Current research interests
My research covers a wide area of theoretical condensed matter science and statistical physics. The properties of disordered systems are of particular interest, including the spectral properties of single-particle electronic and vibrational excitations in disordered materials and non-equilibrium phase-transitions in disordered complex networks.
Current research activities include:
Non-equilibrium phase transitions in disordered networks. Non-equilibrium phase transitions occur for catalytic chemical reactions, population dynamics and epidemics, growing surfaces and in granular flow and traffic jams. We study, in particular, the non-equilibrium phenomena such as contact process (e.g. epidemics) in disordered environments. Our research interests include the influence of disorder on the universal properties of systems at criticality. The methods used are (i) real-space renormalization-group analysis, (ii) series expansions, (iii) self-consistent mean-field and (iv) cellular-automata simulations.
Spectral properties of complex networks. The methods of quantum and statistical physics can be successfully applied to the study of general networks (e.g. Internet, collaboration networks, power grid, biological networks and many others). The spectral properties of disordered networks (fully-connected disordered graphs, random graphs, small-world and scale-free networks) are of particular interest in our research.
Vibrational excitations in disordered structures. The properties of atomic vibrational excitations (phonons) in ordered solids (crystals) are well studied. The picture is less clear in atomic systems where the order is lost, especially, in real glassy systems with topological disorder. Disorder brings a number of peculiar features to atomic vibrations, e.g. unusual behaviour in the low-frequency regime (boson peak, Ioffe-Regel crossover, zero-energy singularity, etc.), localization/delocalization second-order phase transition, peculiar low-temperature thermodynamical properties etc. We study these phenomena analytically (mean-field, multiple-scattering formalism, etc.) and numerically (molecular dynamics, normal-mode analysis, multifractal analysis).
Electronic excitations in disordered structures. We are mainly interested in comparative analysis of the single-particle electronic excitations and vibrational excitations, especially in the universal properties of critical states at the localization/delocalization threshold.
Self-consistent mean-field approaches for vibrational excitations in disordered systems
Decay properties of the single-electron density matrix in solids
Linear scaling time-propagator schemes for linear dynamical systems
Molecular dynamics simulations of glasses
Structural order in disordered systems
Electron (electron pair) self-trapping in glasses (D Sc, 1995, Moscow)
Electron transport in glasses (Ph D, 1985, Moscow)
Elementary particle propagation in scattering media (M Sc, 1979, Moscow)