This article is cited in 4 papers

METHODOLOGICAL NOTES

Translation invariance and the problem of the bipolaron

V. D. Lakhno

Institute of Mathematical Problems of Biology RAS, Pushchino, Moskovskaya obl.

Abstract: Differences between translation-invariant and broken-symmetry bipolaron theories are analyzed in detail. It is shown that the Bogolyubov—Tyablikov canonical transformation allows collective coordinates to be introduced in a regular way for two particles in a quantum field and that for the case of the bipolaron the resulting electron—electron interaction in a phonon field depends on the electron coordinate difference alone. Predictions using a revised solution of the nonlinear differential equations for a bipolaron are given. It is shown that solving bipolaron equations numerically reduces the total bipolaron energies compared to known variational results.

PACS: 71.38.+i

Received: March 1, 1998

DOI: 10.3367/UFNr.0168.199804d.0465

 English version: Physics–Uspekhi, 1998, 41:4, 403–406

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