The Fröhlich Polaron at Strong Coupling -- Part II: Energy-Momentum Relation and Effective Mass
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| Format: | Preprint |
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2022
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| _version_ | 1866915679571017728 |
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| author | Brooks, Morris Seiringer, Robert |
| author_facet | Brooks, Morris Seiringer, Robert |
| contents | We study the Fröhlich polaron model in $\mathbb{R}^3$, and prove a lower bound on its ground state energy as a function of the total momentum. The bound is asymptotically sharp at large coupling. In combination with a corresponding upper bound proved earlier, it shows that the energy is approximately parabolic below the continuum threshold, and that the polaron's effective mass (defined as the semi-latus rectum of the parabola) is given by the celebrated Landau--Pekar formula. In particular, it diverges as $α^4$ for large coupling constant $α$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_03353 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Fröhlich Polaron at Strong Coupling -- Part II: Energy-Momentum Relation and Effective Mass Brooks, Morris Seiringer, Robert Mathematical Physics We study the Fröhlich polaron model in $\mathbb{R}^3$, and prove a lower bound on its ground state energy as a function of the total momentum. The bound is asymptotically sharp at large coupling. In combination with a corresponding upper bound proved earlier, it shows that the energy is approximately parabolic below the continuum threshold, and that the polaron's effective mass (defined as the semi-latus rectum of the parabola) is given by the celebrated Landau--Pekar formula. In particular, it diverges as $α^4$ for large coupling constant $α$. |
| title | The Fröhlich Polaron at Strong Coupling -- Part II: Energy-Momentum Relation and Effective Mass |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2211.03353 |