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arXiv · 2212.14023

Almost Quartic Lower Bound for the Fr\"{o}hlich Polaron's Effective Mass via Gaussian Domination

Mark Sellke
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Abstract

We prove the Fr\"{o}hlich polaron has effective mass at least $\frac{\alpha^4}{(\log \alpha)^6}$ when the coupling strength $\alpha$ is large. This nearly matches the quartic growth rate $C_*\alpha^4$ predicted by Landau and Pekar in 1948 and complements a recent sharp upper bound of Brooks and Seiringer. Our proof works with the path integral formulation of the problem and systematically applies the Gaussian correlation inequality to exploit quasi-concavity of the interaction terms.

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Mark Sellke. 2022-12-28. Almost Quartic Lower Bound for the Fr\"{o}hlich Polaron's Effective Mass via Gaussian Domination. https://arxiv.org/abs/2212.14023

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