 09106 Marcel Griesemer, Jacob Schach Moller
 Bounds on the Minimal Energy of Translation Invariant $N$Polaron Systems
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Jul 4, 09

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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 electronelectron and the
electronphonon 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 phononmediated electronelectron attraction
overcomes the Coulomb repulsion and $E_N$ behaves like $N^{7/3}$.
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