Complete positivity, positivity and long-time asymptotic behavior in a two-level open quantum system
arXiv:2304.01748 · doi:10.1103/PhysRevA.108.032212
Abstract
We study the concepts of complete positivity, positivity and non-Markovianity in a two-level open quantum system whose dynamics are governed by a time-local quantum master equation. We establish necessary and sufficient conditions on the time-dependent relaxation rates to ensure complete positivity and positivity of the dynamical map. We discuss their relations with the non-Markovian behavior of the open system. We also analyze the long-time asymptotic behavior of the dynamics as a function of the rates. We show under which conditions on the rates the system tends to the equilibrium state. Different examples illustrate this general study.
22 pages, 2 figures
References in corpus (13)
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Assessing non-Markovian dynamics
- Optimal state pairs for non-Markovian quantum dynamics
- Finding the Kraus decomposition from a master equation and vice versa
- Quantum Semi-Markov Processes
- Stochastic Representation of a Class of Non-Markovian Completely Positive Evolutions
- Quantification of memory effects in the spin-boson model
- Generalized master equations leading to completely positive dynamics
- Orbits of quantum states and geometry of Bloch vectors for -level systems
- Non-unital non-Markovianity of quantum dynamics
- Efficiency of quantum controlled non-Markovian thermalization
- Open system dynamics from thermodynamic compatibility
- Non-Markovian dynamics under time-translation symmetry