On decoherence and preservation of coherences in solutions of the GKSL equation in the theory of open quantum systems

We consider the properties of solutions of the Gorini – Kossakovsky – Sudarshan – Lindblad (GKSL) equation for the density operator (density matrix) for a system with a nondegenerate energy spectrum that weakly interacts with the reservoir. Conditions for the existence of solutions with off-diagonal elements of the density matrix (“coherences”) that do not tend to zero at large times are derived.