Keldysh Institute of Applied Mathematics eBooks

Mathematical foundations of the translation-invariant bipolaron theory of superconductivity

Victor Dmitrievich Lakhno

Published Jan 1, 2021• 3 citations

Abstract

The monograph presents the theory of translation-invariant polarons and bipolarons based on the theory of squeezed vacuum wave functions. It is shown that the Tulub ansatz, which establishes a connection between the generalized Bogolyubov transformation with the unitary squeezed operator gives a solution to the spectral problem for a bipolaron. The solutions obtained are used to construct a theory of superconductivity based on the Froehlich Hamiltonian with a strong electron-phonon interaction. The role of Cooper pairs in it is played by TI bipolarons of spatially delocalized electrons with a small correlation length. The theory developed explains a large number of experiments on the thermodynamic, spectroscopic and transport characteristics of high-temperature superconductors, Josephson tunneling, angle-resolved photoemission spectroscopy, neutron scattering, etc. The book is intended for physicists and mathematicians who work in the field of the theory of condensed matter, as well as graduate students and senior students of universities.

DOI: 10.20948/mono-2021-lakhno

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A detailed consideration is given to the translation-invariant theory of Tulub polaron constructed without the use of Pekar ansatz.A fundamental result of the theory is that the value of the polaron energy is lower than that obtained on the basis of Pekar ansatz which was considered as an asymptotically exact solution in the strong coupling limit.In the case of bipolarons the theory yields the best values of the coupling energy and critical parameters of their stability.Numerous physical consequences of the existence of translation-invariant polarons and bipolarons are discussed.

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