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

Theoretical Studies of Nonlinear Relaxation Electrophysical Phenomena in Dielectrics with Ionic–Molecular Chemical Bonds in a Wide Range of Fields and Temperatures

“…Theoretical developments aimed at applying quantum kinetic theory of proton conductivity and polarization [7,[12][13][14][15][16]29,30] to questions and quantum theory of hightemperature superconductivity [43] are relevant.…”

“…Semi-empirical studies of migration of adsorbed protons on the surface of singlelayer carbonaceous nanotubes [44] are not complete, due to the lack of a strict theoretical justification: (1) the relationship between the configuration of the tube surface and the dominant physical mechanism of proton transfer (tunnel or thermally activated proton transfer through a potential barrier); (2) temperature dependence of the probability of tunnel crossings of protons; (3) the forms of potential relief and activation energy for protons. The methods of quantum kinetic theory, the foundations of which are laid by the authors [1,2], will allow, using the apparatus of the density matrix [12,13,15,16,26,27], to consider in more detail the quantum mechanism of the tunnel transfer of protons in nanoscale materials with high-proton conductivity at a stricter theoretical level.…”

“…In [3], nonlinear solutions of the semi-classical kinetic equation in complex with the Poisson equation for the model of blocking electrodes were obtained with accuracy to the cubic term (by a small parameter γ [3], pp. [13][14]. By the method of mathematical induction in the infinite approximation of the perturbation theory at the main frequency ω, the frequency harmonic of polarization P (ω) (𝑡) ( [3], p. 16) was calculated and the nonlinear frequency-temperature spectra of the CDP were constructed and studied in detail ( [1], pp.…”

“…This allows us, with a certain degree of accuracy, to judge the significant influence of the temperature range on the mechanism of the nonlinear relaxation processes when generating polarization of the dielectric in the wide range of field parameters. It is obvious that in the region of weak fields (0.1-1 MV/m) the non-linearities will appear due to low-temperature (10-50 K) polarization effects (quantum diffusion polarization), and in the region of strong fields (10-1000 MV/m) the non-linearities will appear due to high-temperature (550-1500 K) polarization effects (nonlinear bulk-charge polarization of the mixed type) [7,[12][13][14][15][16].…”

“…Another criterion of validity of formulae ( 8) and ( 25) of the nonlinear approximation of the perturbation theory investigated above is their ultimate transition to results of the linear kinetic theory of the relaxation polarization [7,[12][13][14][15][16]. To this end, we simplify the expression for the polarization (8).…”