  We investigate the Su-Schrieffer-Heeger model in presence of an injection and
removal of particles, introduced via a master equation in Lindblad form. It is
shown that the dynamics of the density matrix follows the predictions of
calculations in which the gain and loss are modeled by complex
$\mathcal{PT}$-symmetric potentials. In particular it is found that there is a
clear distinction in the dynamics between the topologically different cases
known from the stationary eigenstates.
