On the dynamics of the mean-field polaron in the weak-coupling limit

TL;DR

This paper investigates the behavior of the mean-field polaron in the weak-coupling limit, demonstrating that the nonlinear Choquard equation accurately predicts the system's dynamics as the electron-phonon interaction vanishes.

Contribution

It establishes rigorous estimates showing the validity of the Choquard equation as an approximation for the mean-field polaron dynamics in the weak-coupling limit.

Findings

Choquard equation accurately predicts polaron dynamics for small coupling

Established estimates linking approximate and true solutions

Validated the nonlinear equation as a reliable model in the limit

Abstract

We consider the dynamics of the mean-field polaron in the weak-coupling limit of vanishing electron-phonon interaction, $\varepsilon \to 0$. This is a singular limit formally leading to a Schr\"odinger--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 $\varepsilon > 0$.