A statistical approach to description of the charge carrier transfer processes in hybrid nanostructures taking into account electromagnetic fields is proposed using the method of the nonequilibrium statistical operator Zubarev. Generalized transfer equations are obtained, which describe non-Markov processes of charge transfer in the system taking into account magnetic and polarization processes under the influence of external and induced internal electromagnetic fields. Weakly nonequilibrium charge transfer processes in nanostructures are considered, and a nonequilibrium statistical operator is obtained, by means of which the magneto-diffusion transfer equations for electrons in layered nanostructures are obtained. A generalized Cattaneo-type diffusion equation in time fractional derivatives is obtained for electrons with a characteristic relaxation time and a generalized model is proposed that takes into account the complexity of relaxation electro-magnetic diffusion processes for electrons in layered nanostructures.
- Chabecki P., Calus D., Ivashchyshyn F., Pidluzhna A., Hryhorchak O., Bordun I., Makarchuk O., Kityk A. V. Function Energy Accumulation Photo- and Magnetosensitive Hybridity in the GaSe-Based Hierarchical Structures. Energies. 13 (17), 4321 (2020).
- Grygorchak I., Calus D., Pidluzhna A., Ivashchyshyn F., Hryhorchak O., Chabecki P., Shvets R. Thermogalvanic and local field effects in SiO2<SmCl3> structure. Applied Nanoscience. 10 (12), 4725–4731 (2020).
- Klapchuk M. I., Ivashchyshyn F. O. Giant magnetoresistance effect in InSe <beta-CD<FeSO4>> clatrate. Mathematical Modeling and Computing. 7 (2), 322–333 (2020).
- Grygorchak I. I., Kostrobiy P. P., Stasyuk I. V., et al. Fizychni protsesy ta yikh mikroskopichni modeli v periodychnykh neorhanichno/orhanichnykh klatratakh. Lviv, Rastr-7 (2015), (in Ukrainian).
- Kostrobij P. P., Grygorchak I. I., Ivaschyshyn F. O., Markovych B. M., Viznovych O. V., Tokarchuk M. V. Mathematical modeling of subdiffusion impedance in multilayer nanostructures. Mathematical Modeling and Computing. 2 (2), 154–159 (2015).
- Kostrobij P., Grygorchak I., Ivashchyshyn F., Markovych B., Viznovych O., Tokarchuk M. Generalized Electrodiffusion Equation with Fractality of Space–Time: Experiment and Theory. Journal of Physical Chemistry A. 122 (16), 4099–4110 (2018).
- Kostrobij P. P., Markovych B. M., Viznovych O. V., Tokarchuk M. V. Generalized transport equation with nonlocality of space–time. Zubarev’s NSO method. Physica A: Statistical Mechanics and its Applications. 514, 63–70 (2019).
- Sibatov R. T., Uchaikin V. V. Fractional differential approach to dispersive transport in semiconductors. Physics-Uspekhi. 52 (10), 1019–1043 (2009).
- Sibatov R. T. Drobno-differencial'naja teorija anomal'noj kinetiki nositelej zarjada v neuporjadochennyh poluprovodnikovyh sistemah. Thesis for the Degree of Doctor of Sciences in Physics and mathematics. Uljanovsk (2012), (in Russian).
- Rekhviashvili S. S., Mamchuev M. O., Mamchuev M. O. Model of diffusion-drift charge carrier transport in layers with a fractal structure. Physics of the Solid State. 58 (4), 788–791 (2016).
- Rekhviashvili S. S., Alikhanov A. A. Simulation of drift-diffusion transport of charge carriers in semiconductor layers with a fractal structure in an alternating electric field. Semiconductors. 51 (6), 755–759 (2017).
- Uchaikin V. V. Fractional Derivatives Method. Uljanovsk, Artishock-Press (2008), (in Russian).
- Klafter J., Lim S. C., Metzler R. Fractional dynamics: recent advances. New Jersey, World Scientific (2012).
- Zubarev D. N. Modern methods of the statistical theory of nonequilibrium processes. Journal of Soviet Mathematics. 16 (6), 1509–1571 (1981).
- Kostrobij P. P., Tokarchuk M. V., Markovych B. M., Ihnatiuk V. V., Hnativ B. V. Reaktsiino-dyfuziini protsesy v systemakh "metal–gaz''. Lviv, Lviv Polytechnic National University (2009), (in Ukrainian).
- Kostrobij P. P., Markovych B. M., Tokarchuk M. V. Generalized diffusion equation with nonlocality of space-time. Memory function modelling. Condens. Matter Phys. 23 (2), 23003 (2020).