Markovian Master Equations and Resonances in Quantum Open Systems

S. L. Wu, X. L. Huang, X. X. Yi

We derive a Markovian master equation for driven open quantum systems based on the Lewis-Riesenfeld-invariants theory, which is available for arbitrary driving protocols. The role of the Lewis-Riesenfeld invariants is to help us bypass the time-ordering obstacle in expanding the propagator of the free dynamics, such that the Lindblad operators in our driven Markovian master equation can be determined easily. We also illustrate that, for the driven open quantum systems, the spontaneous emission and the thermal excitation induce the transitions between eigenstates of the Lewis-Riesenfeld invariant, but not the system Hamiltonian's. As an example, we present the driven Markovian master equation for a driven two-level system coupled to a heat reservoir. By comparing to the exactly solvable models, the availability of the driven Markovian master equation is verified. Meanwhile, the adiabatic limit and inertial limit of the driven Markovian master equation are also discussed, which result in the same Markovian master equations as those presented before in the corresponding limits.

Ting Yu, Lajos Diósi, Nicolas Gisin +1 more

Vittorio Gorini, Alberto Frigerio, Maurizio Verri +2 more

Shuang Cong

Based on the exact non-Markovian system dynamic equation about the reduced density matrix of quantum system,which is a non-closed,unequal in time,integral-differential equation,a closed,equal in time,differential Markovian master equation was derived about the reduced density matrix of quantum system by means of Born approximation and Markov approximation.The Lindblad form of the Markovian master equation,GKS expression for the convenience of testing positivity,Bloch sphere expression for single qubit system,Kraus expression describing dissipative quantum system without specific information of environment were analyzed respectively.Four kinds of Markov approximations that can remove the non-Markovian property were compared.The post-Markovian master equation was analyzed that can meet the perfect requirements of dissipative dynamic when the Markov approximation is not suitable to the open quantum system.When energy exchange existed between the heat bath and quantum system,and the total system composed of the bath and the quantum system has a conservation of energy,the dynamic equation of open quantum system was presented when the bath does not have a constant state,and the Markovian master equation was derived by the Markov approximation.

Wei-Min Zhang

Tanmay Saha, Sahil Sahil, K. P. Athulya +1 more

We derive a completely positive post-Markovian master equation (PMME) from a microscopic Markovian collisional model framework, incorporating bath memory effects via a probabilistic single-shot measurement approach. This phenomenological master equation is both analytically solvable and numerically tractable. Depending on the choice of the memory kernel function, the PMME can be reduced to the exact Nakajima-Zwanzig equation or the Markovian master equation, enabling a broad spectrum of dynamical behaviors. We also investigate thermalization using the derived equation, revealing that the post-Markovian dynamics accelerates the thermalization process, exceeding rates observed within the Markovian framework. Our approach solidifies the assertion that "collisional models can simulate any open quantum dynamics", underscoring the versatility of the models in realizing open quantum systems.