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

Computational Physics;Numerical Analysis;Numerical Analysis;Quantum Physics