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Theory of Complex Systems and Advanced Materials

• Investigation of strongly-correlated electron superconductivity within the t-J model on the two-dimensional honeycomb lattice: determination of the superconducting order parameter symmetry and calculation of the superconducting transition temperature.
  
  Model and ab initio calculations of magnetic and electronic band structure of rare-earth metals under high external presure.
  
  Structural investigations of mass and surface fractals at nano- and micro-scale using the small-angle scattering technique.
  
  Study of the Bose-Hubbard model with repulsive interactions and its classical limit, discrete nonlinear Schroedinger equation, at negative temperatures.
  
  Investigation of the possibility of regulating spin dynamics in dipolar and spinor systems by using the quadratic Zeeman effect.
  Development of the theory of fast magnetization reversal by influencing effective magnetic anisotropy with the help of external alternating fields.
  
  
• Investigation of the effect of strong magnetic field in changing the electronic structure of the hole-doped cuprates; revealing of the role of the superconducting fluctuations in the formation of the pseudogap Fermi surface consisting of electron-like nodal pockets.
  
  Study of the transport properties of Weyl-semimetal/superconductor junctions in the presence of the external magnetic field.
  
  Investigation of the dynamics and current-voltage characteristics of superconductor - ferromagnet - superconductor structures for superconducting spintronics. Manifestation of the Kapitza pendulum features in these structures. Development of a model "nanomagnet + stack of interinsic Josephson junctions".
  Investigation of the possibility of synchronizing a system of coupled Josephson junctions under the influence of a single nanomagnet and a chain of coupled nanomagnets.
  
  Calculation of the density of states, conductivity and electron mobility in fluorinated graphene and phosphorene taking into account the influence of various types of defects and electron-phonon interaction. Calculation of the concentration and temperature dependences of the electron mobility in polycrystalline graphene.
  Analysis of the thermoelectric transport coefficients of polycrystalline graphene.
  
  Calculation of a conductivity of electrolyte field effect transistors based on various types of low-dimensional structures, for example carbon nanotubes, graphene nanoribbon, phosphorene, hexagonal boron nitride and their heterostructures with biomolecules-detectors, such as DNAzymes, antibodies, etc. Investigation of the influence of different concentrations of detected material on the conductivity.
  
  Investigation of the time behavior of quantum correlations between various structural elements in a quasi-one-dimensional macromolecular structure, including their entanglement, depending on the initial vibronic excitation of the macromolecule.
  
  
• Derivation of exact expressions for the cumulants of an avalanche flow in the Raise and Peel model. Calculation of the second cumulant of the particle flow in the q-boson zero range process. Analysis of its asymptotics and construction of the function describing the KPZ - Edward-Willkinson crossover.
  
  Investigation of the growth of the cluster of visited sites in the model of Eulerian walkers.
  Characterization of the properties of the boundary of the growing cluster.
  
  Calculation of the probability of formation of configurations with N bridges near the boundary in the branching polymers model or spanning trees on the lattice for the isotropic and anisotropic cases.
  
  Finding of symmetries of elliptic hypergeometric integrals generated by Bailey lemmas mixing the A_n and C_n root systems and investigation of their consequences for superconformal indices of four-dimensional supersymmetric quantum field theories.
  
  Generalization and proof of the structure Cayley-Hamilton theorems for classical infinite series of the quantum matrix (super)algebras, investigation of the structure of the Cartan calculus for the linear quantum groups in detail, i.e. description of the center of the commutative subalgebras possibilities and consideration of a possibility for the SL-reduction.
  
  Investigation of low-energy limit of the (super)-Yang-Mills theories in 4,5,6, dimensions compactified to the circle of the small radius of the Riemann surface. Proof that the Yang-Mills theories are reduced to sigma models with target space depending on geometric conditions imposed on gauge fields.
  
  

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