A Theory of Quantum Jumps
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911883057954816 |
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| author | Fröhlich, Jürg Gang, Zhou Pizzo, Alessandro |
| author_facet | Fröhlich, Jürg Gang, Zhou Pizzo, Alessandro |
| contents | Using the principles of the ETH - Approach to Quantum Mechanics we study fluorescence and the phenomenon of ``quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. In a limiting regime where the orbital motion of the atoms is neglected and the velocity of light tends to infinity we derive explicit non-linear stochastic differential equations describing the effective time evolution of states of individual atoms. These equations give rise to a measure on state-trajectories with quantum jumps which is a quantum-mechanical analogue of the Wiener measure of Brownian motion. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems from basic principles in the context of some simple models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10460 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Theory of Quantum Jumps Fröhlich, Jürg Gang, Zhou Pizzo, Alessandro Quantum Physics Mathematical Physics 81Sxx, 82C10 Using the principles of the ETH - Approach to Quantum Mechanics we study fluorescence and the phenomenon of ``quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. In a limiting regime where the orbital motion of the atoms is neglected and the velocity of light tends to infinity we derive explicit non-linear stochastic differential equations describing the effective time evolution of states of individual atoms. These equations give rise to a measure on state-trajectories with quantum jumps which is a quantum-mechanical analogue of the Wiener measure of Brownian motion. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems from basic principles in the context of some simple models. |
| title | A Theory of Quantum Jumps |
| topic | Quantum Physics Mathematical Physics 81Sxx, 82C10 |
| url | https://arxiv.org/abs/2404.10460 |