Marcel Griesemer, Jacob Schach Moller
Bounds on the Minimal Energy of Translation Invariant $N$-Polaron Systems
(301K, pdf)

ABSTRACT.  For systems of $N$ charged fermions (e.g. electrons) interacting with 
longitudinal optical quantized lattice vibrations of a polar 
crystal we derive upper and lower bounds on the minimal 
energy within the model of H.~Fr\"ohlich. The only parameters of 
this model, after removing the 
ultraviolet cutoff, are the constants $U>0$ and $\alpha>0$ measuring the electron-electron and the 
electron-phonon coupling strengths. They are constrained by the 
condition $\sqrt{2}\alpha<U$, which follows from 
the dependence of $U$ and $\alpha$ on electrical properties of the 
crystal. We show that the large $N$ asymptotic behavior of the minimal 
energy $E_N$ changes at $\sqrt{2}\alpha=U$ and that 
$\sqrt{2}\alpha\leq U$ is necessary for thermodynamic stability: for $\sqrt{2}\alpha > U$ the phonon-mediated electron-electron attraction 
overcomes the Coulomb repulsion and $E_N$ behaves like $-N^{7/3}$.