  The dynamics of open quantum systems can be described by a Liouvillian, which
in the Markovian approximation fulfills the Lindblad master equation. We
present a family of integrable many-body Liouvillians based on
Richardson-Gaudin models with a complex structure of the jump operators. Making
use of this new region of integrability, we study the transition to chaos in
terms of a two-parameter Liouvillian. The transition is characterized by the
spectral statistics of the complex eigenvalues of the Liouvillian operators
using the nearest neighbor spacing distribution and by the ratios between
eigenvalue distances.
