Infinite Dimensional Mean-Field Belavkin Equation: Well-posedness and Derivation
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912501126397952 |
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| author | de Bouard, Anne Guo, Gaoyue Hérouard, Théo |
| author_facet | de Bouard, Anne Guo, Gaoyue Hérouard, Théo |
| contents | We analyze the mean-field limit of a stochastic Schr{ö}dinger equation arising in quantum optimal control and mean-field games, where N interacting particles undergo continuous indirect measurement. For the open quantum system described by Belavkin's filtering equation, we derive a mean-field approximation under minimal assumptions, extending prior results limited to bounded operators and finitedimensional settings. By establishing global well-posedness via fixed-point methods-avoiding measure-change techniques-we obtain higher regularity solutions. Furthermore, we prove rigorous convergence to the mean-field limit in an infinitedimensional framework. Our work provides the first derivation of such limits for wave functions in $L^2 (R^d)$, with implications for simulating and controlling large quantum systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite Dimensional Mean-Field Belavkin Equation: Well-posedness and Derivation de Bouard, Anne Guo, Gaoyue Hérouard, Théo Analysis of PDEs Mathematical Physics Probability We analyze the mean-field limit of a stochastic Schr{ö}dinger equation arising in quantum optimal control and mean-field games, where N interacting particles undergo continuous indirect measurement. For the open quantum system described by Belavkin's filtering equation, we derive a mean-field approximation under minimal assumptions, extending prior results limited to bounded operators and finitedimensional settings. By establishing global well-posedness via fixed-point methods-avoiding measure-change techniques-we obtain higher regularity solutions. Furthermore, we prove rigorous convergence to the mean-field limit in an infinitedimensional framework. Our work provides the first derivation of such limits for wave functions in $L^2 (R^d)$, with implications for simulating and controlling large quantum systems. |
| title | Infinite Dimensional Mean-Field Belavkin Equation: Well-posedness and Derivation |
| topic | Analysis of PDEs Mathematical Physics Probability |
| url | https://arxiv.org/abs/2507.19231 |