By A. S. Davydov (auth.), Peter Leth Christiansen, Alwyn C. Scott (eds.)
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Extra resources for Davydov’s Soliton Revisited: Self-Trapping of Vibrational Energy in Protein
2 WOb n -(L/I-/)cos(ka) (b n+l+b n- 1)+(L/2 r11 W) (b n+2+b n- 2-2b n )-F(b n )= W bn • L! =Lsin(ka). 6) The result obtained here is very different from the conventional ones obtained by the continuum approximation. Namely, the spatio-time evolution 43 of the self-induced localized mode is described by the Bessel functions, and the dispersion relation for the eigenfrequency of the localized mode constitutes a frequency band, where its binding energy generally depends on the wave number of the localized mode as well.
The Hubbard model. In your approach, the electron-electron correlations enter only indirectly via the electron-phonon coupling. Could you elaborate on the justification for neglecting the direct electron-electron interaction in your Hamiltonian? Reply: I think a model that assumes only electron-electron interactions does not explain the pairing of electrons. In the Hubbard model, the energy of a pair on one site is higher than the energy of free particles. So one finds not stationary but virtual states, which decay.
N. Ermakov, The Magnetic Field Influence on a Superconduction Bisoliton Condensate: Preprint ITP-88-8E lnst. Theor. Phys. Ukr. SSR, Kiev, 1988.  A. Khurana. Superconductivity seen above the boiling point of nitrogen. Physics Today 40, no. 4,17 (1987). 21 Question by Kenkre: Solitons are, as is generally known, one-dimensional objects. HighTc superconductors, on the other hand, have 2-dimensional and 3-dimensional structure. Why does this not present problems for your theory? Is it perhaps that by bisolitons you merely mean bipolarons?