# Open-quantum-system dynamics: Recovering positivity of the Redfield equation via the partial secular approximation

@article{Farina2019OpenquantumsystemDR, title={Open-quantum-system dynamics: Recovering positivity of the Redfield equation via the partial secular approximation}, author={D. Farina and Vittorio Giovannetti}, journal={Physical Review A}, year={2019} }

We show how to recover complete positivity (and hence positivity) of the Redfield equation via a coarse grain average technique. We derive general bounds for the coarse graining time scale above which the positivity of the Redfield equation is guaranteed. It turns out that a coarse grain time scale has strong impact on the characteristics of the Lamb shift term and implies in general non-commutation between the dissipating and the Hamiltonian components of the generator of the dynamical semi…

## 31 Citations

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## References

SHOWING 1-10 OF 57 REFERENCES

### From completely positive maps to the quantum Markovian semigroup master equation

- Mathematics, Physics
- 2001

### 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…

### Refined weak-coupling limit: Coherence, entanglement, and non-Markovianity

- Physics
- 2016

We study the properties of a refined weak coupling limit that preserves complete positivity in order to describe non-Markovian dynamics in the spin-boson model. With this tool, we show the system…

### Systematic perturbation theory for dynamical coarse-graining

- Physics
- 2009

We demonstrate how the dynamical coarse-graining approach can be systematically extended to higher orders in the coupling between system and reservoir. Up to second order in the coupling constant we…

### Environment-induced entanglement in a refined weak-coupling limit

- Physics
- 2009

Two non-directly interacting qubits with equal frequencies can become entangled via a Markovian, dissipative dynamics through the action of a weakly coupled Ohmic heat bath. In the standard…

### Decoherence and dissipation of a quantum harmonic oscillator coupled to two-level systems

- Physics
- 2008

We derive and analyze the Born-Markov master equation for a quantum harmonic oscillator interacting with a bath of independent two-level systems. This hitherto virtually unexplored model plays a…

### ABOUT QUANTUM-SYSTEMS

- Physics
- 2004

The damping of the harmonic oscillator is studied in the framework of the Lindblad theory for open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion…

### Extending the validity range of quantum optical master equations

- Physics
- 2012

This paper derives master equations for an atomic two-level system for a large set of unitarily equivalent Hamiltonians without employing the rotating wave and certain Markovian approximations. Each…

### 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…

### Phenomenological position and energy resolving Lindblad approach to quantum kinetics

- Physics
- 2018

A general theoretical approach to study the quantum kinetics in a system coupled to a bath is proposed. Starting with the microscopic interaction, a Lindblad master equation is established, which…