On the ground-state wave function of the one-dimensional polaron in the strong-coupling limit

TL;DR

This paper proves that in the strong-coupling limit, the ground-state wave functions of a one-dimensional polaron model converge to the unique minimizer of the Pekar functional, confirming the model's expected behavior.

Contribution

It demonstrates the weak convergence of approximate ground-state wave functions to the Pekar minimizer in the strong-coupling limit for a one-dimensional polaron.

Findings

Weak convergence of wave functions to the Pekar minimizer

Uniqueness of the minimizer in the model

Validation of the strong-coupling limit behavior

Abstract

We consider the one-dimensional Froehlich polaron localized in a symmetric decreasing electric potential. It is known that the non-linear Pekar functional corresponding to our model admits a unique minimizer. In the strong-coupling limit, we show that any approximate ground-state wave function of our model- after integrating out its phonon modes- converges in the weak sense to this unique minimizer.