Universality of cubic-level repulsion for dissipative quantum chaos

The quantum signature of chaos in dissipative systems is cubic repulsion of their generalized energies (eigenvalues of the generators of the dynamics) in the complex plane. As in the Hamiltonian case the degree of repulsion is the same under temporally homogeneous conditions and periodic driving. Somewhat surprisingly, however, cubic repulsion prevails irrespective of whether or not the Hamiltonian embedding of the dissipative system obeys time-reversal invariance. More-over, even antiunitary symmetries of the dissipative generator itself cannot modify the repulsion exponent. In establishing the universality in question we find, as a useful byproduct, the generalization of detailed balance for periodically driven systems with damping.