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The Dynamical Mean Field Theory (DMFT) is a powerful tool for calculatinghighly correlated systems (both bosonic and fermionic) in a state ofthermodynamic equilibrium. However, in the case of non-equilibrium states, themethod has significant limitations that do not allow obtaining correct results.The stumbling block here is the impurity solver: a method for calculating thedynamics of an open system. In this work we present the prototype of auniversal impurity solver for the DMFT method which can solve both equilibriumand non-equilibrium problems. We analyse spectral functions of Bose-Hubbardmodel on the Bethe lattice in different regimes and show that our solver givescorrect and physical results.

Towards out of equilibrium impurity solver for the Dynamical Mean Field Theory