The ground state energy of the multi-polaron in the strong coupling limit

TL;DR

This paper rigorously analyzes the ground state energy of the multi-polaron system in the strong coupling limit, confirming asymptotic equivalence with the Pekar-Tomasevich energy and extending previous results to multiple particles.

Contribution

It generalizes the operator approach and applies a Feynman-Kac formula to establish the asymptotic behavior of the ground state energy for any number of particles.

Findings

Ground state energy asymptotically matches the Pekar-Tomasevich energy in the strong coupling limit.

Extended the analysis from single to multiple polarons.

Provided a rigorous lower bound confirming the asymptotic equivalence.

Abstract

We consider the Fr\"ohlich $N$-polaron Hamiltonian in the strong coupling limit and bound the ground state energy from below. In particular, our lower bound confirms that the ground state energy of the Fr\"ohlich polaron and the ground state energy of the associated Pekar-Tomasevich variational problem are asymptotically equal in the strong coupling limit. We generalize the operator approach that was used to prove a similar result in the N=1 case in Lieb and Thomas (1997) and apply a Feynman-Kac formula to obtain the same result for an arbitrary particle number $N \geq 1$.