The Driven Liouville von Neumann Equation in Lindblad Form

TL;DR

This paper proves that the Driven Liouville von Neumann equation for electron dynamics in molecular electronics can be expressed in Lindblad form, ensuring positivity and trace preservation in the infinite lead limit.

Contribution

It formally demonstrates that the Driven Liouville von Neumann approach can be cast in Lindblad form, providing theoretical justification for its numerical positivity and trace preservation.

Findings

Equation of motion can be cast in Lindblad form in the infinite lead limit

Ensures positivity and trace preservation of the density matrix

Provides theoretical foundation for the Driven Liouville von Neumann method

Abstract

The Driven Liouville von Neumann approach [J. Chem. Theory Comput. 10, 2927-2941 (2014)] 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 earlier 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 positivity and trace preservation obtained numerically.