On the Strong Coupling Limit of Many-Polaron Systems in Electromagnetic Fields

Abstract

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

References in corpus (2)

• Geometric methods for nonlinear many-body quantum systems
• The ground state energy of the multi-polaron in the strong coupling limit