A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations
Mathematical Physics
2019-06-20 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1906.07908,
title = {A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations},
author = {Rupert L. Frank and Zhou Gang},
journal= {arXiv preprint arXiv:1906.07908},
year = {2019}
}
Comments
33 pages