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Non-Hermitian systems with PT symmetry can possess purely real eigenvalue spectra. In this work two one-dimensional systems with two different topological phases, the topological nontrivial Phase (TNP) and the topological trivial phase (TTP) combined with PT -symmetric non-Hermitian potentials are investigated. The models of choice are the Su-Schrieffer-Heeger (SSH) model and the Kitaev chain. The interplay of a spontaneous PT -symmetry breaking due to gain and loss with the topological phase is different for the two models. The SSH model undergoes a PT -symmetry breaking transition in the TNP immediately with the presence of a non-vanishing gain and loss strength γ, whereas the TTP exhibits a parameter regime in which a purely real eigenvalue spectrum exists. For the Kitaev chain the PT -symmetry breaking is independent of the topological phase. We show that the topological interesting states -the edge states -are the reason for the different behaviors of the two models and that the intrinsic particle-hole symmetry of the edge states in the Kitaev chain is responsible for a conservation of PT symmetry in the TNP.

We study the behavior of the non-adiabatic population transfer between resonances at an exceptional point in the spectrum of the hydrogen atom. It is known that, when the exceptional point is encircled, the system always ends up in the same state, independent of the initial occupation within the two-dimensional subspace spanned by the states coalescing at the exceptional point. We verify this behavior for a realistic quantum system, viz. the hydrogen atom in crossed electric and magnetic fields. It is also shown that the non-adiabatic hypothesis can be violated when resonances in the vicinity are taken into account. In addition, we study the non-adiabatic population transfer in the case of a third-order exceptional point, in which three resonances are involved.

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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 PTsymmetric 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.