Quantum Effects Under Migratory Polarization in Nanometer Layers of Proton Semiconductors and Dielectrics at Ultralow Temperatures

Quantum mechanism of interlayer polarization in condensed media in an alternating electric field at low and ultralow temperatures is studied. The nonstationary Liouville equation is solved jointly with the stationary Schrödinger equation and operator Poisson equation without taking into account the proton-proton and proton-phonon interaction. The nonequilibrium density matrix is calculated for an ensemble of non-interacting protons moving in a one-dimensional multi-well potential relief of rectangular shape in an alternating polarizing field. With the help of the non-stationary density matrix, anomalous effects associated with the displacement of the low-temperature maximum of the angle of tangent of dielectric loss in the layered crystals to the temperature of liquid helium are investigated. The results of quantum-mechanical calculations of the complex dielectric permittivity spectra (SCDP) can be used to study the tunneling mechanism of spontaneous polarization in ferroelectrics (KDP, DKDP).