The strong-coupling polaron in static electric and magnetic fields

Abstract

This paper is concerned with Fröhlich polarons subject to external electromagnetic fields in the limit of large electron-phonon coupling. To leading order in the coupling constant, √ α, the ground state energy is shown to be correctly given by the minimum of the Pekar functional including the electromagnetic fields, provided these fields in the Fröhlich model are scaled properly with α. As a corollary, the binding of two polarons in strong magnetic fields is obtained.

On the strong coupling limit of many-polaron systems in electromagnetic fields

“…for q ≥ 1 and the energy inequality (10). If the fields A, V are not rescaled, an analogous calculation as above proves (4), where Corollary 4.3 and Lemma 5.3 are used.…”

“…In the case N = 1 Theorem 1.1 was recently proved in [10]. The previous results without external fields are discussed further below.…”

“…The translation invariance seems to play some role in [13], however after a little modification it is not necessary for our proof to work. In the case N = 1 this issue was already noticed in [10].…”

“…They argued that in the strong coupling regime, binding for bipolarons is implied by the binding for Pekar-Tomasevich bipolarons and the fact that in the leading order for α → ∞ the Fröhlich ground state energy is exactly described by the Pekar minimal energy. By a similar reasoning, the existence of bipolarons subject to electromagnetic fields was recently derived in [10] with the help of binding of the corresponding Pekar bipolarons [9]. For binding of N -polarons, but without external fields we refer to [2,11].…”

“…Later, Lieb and Thomas [13] gave another proof using operator theoretical methods, which was the basis for subsequent generalizations, i.e. to the case of polarons subject to electromagnetic fields [10] and to the case of N -polarons without external fields [2]. Since the idea of the proof in [13] only applies to multipolarons in a neighborhood of one another, Theorem 1.1 can not simply be adapted.…”