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arXiv · 1906.07908

A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations

Rupert L. Frank·Zhou Gang
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Abstract

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 Schrödinger equation with time-dependent potential are a key technical ingredient in our proof.

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Rupert L. Frank, Zhou Gang. 2019-06-19. A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations. https://arxiv.org/abs/1906.07908

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