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Nanoscale devices - either biological or artificial - operate in a regimewhere the usual assumptions of a structureless, Markovian, bath do not hold.Being able to predict and study the dynamics of such systems is crucial and isusually done by tracing out the bath degrees of freedom, which implies losinginformation about the environment. To go beyond these approaches we use anumerically exact method relying on a Matrix Product State representation ofthe quantum state of a system and its environment to keep track of the bathexplicitly. This method is applied to a specific example of interaction thatdepends on the spatial structure of the system. The result is that we predict anon-Markovian dynamics where long-range couplings induce correlations into theenvironment. The environment dynamics can be naturally extracted from ourmethod and shine a light on long time feedback effects that are responsible forthe observed non-Markovian recurrences in the eigen-populations of the system.

Unveiling non-Markovian spacetime signalling in open quantum systems with long-range tensor network dynamics