KLEIN–GORDON EQUATION, QUNTUM RELATIVISTIC HYDRODYNAMICS AND QUANTUM SHOCK WAVES IN DESCRIBING COLLISIONS OF ATOMIC NUCLEI

In this work, the equations of quantum relativistic hydrodynamics are obtained from the effective Klein–Fock–Gordon equation taking into account dissipation. Taking into account dissipation in the Klein–Gordon equation leads to the need to introduce an additional thermal term and an equation for it. As a result, a closed system of equations was obtained taking into account non-equilibrium processes, which makes it possible to describe the dynamics of the process of collisions of atomic nuclei and calculate the yield of secondary particles. Solving the resulting equations makes it possible to identify quantum shock waves and the time evolution of the resulting hot spot. The calculated spectra of emitted protons in heavy ion collisions are compared with available experimental data.