Proof of the Landau-Pekar Formula for the effective Mass of the Polaron at strong coupling

Abstract

We study the Fröhlich polaron in the regime of strong coupling and prove the asymptotically sharp lower bound on the effective mass $m_{\mathrm{eff}}(\alpha )\ge {\alpha }^4{m}_{\mathrm{LP}}-C{\alpha }^{4-\epsilon }$, where $m_{\mathrm{LP}}$ is an explicit constant. Together with the corresponding upper bound, which has been verified recently in [5], we confirm the validity of the celebrated Landau-Pekar formula [12] from 1948 for the effective mass $\underset{\alpha \to \infty }{\lim }{\alpha }^{-4}{m}_{\mathrm{eff}}(\alpha )=m_{\mathrm{LP}}$ as conjectured by Spohn [25] in 1987.