to establish the transition from quantum to classical dynamics. We use a Wigner measure approach to study such transition. Then, as a consequence of this interplay between classical and quantum dynamics, we establish the global well-posedness of the classical particle-field interacting system, despite the low regularity of the related vector field, which prevents the use of a fixed point argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12702 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum-classical motion of charged particles interacting with scalar fields Farhat, Shahnaz Mathematical Physics The goal of this article is to investigate the dynamics of semi-relativistic or non-relativistic charged particles in interaction with a scalar meson field. Our main contribution is the derivation of the classical dynamics of a particle-field system as an effective equation of the quantum microscopic Nelson model, in the classical limit where the value of the Planck constant approaches zero ($\hbar\to 0$). Thus, we prove the validity of Bohr's correspondence principle, that is to establish the transition from quantum to classical dynamics. We use a Wigner measure approach to study such transition. Then, as a consequence of this interplay between classical and quantum dynamics, we establish the global well-posedness of the classical particle-field interacting system, despite the low regularity of the related vector field, which prevents the use of a fixed point argument. |
| title | Quantum-classical motion of charged particles interacting with scalar fields |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2405.12702 |