An easily solvable quantum master equation has long been sought that takes into account memory effects induced on the system by the bath, i.e., non-Markovian effects. We briefly review the post-Markovian master equation (PMME), which is relatively easy to solve, and analyze a simple example where solutions obtained exhibit non-Markovianity. We apply the distinguishability measure introduced by Breuer et al., and we also explicitly analyze the divisibility of the associated quantum dynamical maps. We give a mathematical condition on the memory kernel used in the PMME that guarantees non- $CP$ -divisible dynamics.An easily solvable quantum master equation has long been sought that takes into account memory effects induced on the system by the bath, i.e., non-Markovian effects. We briefly review the post-Markovian master equation (PMME), which is relatively easy to solve, and analyze a simple example where solutions obtained exhibit non-Markovianity. We apply the distinguishability measure introduced by Breuer et al., and we also explicitly analyze the divisibility of the associated quantum dynamical maps. We give a mathematical condition on the memory kernel used in the PMME that guarantees non-$CP$-divisible dynamics.

arXiv:1805.04806Physical Review AOct 17, 201810 citations

Properties of quantum Markovian master equations

Vittorio Gorini, Alberto Frigerio, Maurizio Verri +2 more

Reports on Mathematical PhysicsApr 1, 1978467 citations

Range of applicability of the Hu-Paz-Zhang master equation

Gábor Homa, András Csordás, Mihály A. Csirik +1 more

We investigate a case of the Hu-Paz-Zhang master equation of the Caldeira-Leggett model without Lindblad form obtained in the weak-coupling limit up to the second-order perturbation. In our study, we use Gaussian initial states to be able to employ a sufficient and necessary condition, which can expose positivity violations of the density operator during the time evolution. We demonstrate that the evolution of the non-Markovian master equation has problems when the stationary solution is not a positive operator, i.e., does not have physical interpretation. We also show that solutions always remain physical for small times of evolution. Moreover, we identify a strong anomalous behavior, when the trace of the solution is diverging. We also provide results for the corresponding Markovian master equation and show that positivity violations occur for various types of initial conditions even when the stationary solution is a positive operator. Based on our numerical results, we conclude that this non-Markovian master equation is superior to the corresponding Markovian one.We investigate a case of the Hu-Paz-Zhang master equation of the Caldeira-Leggett model without Lindblad form obtained in the weak-coupling limit up to the second-order perturbation. In our study, we use Gaussian initial states to be able to employ a sufficient and necessary condition, which can expose positivity violations of the density operator during the time evolution. We demonstrate that the evolution of the non-Markovian master equation has problems when the stationary solution is not a positive operator, i.e., does not have physical interpretation. We also show that solutions always remain physical for small times of evolution. Moreover, we identify a strong anomalous behavior, when the trace of the solution is diverging. We also provide results for the corresponding Markovian master equation and show that positivity violations occur for various types of initial conditions even when the stationary solution is a positive operator. Based on our numerical results, we conclude that this non-Markovian master equation is superior to the corresponding Markovian one.

arXiv:2002.06272Physical Review AAug 10, 202010 citations

Non-Markovian and Markovian Dynamics of a V-type Three-Level Atom

Xiaoyun Wang, Bang-Fu Ding, Jinfeng Liu +2 more

The reduced dynamics of a V-type three-level atom in a structure reservoir is presented, which has the exact solution in certain special condition. The Markovian and non-Markovian master equations for this composite system are solved and compared with the exact solution. The solving approach can be directly generalized to the solution of a V-type multilevel system dynamics interacting with a reservoir. The results further testify that these two kinds of master equations are exploited in different coupling regime, providing guidance for further application of these variants master equations to solve multilevel system dynamics without the exact solution.The reduced dynamics of a V-type three-level atom in a structure reservoir is presented, which has the exact solution in certain special condition. The Markovian and non-Markovian master equations for this composite system are solved and compared with the exact solution. The solving approach can be directly generalized to the solution of a V-type multilevel system dynamics interacting with a reservoir. The results further testify that these two kinds of master equations are exploited in different coupling regime, providing guidance for further application of these variants master equations to solve multilevel system dynamics without the exact solution.

Communications in Theoretical PhysicsFeb 1, 20123 citations

On the quantum master equation under feedback control

Bo Qi

Science in China Series F Information SciencesNov 1, 20099 citations

CP

-divisible dynamics.