Topological edge states in the Su-Schrieffer-Heeger model subject to balanced particle gain and loss

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 $\mathcal{P}\mathcal{T}$-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.