  The study of noise assisted transport in quantum systems is essential in a
wide range of applications from near-term NISQ devices to models for quantum
biology. Here, we study a generalised XXZ model in the presence of stochastic
collision noise, which allows to describe environments beyond the standard
Markovian formulation. Our analysis through the study of the local
magnetization, the inverse participation ratio (IPR) or its generalisation, the
Inverse Ergodicity Ratio (IER), showed clear regimes where the transport rate
and coherence time can be controlled by the dissipation in a consistent manner.
In addition, when considering several excitations, we characterize the
interplay between collisions and system interactions identifying regimes in
which transport is counterintuitively enhanced when increasing the collision
rate, even in the case of initially separated excitations. These results
constitute an example of the essential building blocks for the understanding of
quantum transport in structured noisy and warm disordered environments.
