Selected Aspects of Markovian and Non-Markovian Quantum Master Equations

Amel Aïssani, K. Lendi

Dariusz Chruściński

Some mathematical aspects of quantum evolution described by local in time master equations are discussed. We analyze the basic characterization of quantum evolution in terms of the corresponding dynamical map. Simple criteria which enable us to discriminate between Markovian and non-Markovian evolution are provided.

Abhaya S. Hegde, K. P. Athulya, Vijay Pathak +2 more

Master equations describing open quantum dynamics are typically first-order differential equations. When such dynamics brings the trajectories in state space of more than one initial state to the same point at finite instants in time, the generator of the corresponding master equation becomes singular while the dynamical map becomes noninvertible. The first-order, time-local, homogeneous master equations then fail to describe the dynamics beyond the singular point. Retaining time locality in the master equation necessitates a reformulation in terms of higher-order differential equations. We formulate a method to eliminate the divergent behavior of the generator by using a combination of higher-order derivatives of the generator with suitable weights and illustrate it with several examples. We also present a detailed study of the central spin model and we propose the average rate of information inflow in non-Markovian processes as a quantity that captures a different aspect of non-Markovian dynamics.

Alireza Shabani, Daniel A. Lidar

Miralem Sinanović, Alessandro Ciani, Shai Machnes +1 more

Open quantum systems are ubiquitous in nature and central to quantum technologies. A common description of their dynamics is given by the celebrated Lindblad master equation, which can be generalized to the non-Markovian scenario. In this work, we introduce the non-Markovian ensemble propagation (NMEP) method, which extends the Monte Carlo wave-function (MCWF) method to the non-Markovian case in a simple and general manner. We demonstrate its accuracy and effectiveness in a selection of examples, and compare the results with either analytic expressions or direct numerical integration of the master equation.

Ting Yu, Lajos Diósi, Nicolas Gisin +1 more