My research focuses on the following aspects of theoretical condensed matter physics
Brief description of my research activities 

I specialize in theoretical condensed matter physics.  I have been  developing novel theoretical techniques to describe front-line experiments in quantum electronics and related fields. My primary interest is understanding the kinetics of out-of-equilibrium quantum systems. In such systems, the electron behavior is determined not only by the low-energy electron quantum states, but also by various relaxation mechanisms, which usually originate from the many-particle interaction of electrons with each other or with phonons. Kinetic theory on which I focus analyzes the current experiments and paves the way for further development of quantum electronics.  Examples of quantum electron systems are semiconducting quantum dots, ultra-small metal grains and wires, and two-dimensional electron heterostructures.

Kinetics of quantum systems is a fast growing field, which is important for understanding and characterization of electron properties of new materials and for development of nanoscale electronics.  The latter promises  such fundamental breakthroughs as a realization of solid state devices for quantum information technologies.

In collaboration with other researchers, I have succeeded  in presenting  an analytical description of several puzzling phenomena discovered experimentally. Particularly, together with I. Aleiner and V. Ambegaokar, I have described the transport through a constrained metallic region, known as a quantum dot, subject to time-dependent perturbations. By  working beyond the adiabatic approximation, we demonstrated that at high frequencies the generated direct current can be attributed to a new shape of the electron distribution function in the dot. My further work on the analysis of such system led to characterization of other measurable parameters of the system and a quantitative comparison of the theory with experiments done at Harvard University (Picture on the left: microphoto of the device used in Harvard experiments).

I. Aleiner and I have also constructed a kinetic theory of two-dimensional electron systems (2DES) placed in a magnetic field in the presence of high-frequency electric fields. Later,  together with I. Dmitriev, A. Mirlin and D. Polykov, we applied this theory to the description of the experiments on 2DES subject to high-frequency radiation. We demonstrated that the large amplitude of magneto-oscillations in the experimentally relevant regime is arising from a specific non-monotonic form of the distribution function of electrons in 2DES due to the high-frequency fields. I plan to consider an arbitrary shape of the impurity scattering potential and to investigate the non-linear current in response to a constant electric field investigated experimentally very recently. Another important direction of my research would be to re-apply this theory to  an atomic sheet of carbon, a new type of 2DES called graphene.

In the above cases, the external field was considered classically. To describe the interaction effects with quantized electromagnetic fields, such as fields containing small number of  photons in its modes or fields describing electron-electron interactions, one has to modify the developed techniques. Such modification was carried out in my recent paper with A. D. Stone, where we calculated electric current through a quantum dot coupled to quantized electromagnetic field (A schematic picture of the device is shown on the right). In the near future, I plan to further develop the theory of electron transport through quantum systems and consider how different types of interaction influence transport characteristics of these systems. In addition to the Coulomb interaction, I will analyze the interaction between electrons in the Cooper channel that leads to the appearance of superconductivity. Of particular importance is to calculate the charge and heat conductances and current noise of small superconducting devices close to the superconducting phase transition because these devices are currently the subject a broad experimental investigation. Such devices are important  for practical realizations of ultra-sensitive detectors of various spectra of electromagnetic radiation. They also address such fundamental questions as the thermodynamic and quantum phase transitions in metal-superconductor systems.