Participating Countries and International organizations:
Armenia, Australia, Austria, Belarus, Belgium, Brazil, Bulgaria, Canada, Czech Republic, France, Germany, Hungary, India, Ireland, Italy, Japan, Moldova, Mongolia, Poland, Romania, Russia, Serbia, Slovakia, Slovenia, Spain, Switzerland, Taiwan, Ukraine, USA, Uzbekistan, Vietnam. 

Scientific Programme:
Effects of strong electron correlations in high-temperature superconductors, colossal magneto-resistance compounds (manganites), heavy-fermion systems, low-dimensional quantum magnets with strong spin-orbit interaction, topological insulators, etc. will be investigated based on a variety of underlying many-band electronic models including the extended Hubbard model, Anderson model, super-exchange spin-orbital models of transition of metal oxides with strong relativistic spin-orbital coupling. The electronic band structure, spectral properties of charge carrier quasiparticles, magnetic and charge collective excitations, metal-insulator and magnetic phase transitions, Cu- and Fe-based high-Tc superconductivity, charge and spin-orbital ordering will be studied. The obtained results will be used to support neutron scattering experiments performed at FLNP, JINR. 

Investigations in the field of nanostructures and nanoscaled phenomena will be addressed to a study of physical characteristics of nanomaterials promising for various applications in modern nanotechnologies. The electronic, thermal and transport properties of carbon nanostructures will be investigated. It is planned to study the problem of quantum transport in molecular devices. Spin dynamics of magnetic nanoclusters will be investigated. The analysis of resonance tunneling phenomena in the layered superconductors and superconducting nanostructures in the external fields will be performed. Numerical modeling of resonance, radiative and chaotic properties of intrinsic Josephson junctions in high temperature superconductors is planned to be carried out. 

Мodels in condensed matter physics will be studied by using methods of equilibrium and non-equilibrium statistical mechanics with the aim of revealing general properties of many-particle systems based on the ideas of self-similarity and universality. Mathematical mechanisms, underlying the kinetic and stationary behavior of model systems, as well as possible links between different models, will be investigated. The study of two-dimensional lattice models by the transfer matrix method will be focused on confirming the predictions of the logarithmic conformal field theory. The theory of integrable systems will be developed in the aspect of finding new integrable boundary conditions for two-dimensional spin systems and the solution of the corresponding Yang-Baxter equations. The universal behavior of correlation functions in non-equilibrium systems will be studied as well. The research in the structure theory and the theory of representations of quantum groups and matrix algebras will be directed to further applications in the theory of integrable models in quantum mechanics and statistical physics. Applications of the elliptic hypergeometric integrals, defining the most general solutions of the Yang-Baxter equation and most complicated known exactly computable path integrals in four-dimensional quantum field theory, to two-dimensional spin systems will be studied. 

Expected main results in 2018:

• 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.