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Long-range interactions play a central role in electron transport. At thesame time, they present a challenge for direct computer simulations, sincesufficiently large portions of the bath have to be included in the computationto accurately compute the Coulomb potential. This article presents areduced-order approach, by deriving an open quantum model for the reduceddensity-matrix. To treat the transient dynamics, the problem is placed in areduced-order framework. The dynamics, described by the Liouville von Neumannequation, is projected to subspaces using a Petrov-Galerkin projection. Inorder to recover the global electron density profile as a vehicle to computethe Coulomb potential, we propose a domain decomposition approach, where thecomputational domain also includes segments of the bath that are selected usinglogarithmic grids. This approach leads to a multi-component self-energy thatenters the effective Hamiltonian. We demonstrate the accuracy of the reducedmodel using a molecular junction built from a Lithium chains.

A Projection-based Reduced-order Method for Electron Transport Problems with Long-range Interactions