## 1 Introduction
### Basic Principles of Quasi-Classical Model of Ion Relaxation Polarization
\begin{array}{l}W^{(l)}(\mathrm{T})=\frac{\mathrm{v}_{0}}{2}\left(\mathbf{ exp}(-\mathbf{X}(\mathrm{T}))+\mathbf{D}^{(l)}(\mathrm{T})\right)\text{, }\mathbf{D}^{(l)}(\mathrm{T})=\frac{\left(\frac{\mathbf{\Lambda}}{\mathbf{X}(\mathrm{ T})}\right)^{l}\mathbf{exp}\left(-\mathbf{\Lambda}\right)-\mathbf{exp}\left(-\mathbf{X}( \mathrm{T})\right)}{1-\frac{\mathbf{\Lambda}}{\mathbf{\Lambda}(\mathrm{T})}},\end{array}  \tag{10}\]  
\[ \begin{array}{l}\text{where }\mathbf{X}(\mathrm{T})=\frac{\mathrm{U}_{0}}{\mathrm{k}_{ \mathrm{B}}\mathrm{T}}\text{, }\Lambda=\frac{\pi\mathrm{s}_{0}\sqrt{\mathrm{m}\mathrm{U}_{0}}}{\hbar\sqrt{2} }\text{. The equation }\frac{\mathbf{\Lambda}}{\mathbf{\Lambda}}=\frac{\mathbf{\eta}(\mathbf{x};\mathbf{t})}{ \zeta(\mathbf{x};\mathbf{t})}\text{ holds.}\\ \text{Let us represent (\ref{eq:D}) in the following form:}\\ \end{array} \]  
\[ \begin{array}{l}W^{(l)}(\mathrm{T})=W^{(l)}_{therm,\;active}(\mathrm{T})+W^{( l)}_{quant,tunn}(\mathrm{T}),\end{array} \] (10a) where \(W^{(l)}_{therm,active}(\mathrm{T})=\frac{\mathrm{v}_{0}}{2}\exp(-\mathbf{X}( \mathrm{T}))\), \(W^{(l)}_{quant,tunn}(\mathrm{T})=\frac{\mathrm{v}_{0}}{2}D^{(l)}(\mathrm{T})\). On the basis of (10), at \(l=0\),  
\[ \begin{array}{l}W^{(0)}(\mathrm{T})=\frac{\mathrm{v}_{0}}{2}\left(\frac{\exp \left(-\Lambda\right)-\frac{\Lambda}{\mathrm{X}(\mathrm{T})}\exp\left(-\mathbf{X} (\mathrm{T})\right)}{1-\frac{\Lambda}{\mathrm{X}(\mathrm{T})}}\right),\end{array}  \tag{10b}\]  
and, at \(l\geq 1\),  
\[\begin{array}{l}W^{(l)}(\mathrm{T})=\frac{\mathrm{v}_{0}}{2}\times\frac{ \Lambda}{\mathrm{X}(\mathrm{T})}\left(\frac{\left(\frac{\Lambda}{\mathrm{X}( \mathrm{T})}\right)^{l-1}\exp\left(-\Lambda\right)-\exp\left(-\mathbf{X}(Expressions for kinetic coefficients in the form of (4) and (6) are suitable for constructing the quasi-classical kinetic equation of dielectric relaxation in a mathematical model in which the electric field strength and concentration of relaxers (particles) are continuous functions of \(\mathrm{E_{i}(x;t)}\) and \(n_{\mathrm{i}}(x;t)\), spatial variables interpretable at a plurality of points near the equilibrium positions of the relaxer in individual potential wells \(\mathrm{x_{i}}\) (a coordinate of the equilibrium position of the particle at its undisturbed (stationary) oscillations in the i-th potential well). For the model of a one-dimensional continuous crystal lattice, the above lattice expansion is performed for the functions \(\mathrm{E_{i\pm 1}(x;t)}\) and \(n_{\mathrm{i\pm 1}(x;t)}\) describing relaxation phenomena in symmetric potential wells of a certain order number \(\mathrm{i\pm 1}\), interpreted as decompositions via derivatives of functions of a fixed order \(\mathrm{i}\): \(\mathrm{E_{i}(x;t)}\), \(n_{\mathrm{i}}(x;t)\). This mathematical technique is fully consistent with the symmetric properties of the crystalline potential, including its external perturbations, when the probability rates of microscopic actions of the relaxer transfer from a fixed potential well number \(\mathrm{i}\) to neighboring potential wells with numbers \(\mathrm{i\pm 1}\) (in the adopted model, the sign \"-\" corresponds to the movement of a positively charged particle in the direction of the electric field (with the field), and the sign \"+\" corresponds to the movement against the field) are subject to the generalized statistical law reflected in expressions (2), (4) and (6). According to this law, the kinetic processes associated with one-act transitions of relaxers between neighboring potential wells can be described by expressions that are equivalent in structure and symmetrical in the directions of movement of particles in the outer field, making it possible to construct a field that is symmetrical in its directions (regardless of the type of field, constant, or variable). At the same time, this quasi-classical non-linear kinetic equation's statistical properties will significantly depend on the parameters of external perturbation (amplitude and the frequency of the variable field) and temperature.