Using the methods of quasi-classical kinetic theory, continuum electrodynamics, and non-relativistic quantum theory, we construct and study the quantum kinetic equation of proton relaxation, which, together with the Poisson operator equation describes the mechanism of diffusion tunneling transport of hydrogen ions (protons) in the potential field of a crystal lattice perturbed by a polarizing field (quantum diffusion polarization) in crystals with hydrogen bonds. Using the apparatus of the density matrix (statistical matrix), by complete quantum-mechanical averaging of the polarization operator, studies are carried out of the experimental value of the polarization of the dielectric, as a function of the parameters of the external electric field (amplitude, frequency of electromotive force) and temperature. When calculating the equilibrium density matrix for an ensemble of basic relaxers (hydrogen ions), the proton-proton and proton-phonon interactions are not taken into account, and the Hamilton operator for the phonon subsystem is assumed to be a numerical constant for a given crystal under given experimental conditions (calculated by computer method as a parameter for comparing the theory with the experiment). The influence of the phonon subsystem on the kinetics of the relaxation process is reduced to a weak spatially homogeneous force field acting on protons moving in the field of the main forces of hydrogen bonds. The Hamilton of the proton subsystem is constructed for the model of an ideal proton gas in equilibrium with the ionic subsystem of the crystal lattice, and the equilibrium statistical operator of the proton subsystem is written using the Boltzmann quantum statistics. Theoretically, the size effects are found to be manifested in shifts of the low-temperature (50–100 K) maxima of the dielectric loss angle tangent towards ultra-low temperatures (4–25 K) with a decrease in the amplitudes of the maxima by 3-4 orders of magnitude, with a reduction in the thickness of the crystal layer from 1–10 microns to 1–10 nm. The effect of anomalous displacements of low-temperature maxima, which is explained by the abnormally high quantum transparency of the potential barrier for protons (0.8-0.9) in thin films of a crystal with hydrogen bonds (1-10 nm), causes, near the temperatures of the shifted maxima of dielectric losses (4–25 K), a quasi-ferroelectric state, which is also characterized by abnormally high values of the real component of the complete dielectric permittivity (2.5–3.5millions).
Quantum-mechanical model of dielectric losses in nanometer layers of solid dielectrics with hydrogen bonds at ultra-low temperatures
