Upper and Lower Bounds for the Intermediate-Coupling Polaron Ground-State Energy
1968; American Institute of Physics; Volume: 172; Issue: 3 Linguagem: Inglês
10.1103/physrev.172.967
ISSN1536-6065
Autores Tópico(s)Microwave Dielectric Ceramics Synthesis
ResumoUsing a variational ansatz in which pair correlations between wave vectors of virtually emitted phonons are taken into account, we have obtained better upper bounds to the polaron ground-state energy than have been available heretofore for $\ensuremath{\alpha}\ensuremath{\le}3.5$. The same variational trial functions are also used to obtain lower bounds for $\ensuremath{\alpha}\ensuremath{\le}2.5$. These lower bounds, although not completely rigorous, represent a considerable improvement over the Lieb-Yamazaki values, which are, to the author's knowledge, the only other lower bounds in the literature. The variational ansatz chosen is also suitable for practical calculations of the polaron effective mass.
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