Driven Liouville von Neumann Equation in Lindblad Form

Area of Science:

• Computational Chemistry
• Quantum Dynamics
• Molecular Electronics

Background:

• The Driven Liouville von Neumann (DLvN) approach is a computationally efficient method for simulating electron dynamics in molecular electronics.
• Previous studies indicated DLvN reproduces exact single-particle dynamics and avoids density matrix positivity violations.

Purpose of the Study:

• To provide a formal theoretical justification for the observed density matrix positivity conservation in the DLvN approach.
• To demonstrate the mathematical foundation of DLvN's accuracy in molecular electronics simulations.

Main Methods:

• Theoretical analysis of the Driven Liouville von Neumann equation of motion.
• Mathematical derivation in the limit of infinite lead models.
• Demonstration of the equation's transformation into Lindblad form.

Main Results:

• The study proves that the DLvN equation of motion can be expressed in Lindblad form under the condition of infinite lead models.
• This mathematical transformation provides a formal basis for the method's conservation of density matrix positivity.

Conclusions:

• The Lindblad form of the equation of motion formally justifies the numerical observation of density matrix positivity conservation in the DLvN approach.
• This work strengthens the theoretical foundation of the DLvN method for accurate electron dynamics modeling in molecular electronics.