Driven Liouville von Neumann Equation in Lindblad Form

Driven Liouville von Neumann Equation in Lindblad Form Driven Liouville von Neumann Equation in Lindblad Form

Oded Hod,¹, César A. Rodríguez-Rosario,² Tamar Zelovich,¹ and Thomas Frauenheim²

1) Department of Physical Chemistry, School of Chemistry, The Sackler Faculty of Exact Sciences and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel.
2) Bremen Center for Computational Materials Science, University of Bremen, Am Falturm 1, Bremen, 28359, Germany.

The Driven Liouville von Neumann approach [J. Chem. Theory Comput. 2014, 10, 2927-2941] is a computationally efficient simulation method for modeling electron dynamics in molecular electronics junctions. Previous numerical simulations have shown that the method can reproduce the exact single-particle dynamics while avoiding density matrix positivity violation found in previous implementations. In this study we prove that in the limit of infinite lead models the underlying equation of motion can be cast in Lindblad form. This provides a formal justification for the numerically observed density matrix positivity conservation.

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