Tensor network and open system simulation of transport through semiconductor arrays

There has been significant progress in semiconductor-based nanoscale device fabrication, where phosphorus (P) dopants can be precisely placed in bulk silicon (Si) to form locally confined donor arrays—platforms for analog quantum simulations. Whereas traditional transport simulations often emphasize long-time observables such as steady-state properties, we shift the focus to transient dynamics that are harder to access with approaches like Green’s functions and that lie beyond the practical limits of exact diagonalization. We employ state-of-the-art tensor-network methods together with a mixed momentum–real-space “extended reservoir” construction to curb entanglement growth that would otherwise arise from a naïve mapping of the physical Hamiltonian. This framework reveals how transient electronic states develop on the device at the onset of transport and how distinct relaxation processes unfold following perturbations. We systematically vary simulation parameters to elucidate how qualitatively different dynamical regimes can emerge. Finally, we explore the limits of tensor-network-based simulations and outline connections to open-system formalisms, helping to bridge these approaches. Our results highlight the richness of transient transport dynamics and motivate the development of more sensitive experimental techniques to probe them.