Effective Mass of the Fröhlich Polaron and the Landau-Pekar-Spohn Conjecture
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916830398906368 |
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| author | Bazaes, Rodrigo Mukherjee, Chiranjib Sellke, Mark Varadhan, S. R. S. |
| author_facet | Bazaes, Rodrigo Mukherjee, Chiranjib Sellke, Mark Varadhan, S. R. S. |
| contents | We prove that there is a constant $\overline C\in (0,\infty)$ such that the effective mass $m(α)$ of the Fröhlich Polaron satisfies $m(α) \geq \overline C α^4$, which is sharp according to a long-standing prediction of Landau-Pekar [19] from 1948 and of Spohn [36] from 1987.
The method of proof, which demonstrates how the sharp quartic divergence rate of $m(α)$ appears in a natural way, is based on analyzing the Gaussian representation of the Polaron measure and that of the associated tilted Poisson point process developed in [26]. Additionally, our technique here leads to accompanying results including, 1) an explicit identification of local interval process from [26] in the strong coupling limit in terms of functionals of the Pekar process [27], 2) strict monotonicity of the effective mass $m(α)$ for all $α>0$ and 3) the quartic divergence of $m(α)$ for a generalized class of Polaron type interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13058 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Effective Mass of the Fröhlich Polaron and the Landau-Pekar-Spohn Conjecture Bazaes, Rodrigo Mukherjee, Chiranjib Sellke, Mark Varadhan, S. R. S. Mathematical Physics Probability We prove that there is a constant $\overline C\in (0,\infty)$ such that the effective mass $m(α)$ of the Fröhlich Polaron satisfies $m(α) \geq \overline C α^4$, which is sharp according to a long-standing prediction of Landau-Pekar [19] from 1948 and of Spohn [36] from 1987. The method of proof, which demonstrates how the sharp quartic divergence rate of $m(α)$ appears in a natural way, is based on analyzing the Gaussian representation of the Polaron measure and that of the associated tilted Poisson point process developed in [26]. Additionally, our technique here leads to accompanying results including, 1) an explicit identification of local interval process from [26] in the strong coupling limit in terms of functionals of the Pekar process [27], 2) strict monotonicity of the effective mass $m(α)$ for all $α>0$ and 3) the quartic divergence of $m(α)$ for a generalized class of Polaron type interactions. |
| title | Effective Mass of the Fröhlich Polaron and the Landau-Pekar-Spohn Conjecture |
| topic | Mathematical Physics Probability |
| url | https://arxiv.org/abs/2307.13058 |