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Theory of Condensed Matter

• Calculation of the spectrum of spin fluctuations in the quasi-two-dimensional Heisenberg model on the honeycomb lattice within the t - J model with doped holes.
  
  Calculation of the dynamical charge susceptibility and studies of charge density waves within the projection technique for the Green functions in the t - J model.
  
  Model description of electron structure of lead halide perovskites for the next generation of solar cells and spintronics.
  
  Structural investigations of mass and surface fractals at nano- and micro-scale using the small-angle scattering technique.
  
  Development of the theory of spin dynamics of dipolar and spinor molecules in optical lattices.
  
  Derivation and investigation of the equations of evolution of the open nonequilibrium systems under some special boundary conditions.
  
  Investigation of charge density wave instability in the underdoped cuprates by employing the continuous quantum Monte Carlo numerical method.
  
  Development of the different protocols for the effect of superconducting current on the magnetic moment in the superconductor-ferromagnet-superconductor system.
  
  Investigation of the problem of quantum transport in graphene and phosphorene with taking account of the presence of localized edge states and the effect of lattice thermal vibrations.
  
  Calculation of the electron mobility in phosphorene, phosphorene nanoribbons, as well as in silicene and other novel 2D materials and nanostructures based on these materials.
  
  Study of the electron and transport properties in the systems consisting of carbon nanostructures with biomolecules attached to their surface. Analysis of the influence of the surrounding solution composition on the transport characteristics. Study of the mechanism of quantum transport in the ion liquid gate type field effect transistor based on similar systems.
  
  Calculation of the thermal conductivity of a wide class of nanocrystalline materials.
  
  Investigation of properties of transport of the intra molecular vibrational excitation (vibron) in a quasi 1D macromolecular structure taking into account the process of damping depending on the vibron-phonon coupling strength and temperature.
  
  
• Calculation of the density profile in the model of dense traffic constructed on the basis of the generalized totally asymmetric exclusion process.
  
  Solution in one dimension and numerical computation in higher dimensions of the problem of spreading of information analogous to the model of directed percolation below the percolation threshold.
  
  Evaluation of large deviation functions of the avalanche sizes in the Raise and Peel model in the thermodynamic limit.
  
  Derivation of the universal asymptotics of correlation functions in the generalized simple exclusion process.
  
  A detailed investigation of the rotor-router aggregation model.
  
  The phase diagram of the generalized totally asymmetric simple exclusion process will be constructed for generic values of the probabilities for hopping, injection and ejection of particles on open chains. The results of theoretical analysis and computer simulations will be used for modeling processes of the particle aggregation and development of jams in one-dimensional traffic.
  
  Investigation of eigenfunctions of the elliptic Fourier transformation for the gauge group SU(2) and demonstration of their connection with the Nekrasov instanton partition function in five dimensional gauge field theories (Gaiotto-Kim conjecture).
  
  Investigation of a stochastic regime for the Fateev-Zamolodchikov spin chain, namely, stochastic reinterpretation of the model, study of combinatorial properties of the ground states and revealing of underlying symmetry algebra.
  
  Construction of solutions of the 3-body quantum Calogero-Moser system with the pairwise 2-body interaction described by the Weierstrass elliptic function for special coupling constants using the Sklyanin method of separation of variables.
  
  Construction of solutions of the Yang-Mills equations on AdS_p x S ^q and dS_p x H ^q, i.e. on the direct product of anti-de Sitter spaces, spheres, de Sitter and hyperbolic spaces.
  
  

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