标题： 波拉隆有效质量的Landau-Pekar公式的证明在强耦合下 显示英文标题

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

摘要： 我们研究强耦合 regime 中的 Fröhlich 极化子，并证明有效质量的渐近精确下界$m_{\mathrm{eff}}(\alpha)\geq \alpha^4 m_{\mathrm{LP}}-C\alpha^{4-\epsilon}$，其中$m_{\mathrm{LP}}$是一个显式常数。 与最近在 [5] 中验证的相应上界一起，我们确认了由 Spohn [25] 于 1987 年提出的关于有效质量$\underset{\alpha\rightarrow \infty}{\lim}\alpha^{-4}m_{\mathrm{eff}}(\alpha)=m_{\mathrm{LP}}$的著名 Landau-Pekar 公式 [12] 的有效性。 显示英文摘要

摘要： We study the Fr\"ohlich polaron in the regime of strong coupling and prove the asymptotically sharp lower bound on the effective mass $m_{\mathrm{eff}}(\alpha)\geq \alpha^4 m_{\mathrm{LP}}-C\alpha^{4-\epsilon}$, 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 $\underset{\alpha\rightarrow \infty}{\lim}\alpha^{-4}m_{\mathrm{eff}}(\alpha)=m_{\mathrm{LP}}$ as conjectured by Spohn [25] in 1987.