We discuss a one-dimensional version of the Landau-Pekar equations, which are a system of coupled differential equations with two different time scales. We derive an approximation on the slow time scale in the spirit of a non-linear adiabatic theorem. Dispersive estimates for solutions of the Schrodinger equation with time-dependent potential are a key technical ingredient in our proof.

中文翻译：

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一维Landau-Pekar方程的非线性绝热定理

我们讨论了 Landau-Pekar 方程的一维版本，它是具有两个不同时间尺度的耦合微分方程系统。我们本着非线性绝热定理的精神推导出慢时间尺度的近似值。具有时间相关势的薛定谔方程解的色散估计是我们证明的关键技术要素。