A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations
classification
🧮 math-ph
math.APmath.MP
keywords
equationsadiabaticlandau-pekarnon-linearone-dimensionaltheoremtimeapproximation
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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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