Breakdown of perturbation theory for the deformation potential polaron

Abstract

By comparing variational forms of weak and strong coupling we show that the crossover point is near $\ensuremath{\alpha}K\ensuremath{\approx}1$, where $\ensuremath{\alpha}$ is the coupling constant and $K$ is the largest allowed (dimensionless) wave vector. Analysis of the perturbation series gives a leading term of the form ${K}^{2}\ensuremath{\Sigma}{b}_{n}{\ensuremath{\alpha}}^{n}$, which contains no indication that when $\ensuremath{\alpha}K>1$ the ground state is better described by strong coupling. It is suggested that when $\ensuremath{\alpha}K>1$ the perturbation series approximates a metastable state of the system.