**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.

**Past Projects:**

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)