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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.05940 |
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| _version_ | 1866916596096696320 |
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| author | Falconi, Marco Olgiati, Alessandro Rougerie, Nicolas |
| author_facet | Falconi, Marco Olgiati, Alessandro Rougerie, Nicolas |
| contents | We consider the quasi-classical limit of Nelson-type regularized polaron models describing a particle interacting with a quantized bosonic field. We break translation-invariance by adding an attractive external potential decaying at infinity, acting on the particle. In the strong coupling limit where the field behaves classically we prove that the model's energy quasi-minimizers strongly converge to ground states of the limiting Pekar-like non-linear model. This holds for arbitrarily small external attractive potentials, hence this binding is fully due to the interaction with the bosonic field. We use a new approach to the construction of quasi-classical measures to revisit energy convergence, and a localization method in a concentration-compactness type argument to obtain convergence of states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05940 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convergence of states for polaron models in the classical limit Falconi, Marco Olgiati, Alessandro Rougerie, Nicolas Analysis of PDEs Spectral Theory We consider the quasi-classical limit of Nelson-type regularized polaron models describing a particle interacting with a quantized bosonic field. We break translation-invariance by adding an attractive external potential decaying at infinity, acting on the particle. In the strong coupling limit where the field behaves classically we prove that the model's energy quasi-minimizers strongly converge to ground states of the limiting Pekar-like non-linear model. This holds for arbitrarily small external attractive potentials, hence this binding is fully due to the interaction with the bosonic field. We use a new approach to the construction of quasi-classical measures to revisit energy convergence, and a localization method in a concentration-compactness type argument to obtain convergence of states. |
| title | Convergence of states for polaron models in the classical limit |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2311.05940 |