On the dynamics of the mean-field polaron in the high-frequency limit

We consider the dynamics of the mean-field polaron in the limit of infinite phonon frequency \(\omega \rightarrow \infty \). This is a singular limit formally leading to a Schrödinger–Poisson system that is equivalent to the nonlinear Choquard equation. By establishing estimates between the approximation obtained via the Choquard equation and true solutions of the original system we show that the Choquard equation makes correct predictions about the dynamics of the polaron mean-field model for small values of \(\varepsilon = 1/\omega \).