The Landau–Pekar equations describe the dynamics of a strongly coupled polaron. Here, we provide a class of initial data for which the associated effective Hamiltonian has a uniform spectral gap for all times. For such initial data, this allows us to extend the results on the adiabatic theorem for the Landau–Pekar equations and their derivation from the Fröhlich model obtained in previous works to larger times.

中文翻译：

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Landau-Pekar方程谱隙的持久性

Landau–Pekar方程描述了强耦合极化子的动力学。在这里，我们提供了一类初始数据，其相关的有效哈密顿量始终具有均匀的光谱间隙。对于此类初始数据，这使我们能够将Landau-Pekar方程的绝热定理及其从先前工作中获得的Fröhlich模型的推导得到的结果扩展到更大的时间。