强耦合下的弗洛希克极子——第二部分：能量-动量关系和有效质量
The Fröhlich Polaron at Strong Coupling -- Part II: Energy-Momentum Relation and Effective Mass
AI总结：
该研究通过证明强耦合下弗洛希克极子模型的能量-动量关系，揭示了有效质量与耦合常数的关系，证实了兰道-佩卡尔公式并展示了其发散特性。
摘要：
我们研究了在R^3中的弗洛希克极子模型，并证明了其基态能量作为总动量函数的下界。该下界在强耦合下渐近趋于精确。结合之前证明的对应上界，表明能量在连续阈值以下近似为抛物线形式，且极子的有效质量（定义为抛物线的半通径）由著名的兰道-佩卡尔公式给出。特别是，其随强耦合常数α增大而发散，发散速率约为α^4。
英文摘要：
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 $α$.
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