Quantum mechanics

Quantum decoherence

Mathematical physics

Mathematical optimization

Hamiltonian (control theory)

Statistical physics

Quantum system

Quantum master equation

Physics

Mathematics

Mathematical analysis

Semigroup

Quantum

Master equation

Harmonic oscillator

Physical review. A/Physical review, A

We show how to recover complete positivity (and hence positivity) of the Redfield equation via a coarse-grained averaging technique. We derive general bounds for the coarse graining timescale above which the positivity of the Redfield equation is guaranteed. It turns out that a coarse grain timescale has strong impact on the characteristics of the Lamb shift term and implies, in general, noncommutation between the dissipating and the Hamiltonian components of the generator of the dynamical semigroup. Finally, we specify the analysis to a two-level system or a quantum harmonic oscillator coupled to a fermionic or bosonic thermal environment via dipolelike interaction.

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