title: Bipolaron and N-polaron binding energies.
abstract: The binding of polarons, or its absence, is an old and subtle topic. Here we prove two things rigorously. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U=2α, where U is the electronic Coulomb repulsion and α is the polaron coupling constant. Second, if U is large enough, there is no multipolaron binding of any kind. Considering the known fact that there is binding for some U>2α, these conclusions are not obvious and their proof has been an open problem for some time.
authors.affiliation: Department of Mathematics, Princeton University, Washington Road, Princeton, New Jersey 08544, USA. rlfrank@math.princeton.edu
authors.forename: Rupert L
authors.initials: RL
authors.lastname: Frank
authors.forename: Elliott H
authors.initials: EH
authors.lastname: Lieb
authors.forename: Robert
authors.initials: R
authors.lastname: Seiringer
authors.forename: Lawrence E
authors.initials: LE
authors.lastname: Thomas