  In this contribution to the memorial issue of G\"oran Lindblad, we
investigate the periodically driven Lindblad equation for a two-level system.
We analyze the system using both adiabatic diagonalization and numerical
simulations of the time-evolution, as well as Floquet theory. Adiabatic
diagonalization reveals the presence of exceptional points in the system, which
depend on the system parameters. We show how the presence of these exceptional
points affects the system evolution, leading to a rapid dephasing at these
points and a staircase-like loss of coherence. This phenomenon can be
experimentally observed by measuring, for example, the population inversion. We
also observe that the presence of exceptional points seems to be related to
which underlying Lie algebra the system supports. In the Floquet analysis, we
map the time-dependent Liouvillian to a non-Hermitian Floquet Hamiltonian and
analyze its spectrum. For weak decay rates, we find a Wannier-Stark ladder
spectrum accompanied by corresponding Stark-localized eigenstates. For larger
decay rates, the ladders begin to dissolve, and new, less localized states
emerge. Additionally, their eigenvalues are exponentially sensitive to
perturbations, similar to the skin effect found in certain non-Hermitian
Hamiltonians.
