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 lithium chains.

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一种基于投影的降阶方法解决具有长程相互作用的电子传输问题

长程相互作用在电子传输中起着核心作用。同时，它们对直接计算机模拟提出了挑战，因为必须在计算中包含足够大的浴液部分才能准确计算库仑势。本文通过推导简化密度矩阵的开放量子模型，提出了一种降阶方法。为了处理瞬态动力学，问题被置于降阶框架中。使用 Petrov-Galerkin 投影将 Liouville-von Neumann 方程描述的动力学投影到子空间。为了恢复全局电子密度剖面作为计算库仑势的工具，我们提出了一种域分解方法，其中计算域还包括使用对数网格选择的浴段。这种方法导致进入有效哈密顿量的多分量自能。我们使用由锂链构建的分子连接来证明简化模型的准确性。