On the Strong Coupling Limit of Many-Polaron Systems in Electromagnetic Fields

TL;DR

This paper analyzes the ground state energy of many-polaron systems in electromagnetic fields under strong coupling, showing it scales with the Pekar-Tomasevich functional and establishing polaron binding in strong magnetic fields.

Contribution

It provides the first rigorous estimate of the ground state energy for many-polarons in electromagnetic fields in the strong coupling limit, linking it to a classical functional and demonstrating binding.

Findings

Ground state energy scales as  times the minimal Pekar-Tomasevich energy.

Binding of N-polarons occurs in strong magnetic fields at large coupling.

Error term in energy estimate is of order 2/23.

Abstract

In this paper estimates on the ground state energy of Fr\"ohlich $N$-polarons in electromagnetic fields in the strong coupling limit, $\alpha\to\infty$, are derived. It is shown that the ground state energy is given by $\alpha^2$ multiplied by the minimal energy of the corresponding Pekar-Tomasevich functional for $N$ particles, up to an error term of order $\alpha^{42/23}N^3$. The potentials $A,V$ are suitably rescaled in $\alpha$. As a corollary, binding of $N$-polarons for strong magnetic fields for large coupling constants is established.