A time-dependent regularization of the Redfield equation

Abstract

We introduce a new regularization of the Redfield equation based on a replacement of the Kossakowski matrix with its closest positive semidefinite neighbor. Unlike most of the existing approaches, this procedure is capable of retaining the time dependence of the Kossakowski matrix, leading to a completely positive divisible quantum process. Using the dynamics of an exactly-solvable three-level open system as a reference, we show that our approach performs better during the transient evolution, if compared to other approaches like the partial secular master equation or the universal Lindblad equation. To make the comparison between different regularization schemes independent from the initial states, we introduce a new quantitative approach based on the Choi-Jamiolkowski isomorphism.

Final published version. 18 pages, 3 figures

References in corpus (7)

• Preservation of Positivity by Dynamical Coarse-Graining
• Staying positive: going beyond Lindblad with perturbative master equations
• Open Quantum System Dynamics: recovering positivity of the Redfield equation via Partial-Secular Approximation
• Structure of completely positive quantum master equations with memory kernel
• A phenomenological position and energy resolving Lindblad approach to quantum kinetics
• Thermodynamic consistency of quantum master equations
• Perturbative Steady States of Completely Positive Quantum Master Equations

Cited by in corpus (12)

• Taming the Bloch-Redfield equation: Recovering an accurate Lindblad equation for general open quantum systems
• Exact finite-time correlation functions for multi-terminal setups: Connecting theoretical frameworks for quantum transport and thermodynamics
• Invalidation of the Bloch-Redfield Equation in Sub-Ohmic Regime via a Practical Time-Convolutionless Fourth-Order Master Equation
• Recovering complete positivity of non-Markovian quantum dynamics with Choi-proximity regularization
• Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity
• Complete Positivity and Thermal Relaxation in Quadratic Quantum Master Equations
• Gravitationally induced decoherence of a scalar field: investigating the one-particle sector and its interplay with renormalisation
• Effective time-dependent temperature for fermionic master equations beyond the Markov and the secular approximations
• Quasiperiodic Floquet-Gibbs states in Rydberg atomic systems
• Numerical implementation of the partial secular approximation and unified master equation in structured open quantum systems
• Relaxation to persistent currents in a Hubbard trimer coupled to fermionic baths
• Unifying quantum stochastic methods using Wick's theorem on the Keldysh contour