The Driven Liouville von Neumann Equation in Lindblad Form

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.

16 pages, 3 figures

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• Master Equations for Electron Transport: The Limits of the Markovian Limit
• Renormalized Lindblad Driving: A Numerically-Exact Nonequilibrium Quantum Impurity Solver
• Open System Tensor Networks and Kramers' Crossover for Quantum Transport
• Lead Geometry and Transport Statistics in Molecular Junctions
• Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach
• Relaxation-limited electronic currents in extended reservoir simulations
• Electron transport in real time from first-principles
• Performance of Reservoir Discretizations in Quantum Transport Simulations
• Quantum transport under AC drive from the leads : A Quantum Master Equation approach
• Evaluation of Dynamical Properties of Open Quantum Systems Using the Driven Liouville-von Neumann Approach: Methodological Considerations
• Driven Liouville-von Neumann Equation for Quantum Transport and Multiple-Probe Green's Functions
• Analytic expressions for the steady-state current with finite extended reservoirs
• Accumulative reservoir construction: Bridging continuously relaxed and periodically refreshed extended reservoirs
• Entropy production in the mesoscopic-leads formulation of quantum thermodynamics
• Simulation of 24,000 Electrons Dynamics: Real-Time Time-Dependent Density Functional Theory (TDDFT) with the Real-Space Multigrids (RMG)
• Transport in a periodically driven tilted lattice via the extended reservoir approach: Stability criterion for recovering the continuum limit
• Unraveling open-system quantum dynamics of non-interacting Fermions
• Effects of internal and external decoherence on the resonant transport and Anderson localization of fermionic particles in the tight-binding chain
• Interplay between external driving, dissipation and collective effects in the Markovian and non-Markovian regimes
• Preserving fermionic statistics for single-particle approximations in microscopic quantum master equations
• Approaching the scaling limit of transport through lattices with dephasing
• Dual current anomalies and quantum transport within extended reservoir simulations