The Ground State Energy of the Multi-Polaron in the Strong Coupling Limit

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 $N \geq 1$.