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This is a concise, pedagogical introduction to the dynamic field of open quantum systems governed by Markovian master equations. We focus on the mathematical and physical origins of the widely used Lindblad equation, its unraveling in terms…
A dynamical symmetry is employed to determine the structure of the quantum non-Markovian time-local master equation. Such a structure is composed from two components: scalar kinetic coefficients and the standard quantum Markovian operator…
Markovian master equations, often called Liouvillians or Lindbladians, are used to describe decay and decoherence of a quantum system induced by that system's environment. While a natural environment is detrimental to fragile quantum…
The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body…
Recent advances in quantum technologies and related experiments have created a need for highly accurate, versatile, and computationally efficient simulation techniques for the dynamics of open quantum systems. Long-lived correlation effects…
A wide class of non-Markovian completely positive master equations can be formulated on the basis of quantum collisional models. In this phenomenological approach the dynamics of an open quantum system is modeled through an ensemble of…
Both conservation laws and practical restrictions impose symmetry constraints on the dynamics of open quantum systems. In the case of time-translation symmetry, which arises naturally in many physically relevant scenarios, the quantum…
We analyze the Markovian dynamics of a quantum system involving the interaction of two quantized fields at finite temperature decay. Utilizing superoperator techniques and applying two non-unitary transformations, we reformulate the…
We address the microscopic derivation of a quantum master equation in Lindblad form for the dynamics of a massive test particle with internal degrees of freedom interacting through collisions with a background ideal gas. When either…
We provide a rigorous construction of Markovian master equations for a wide class of quantum systems that encompass quadratic models of finite size, linearly coupled to an environment modeled by a set of independent thermal baths. Our…
This work is concerned with determination of the steady-state structure of time-independent Lindblad master equations, especially those possessing more than one steady state. The approach here is to treat Lindblad systems as generalizations…
The theory of open quantum systems served as a tool to prepare entanglement at the beginning stage of quantum technology and more recently provides an important tool for state preparation. Dynamics given by time dependent Lindbladians are…
Realistic quantum mechanical systems are always exposed to an external environment. The presence of the environment often gives rise to a Markovian process in which the system loses information to its surroundings. However, many quantum…
The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the…
We investigate the dynamics of open quantum systems which are initially correlated with their environment. The strategy of our approach is to analyze how given, fixed initial correlations modify the evolution of the open system with respect…
The effect of PT-symmetry breaking in coupled systems with balanced gain and loss has recently attracted considerable attention and has been demonstrated in various photonic, electrical and mechanical systems in the classical regime. Here…
We construct a non-Markovian canonical dynamical map that accounts for systems correlated with the environment. The physical meaning of not completely positive maps is studied to obtain a theory of non-Markovian quantum dynamics. The…
Embedding non-Markovian open quantum dynamics into an enlarged Markovian space offers a powerful route to nonperturbative simulations, where the dynamics of the extended space can be governed by multiple distinct Markovian equations. We…
Open quantum system interacting with structured environment is important and manifests non- Markovian behavior, which was conventionally studied using quantum trajectory stochastic method. In this paper, by dividing the effects of the…
The state matrix $\rho$ for an open quantum system with Markovian evolution obeys a master equation. The master equation evolution can be unraveled into stochastic nonlinear trajectories for a pure state $P$, such that on average $P$…