Efficient Steady-State Solver for the Hierarchical Equations of Motion Approach: Formulation and Application to Charge Transport through Nanosystems

An iterative approach is introduced, which allows the efficient solution of the hierarchical equations of motion (HEOM) for the steady-state of open quantum systems. The approach combines the method of matrix equations with an efficient preconditioning technique to reduce the numerical effort of solving the HEOM. Illustrative applications to simulate nonequilibrium charge transport in single-molecule junctions demonstrate the performance of the method.