Microscopic theory and quantum kinetic equations for Bose-Einstein condensation, including discovery of the constraint-cutoff mechanism and universal scaling of the critical phenomena in phase transitions and theorem on the non-polynomial averages in statistical physics (see V.V. Kocharovsky and Vl.V. Kocharovsky, Phys. Rev. A 81, 033615 (2010); V.V. Kocharovsky, Vl.V. Kocharovsky, and M.O. Scully, Phys. Rev. Lett. 84, 2306 (2000), and references therein)
Theory of superradiance and phenomenological quantum electrodynamics of active media, including the negative-energy dissipative-instability mechanism of superradiance (see V.V. Zheleznyakov, V.V. Kocharovsky, and Vl.V.Kocharovsky, Sov. Phys. Uspekhi 32, n.10, 835-870 (1989); V.V.Kocharovsky and Vl.V.Kocharovsky, "Phenomenological quantum electrodynamics of active media and superradiance", In: Nonlinear Waves 3 (eds. A.V.Gaponov-Grekhov et al.), Springer-Verlag, Berlin, Heidelberg, 1990, pp.146-161; A.A.Belyanin, V.V.Kocharovsky, Vl.V.Kocharovsky, Phys. Lett. A 149, 258 (1990); V.V. Kocharovsky, S. Cameron, K. Lehmann, R. Lutch, R. Miles, Yu. Rostovtsev, W. Warren, G.R. Welch, and M.O. Scully, Proc. Nation. Acad. Sci. 102, 7806 (2005), Y.D. Jho, X. Wang, X. Wei, J. Kono, D.H. Reitze, A.A. Belyanin, V.V. Kocharovsky, Vl.V. Kocharovsky, and G.S. Solomon, PRL, 96, 237401, (2006) and Phys. Rev. B 81, 155314 (2010), and references therein)
Discovery of the quantum gravity field theory with the unbounded from below Hamiltonian, including suggestion of the new class of dynamical systems, characterized by the unbounded Hamiltonians, and demonstration of their highly nontrivial nonlinear dynamics with the regions of chaos, fractal structures and dramatic changes in the structural stability in the parameter space for an example of a cosmological model with a self-creation of gravity and massive scalar field of matter solely due to gravity-matter interaction (see V.V. Kocharovsky and Vl.V. Kocharovsky, Foundations of Physics 26, 243 (1996), G.B. Akguc, L. Reichl, E.V. Derishev, Vl.V. Kocharovsky and V.V. Kocharovsky, Phys. Rev. E 70, 066210 (2004), and references therein)
Discovery and theory of the converter acceleration mechanism for the origin of the ultrahigh energy cosmic rays (with the energies greater than 10^19 eV) (see E.V. Derishev, F.A. Aharonian, V.V. Kocharovsky, and Vl.V. Kocharovsky, Phys. Rev. D 68, 043003 (2003); Astrophysics and Space Science 297, 21 (2005), and references therein)
Discovery of the analytical solution for the self-consistent current structures in relativistic plasma (see V.V. Kocharovsky, Vl.V. Kocharovsky, and V.Ju. Martyanov, PRL 104, 215002 (2010) and references therein)