# Accuracy assessment of perturbative master equations: Embracing nonpositivity

@article{Hartmann2020AccuracyAO,
title={Accuracy assessment of perturbative master equations: Embracing nonpositivity},
author={Richard Hartmann and Walter T. Strunz},
journal={Physical Review A},
year={2020}
}
• Published 6 June 2019
• Physics
• Physical Review A
The reduced dynamics of an open quantum system obtained from an underlying microscopic Hamiltonian can in general only approximately be described by a time local master equation. The quality of that approximation depends primarily on the coupling strength and the structure of the environment. Various such master equations have been proposed with different aims. Choosing the most suitable one for a specific system is not straight forward. By focusing on the accuracy of the reduced dynamics we…
22 Citations

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## References

SHOWING 1-10 OF 110 REFERENCES
Preservation of positivity by dynamical coarse graining
• Physics
• 2008
We compare different quantum master equations for the time evolution of the reduced density matrix. The widely applied secular approximation (rotating wave approximation) applied in combination with
Staying positive: going beyond Lindblad with perturbative master equations
The perturbative master equation (Bloch–Redfield) is used extensively to study dissipative quantum mechanics—particularly for qubits—despite the 25-year-old criticism that it violates positivity
Exact Open Quantum System Dynamics Using the Hierarchy of Pure States (HOPS).
• Physics
Journal of chemical theory and computation
• 2017
It is found that it is highly favorable for the HOPS method to use the zero-temperature BCF and include temperature via a stochastic Hermitian contribution to the system Hamiltonian in the strong coupling regime.
Accuracy of perturbative master equations.
• Mathematics, Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2011
It is shown that, contrary to intuition, full-time solutions of order-2n accuracy require an order-(2n+2) master equation, which has a wide-ranging impact on the validity of coupling (or friction) sensitive results derived from second-order convolutionless, Nakajima-Zwanzig, Redfield, and Born-Markov master equations.
Extending the applicability of Redfield theories into highly non-Markovian regimes.
• Physics
The Journal of chemical physics
• 2015
It is found that this Redfield-based dynamical hybrid approach, which is computationally more expensive than bare Redfield dynamics, yields only a marginal improvement over the simpler approximation of complete mode arrest.
Coarse graining can beat the rotating-wave approximation in quantum Markovian master equations
• Physics
• 2013
We present a first-principles derivation of the Markovian semigroup master equation without invoking the rotating-wave approximation (RWA). Instead we use a time coarse-graining approach that leaves
Stochastic Liouville, Langevin, Fokker–Planck, and Master Equation Approaches to Quantum Dissipative Systems
Half century has past since the pioneering works of Anderson and Kubo on the stochastic theory of spectral line shape were published in J. Phys. Soc. Jpn. 9 (1954) 316 and 935, respectively. In this
Phase space approach to theories of quantum dissipation
• Physics
• 1997
Six major theories of quantum dissipative dynamics are compared: Redfield theory, the Gaussian phase space ansatz of Yan and Mukamel, the master equations of Agarwal,
Non-Markovian quantum state diffusion: Perturbation approach
• Physics, Mathematics
• 1999
We present a perturbation theory for non-Markovian quantum state diffusion (QSD), the theory of diffusive quantum trajectories for open systems in a bosonic environment [Physical Review A 58, 1699,