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We investigate the effect of a non-Markovian, structured reservoir on an openHeisenberg spin chain. We establish a coherent self-feedback mechanism as thereservoir couples frequency-dependent to the spin chain. Thus, loss and drivingtake place due to the interaction of the spin chain with its own past. This newparadigm of non-Markovian imposed boundary-driving allows to discuss a new kindof non-equilibrium steady-state. We show that for certain parameters even inthe long-time limit persistent oscillations occur within the chain. Moreover,we demonstrate that the conditions for these oscillations and excitationtrapping depend on the characteristics of the chain, thus making it possible tocharacterize a chain by detection of its emitted signal under influence ofself-feedback.

Non-equilibrium non-Markovian steady-states in open quantum many-body systems: Persistent oscillations in Heisenberg quantum spin chains