Coherence of the lattice polarization in large-polaron motion

Main problems of the large polaron theory are considered. We demonstrate that the problem of searching the ground stationary state of a system of coupled fields with translation-invariant Hamiltonian can have a solution of the form f(r−vt), v→0, i.e., the solution with the spontaneously broken translational symmetry. Such a state can be a ground state of a large polaron in case of strong electron-phonon coupling when the spontaneous break of the translational symmetry results from the phonon vacuum deformation by the electric field of the charge carrier. The correctness of the classical representation of the polarization field in the theory of a strongly coupled large polaron is proved on the base of the theory of the quantum-coherent states of the phonon field. The use of this representation has enabled us to show that extremely high losses of the electron energy in dielectric parts of cold cathodes occurring when the carrier velocity is lower than the threshold for the single-phonon radiation are due to coherent phonon radiation by polarons like Cherenkov effect. It is this radiation that results in the predicted Thornber and Feynman dependence of the carrier steady-state velocity on the applied electric field strength. The coherent phonon radiation generated by polaron current can be detected in experiments on the neutrons scattering. The primary directions of the neutrons scattering depend on the polarons steady-state velocity and, hence, on the applied field strength. The coherent phonon radiation stemming from supersonic thermal motion of polarons causes a giant increase of the resistance in a corresponding temperature interval.