The world's leading laboratories continue intensive research into the properties of nanocomposites-materials that have unique, both physical and chemical properties that are useful in practice. Along with the discovery of new materials, new technologies are being developed and attempts are being made to create mathematical models capable of describing phenomena in hollow quantum resonators-quantum dots, lines, and other cumulative-dissipative 3D structures of nanometer dimensions. Mathematical models make it possible to develop new materials, classify their properties and discover new patterns. As a result of the study of nanocomposites, the author has discovered and classified more than 31 polarization quantum-size effects. In this paper, it is proved that only by applying the foundations of cumulative quantum mechanics (CQM) can one explain and classify all quantum-size effects discovered by the author. These quantum size effects led to the discovery of the principles of physical doping and the classification of doping into physical and chemical doping. During physical doping, the modification of the properties of the nanocomposite is carried out with the help of nano-and microstructures of foreign material, which have a high affinity for free electrons. In this case, the fractions of foreign (alloying, other) material do not penetrate into the crystal lattice. They only decorate the nano-or microcrystals of the support material in the nanocomposite. A dopant with a high affinity for free electrons is charged with a negative charge, while a doped nanocrystal is charged with a positive charge. Therefore, physical doping of nanocomposites leads to the generation of electric fields that act as catalysts for various reactions, contributes to the strengthening of nanocomposites by Coulomb compression, an increase in the luminescent properties of phosphors, an increase in conductivity up to 10 10 times, and other properties, due to quantum size effects due to local violation of electrical neutrality. The models we have developed, which are effective for explaining nano-effects, have been used by us to explain angstrom-and femto-phenomena in cumulative-dissipative structures.