论文标题
FröhlichPolaron的有效质量通过高斯统治几乎是四分之一的下限
Almost Quartic Lower Bound for the Fröhlich Polaron's Effective Mass via Gaussian Domination
论文作者
论文摘要
我们证明，当耦合强度$α$很大时，FröhlichPolaron的有效质量至少$ \ frac {α^4} {（\logα）^6} $很大。这几乎与1948年Landau和Pekar预测的四分之一的增长率$ C_*α^4 $相匹配，并补充了最近的Brooks和Seiringer的敏锐上限。我们的证明与问题的路径积分配方合作，并系统地应用高斯相关性不等式来利用相互作用项的准杂种。
We prove the Fröhlich polaron has effective mass at least $\frac{α^4}{(\log α)^6}$ when the coupling strength $α$ is large. This nearly matches the quartic growth rate $C_*α^4$ 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.
