Open Quantum System Dynamics: recovering positivity of the Redfield equation via Partial-Secular Approximation

Abstract

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-group. Finally we specify the analysis to a two-level system or a quantum harmonic oscillator coupled to a fermionic or bosonic thermal environment via dipole-like interaction.

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Cited by in corpus (5)

• Open system dynamics from thermodynamic compatibility
• Discrimination of thermal baths by single qubit probes
• Thermodynamics of the Coarse-Graining Master Equation
• Transport in Conductors and Rectifiers: Mean-Field Redfield Equations and Non-Equilibrium Green's Functions
• Dynamics of a driven open double two-level system and its entanglement generation