Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866909194039328768 |
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| author | Falconi, Marco Leopold, Nikolai Mitrouskas, David Petrat, Sören |
| author_facet | Falconi, Marco Leopold, Nikolai Mitrouskas, David Petrat, Sören |
| contents | We study the time evolution of the Nelson model in a mean-field limit in which N non-relativistic bosons weakly couple (w.r.t. the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body wave function in norm, with a convergence rate proportional to the number of corrections taken into account in the approximation. We prove an analogous result for the unitary propagator. As an application, we derive a simple system of PDEs describing the time evolution of the first- and second-order approximation to the one-particle reduced density matrices of the particles and the quantum field, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_00458 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model Falconi, Marco Leopold, Nikolai Mitrouskas, David Petrat, Sören Mathematical Physics Analysis of PDEs 35Q40, 35Q55, 81Q05, 81T10, 81V73, 82C10 We study the time evolution of the Nelson model in a mean-field limit in which N non-relativistic bosons weakly couple (w.r.t. the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body wave function in norm, with a convergence rate proportional to the number of corrections taken into account in the approximation. We prove an analogous result for the unitary propagator. As an application, we derive a simple system of PDEs describing the time evolution of the first- and second-order approximation to the one-particle reduced density matrices of the particles and the quantum field, respectively. |
| title | Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model |
| topic | Mathematical Physics Analysis of PDEs 35Q40, 35Q55, 81Q05, 81T10, 81V73, 82C10 |
| url | https://arxiv.org/abs/2110.00458 |