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Quantization of strongly interacting phonons

V. D. Dzhunushaliev
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Abstract

The assumption is considered that the strong interaction between phonons makes a certain contribution to the formation of Cooper pairs. Heisenberg's old idea about the quantization of strong nonlinear fields using the Tamm-Dankoff method is discussed. The approximate solution method of infinite Tamm-Dankoff equations system is suggested. This allows us to obtain an equation for the fixed deformation of the lattice between two Cooper electrons. Such deformations can introduce a significant contribution to the energy of Cooper pairs. The possible approximate model of the appearance of the flux tube (nonlocal object) in the SU(2) Yang-Mills theory is considered. The similar mechanism can play important role in High-$T_c$ superconductivity if there is the strong nonlinear potential.

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V. D. Dzhunushaliev. 1998-02-10. Quantization of strongly interacting phonons. https://arxiv.org/abs/cond-mat/9704062

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