Mathematical methods of equilibrium and nonequilibrium statistical mechanics with applications to the polaron theory, physics of
systems of many interacting particles, physics of electron-phonon interaction, systems of interacting fermions kinetic theory and problems of quantum optics. Upper and lower bounds for the
ground-state energy and energy levels of quantum systems, variational methods in quantum mechanics, methods of intermediate problems in the theory of self-adjoint operators in Hilbert spaces
with apllications to low-dimensional quantum nano-systems including quantum dots. Transport properties of low-dimensional quantum nano-systems. Coherent and squeezed states theory, theory of atomic, low-dimensional and mesoscopic systems interacting with polychromatic electromagnetic fields, alternation and control of
physical properties of quantum systems by means of external fields of various nature. Dynamical systems driven by the colored noise sources, nonequilibrium phase transitions; in dynamical systems driven by the colored noise sources. General problems of quantum mechanics.
Main publications:
A. V. Soldatov, “Generalization of the Peierls-Bogolubov inequality by means of a quantum-mechanical variational principle”, Proceedings of the Bogolubov
Conference “PROBLEMS OF THEORETICAL AND MATHEMATICAL PHYSICS” (Moscow–Dubna–Kyiv, 27 September – 6 October 1999), PEPAN, 31, № 7B, JINR, Dubna, 2000, 138–144
Z. Ficek, J. Seke, A. V. Soldatov, G. Adam, “Fluorescence spectrum of a two-level atom driven by a multiple modulated field”, Phys. Rev. A, 64 (2001), 013813, 10 ñ.
A. V. Soldatov, “Method of intermediate problems in the Frohlich polaron model”, Cond. Matter. Phys., 12:4 (2009), 1–11
A. V. Soldatov, “On lower bound estimates for the energy spectrum of the Fröhlich polaron model”, Phys. of Part. and Nucl., 41:7 (2010), 1079–1082
A. V. Soldatov, “Infinitely improvable upper bounds in the theory of polarons”, Cond. Matter Phys., 13:4 (2010), 43701, 9 ñ.
