Asymptotic behavior of the ground state energy of a Fermionic Fröhlich multipolaron in the strong coupling limit

Ioannis Anapolitanos, Michael Hott

Published 2016-01-20Version 1

In this article, we investigate the asymptotic behavior of the ground state energy of the Fr\"ohlich Hamiltonian for a Fermionic multipolaron in the so-called strong coupling limit. We prove that it is given to leading order by the ground state energy of the Pekar-Tomasevich functional with Fermionic statistics, which is a much simpler model. Our main theorem is new because none of the previous results on the strong coupling limit have taken into account the Fermionic statistics and the spin of the electrons. A binding result for Fr\"ohlich multipolarons is a corollary of our main theorem combined with the binding result for multipolarons in the Pekar-Tomasevich model by the first author and Griesemer in [AG14]. Our analysis strongly relies on the work of Wellig [Well15] which in turn used and generalized methods developed by Lieb and Thomas [LT97], Frank, Lieb, Seiringer and Thomas [FLST11] and Griesemer and Wellig [GW13]. In order to take the Fermionic statistics into account, we employ a localization method given by Lieb and Loss in [LL05].