First, this paper proves the existence of a minimizer for the Pekar functional including a constant magnetic field and possibly some additional local fields that are energy reducing. Second, the existence of the aforementioned minimizer is used to establish the binding of polarons in the model of Pekar-Tomasevich including external fields.

In this paper estimates on the ground state energy of Fröhlich N -polarons in electromagnetic fields in the strong coupling limit, α → ∞, are derived. It is shown that the ground state energy is given by α 2 multiplied by the minimal energy of the corresponding Pekar-Tomasevich functional for N particles, up to an error term of order α 42/23 N 3 . The potentials A, V are suitably rescaled in α. As a corollary, binding of N -polarons for strong magnetic fields for large coupling constants is established.

Abstract:We show that N = 1 supersymmetric Liouville theory can be continued to central charge c = 3/2, and that the limiting non-rational superconformal field theory can also be obtained as a limit of supersymmetric minimal models. This generalises a result known for the non-supersymmetric case. We present explicit expressions for the three-point functions of bulk fields, as well as a set of superconformal boundary states. The main technical ingredient to take the limit of minimal models consists in determining analytic expressions for the structure constants. In the appendix we show in detail how the structure constants of supersymmetric and Virasoro minimal models can be rewritten in terms of Barnes' double gamma functions.

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.

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