“…The generic properties of first and second order dissipative phase transitions can be derived from a spectral analysis of the system's Liouvillian [1,2]. Critical behavior at the phase transition has been studied both, theoretically [2,4,[8][9][10][11][12] and experimentally [6,[12][13][14][15][16][17][18][19][20]. One of the paradigmatic examples exhibiting a dissipative phase transition is a single-mode quantum system, realized, e.g., with a nonlinear optical medium in a cavity, which is coherently pumped by a laser and subject to cavity losses [6,[15][16][17]21].…”