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

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.