The Lieb--Thomas strategy for strongly coupled fermionic multipolarons with general external fields

TL;DR

This paper extends the Lieb--Thomas approach to approximate the ground-state energy of fermionic multipolarons in strong coupling, incorporating general external fields and relaxing previous assumptions, demonstrating the method's robustness.

Contribution

It introduces a new analysis for fermionic multipolarons with general external fields, extending previous methods to more realistic and complex scenarios.

Findings

Ground-state energy approximated by Pekar-Tomasevich model in strong coupling

Method applicable to general external electric and magnetic fields

Demonstrates robustness of Lieb--Thomas strategy for complex systems

Abstract

In this article, we prove that the ground-state energy of a fermionic Fr\"ohlich multipolaron can be approximated, in the strong electron-phonon coupling limit, by the ground-state energy of a corresponding fermionic Pekar-Tomasevich multipolaron, even in the presence of external electric and magnetic fields. Our analysis builds upon Lieb and Thomas' approach \cite{liebthomas}, which was originally developed for a single polaron without external fields, and Wellig's generalization to multipolarons \cite{wellig} with (specialized) external fields. Our main new contributions are twofold. First, we take into account the fermionic statistics of the multipolaron by employing a localization method from \cite{liebloss}. Second, we relax an assumption in \cite{wellig} on the external electric and magnetic fields, which is not easily verifiable unless the fields are periodic. Instead, we allow for general fields that only ensure self-adjointness of the Fr\"ohlich Hamiltonian. In particular, our work demonstrates the robustness of the Lieb--Thomas strategy when extended to fermionic multipolarons and general external potentials.