Bounds on the Minimal Energy of Translation Invariant $N$-Polaron Systems

Details Bounds on the Minimal Energy of Translation Invariant $N$-Polaron Systems Bounds on the Minimal Energy of Translation Invariant $N$-Polaron Systems

2009-07-04

arxiv.org/abs/0907.0752v1

Physics

Mathematical Physics

16 pages

Scientific paper

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 $\sqrt{2}\alpha U$ the phonon-mediated electron-electron attraction overcomes the Coulomb repulsion and $E_N$ behaves like $-N^{7/3}$.

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