Evaluation of dynamical properties of open quantum systems using the driven Liouville-von Neumann approach: methodological considerations

Abstract

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, which 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.

GRAPHICAL ABSTRACT

KEYWORDS:

• Molecular junctions
• molecular machines
• driven Liouville-von Neumann approach
• open quantum systems
• quantum thermodynamics

Acknowledgement

IO gratefully acknowledges the support of the Adams Fellowship Program of the Israel Academy of Sciences and Humanities, and the Naomi Foundation through the Tel-Aviv University GRTF Program. The research of AN is supported by the U.S. National Science Foundation [grant number CHE1665291],the Israel-U.S. Binational Science Foundation, the German Research Foundation (DFG TH 820/11-1), and the University of Pennsylvania. OH is grateful for the generous financial support of the Israel Science Foundation under [grant number 1740/13] and the Center for Nanoscience and Nanotechnology of Tel-Aviv University.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of AN is supported by the U.S. National Science Foundation (grant number CHE1665291), the Israel-U.S. Binational Science Foundation (grant number 2014113), the German Research Foundation (DFG TH 820/11-1), and the University of Pennsylvania. OH is grateful for the generous financial support of the Israel Science Foundation under grant number 1740/13 and the Center for Nanoscience and Nanotechnology of Tel-Aviv University. IO gratefully acknowledges the support of the Adams Fellowship Program of the Israel Ac ademy of Sciences and Humanities, and the Naomi Foundation through the Tel-Aviv University GRTF Program.