  Methodological aspects of using the driven Liouville-von Neumann (DLvN)
approach for simulating dynamical properties of molecular junctions are
discussed. As a model system we consider a non-interacting resonant level
uniformly coupled to a single Fermionic bath. We demonstrate how a finite
system can mimic the depopulation dynamics of the dot into an infinite band
bath of continuous and uniform density of states. We further show how the
effects of spurious energy resolved currents, appearing due to the approximate
nature of the equilibrium state obtained in DLvN calculations, can be avoided.
Several ways to approach the wide band limit that is often adopted in
analytical treatments, using a finite numerical model system are discussed
including brute-force increase of the lead model bandwidth as well as efficient
cancellation or direct subtraction of finite-bandwidth effect. These
methodological considerations may be relevant also for other numerical schemes
that aim to study non-equilibrium thermodynamics via simulations of open
quantum systems.
