Accuracy assessment of perturbative master equations: Embracing nonpositivity

  title={Accuracy assessment of perturbative master equations: Embracing nonpositivity},
  author={Richard Hartmann and Walter T. Strunz},
  journal={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… 
The interplay between local and non-local master equations: exact and approximated dynamics
Master equations are a useful tool to describe the evolution of open quantum systems. In order to characterize the mathematical features and the physical origin of the dynamics, it is often useful to
Going beyond local and global approaches for localized thermal dissipation
Identifying which master equation is preferable for the description of a multipartite open quantum system is not trivial and has led in the recent years to the local vs. global debate in the context
Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation
A Lindblad master equation that approximates the Redfield equation, a well known master equation derived from first principles, without significantly compromising the range of applicability of the Redfields, and is adaptable between its time-independent, time-dependent, and Floquet form.
Full-polaron master equation approach to dynamical steady states of a driven two-level system beyond the weak system-environment coupling
We apply a full-polaron master equation and a weak-coupling non-Markovian master equation to describe the steady-state time-averaged properties of a driven two-level system, an electron coherently
Evolution Equations for Quantum Semi-Markov Dynamics
This work analyzes the emergence of a dephasing term when moving from one type of master equation to the other, and concludes that such an approximation always leads to a Markovian evolution for the considered class of dynamics.
Environmentally Induced Entanglement - Anomalous Behavior in the Adiabatic Regime
It is found that for resonant qubits, even in the adiabatic regime (arbitrarily large $\omega_c$), the entanglement dynamics is still influenced by an environmentally induced Hamiltonian interaction, and the suitability of various perturbative master equations for obtaining approximate entangling dynamics is discussed.
Strong coupling effects in quantum thermal transport with the reaction coordinate method
We present a semi-analytical approach for studying quantum thermal energy transport at the nanoscale. Our method, which is based on the reaction coordinate method, reveals the role of strong
Local master equations bypass the secular approximation
It is shown that the local approach can be more reliable than the global one for weakly interacting open quantum systems, due to the fact that the secular approximation, which underpins the GME, can destroy key dynamical features.
Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation
Derivation of a quantum master equation for a system weakly coupled to a bath which takes into account nonsecular effects, but nevertheless has the mathematically correct Gorini–Kossakowski–
Thermodynamics of the Coarse-Graining Master Equation
It is shown that the coarse-graining approach to derive a generator for the evolution of an open quantum system over a finite time interval generally leads to a Lindblad–Gorini–Kossakowski–Sudarshan generator.


Preservation of positivity by dynamical coarse graining
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).
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.
  • C. Fleming, N. Cummings
  • 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.
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
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
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
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,