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A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations (1906.07908v1)
Published 19 Jun 2019 in math-ph, math.AP, and math.MP
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 Schr\"odinger equation with time-dependent potential are a key technical ingredient in our proof.
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