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Phase covariant qubit dynamics describes an evolution of a two-level system under simultaneous action of pure dephasing, energy dissipation, and energy gain with time-dependent rates $\gamma_z(t)$, $\gamma_-(t)$, and $\gamma_+(t)$,…

Understanding how a quantum many-body state is maintained stably as a nonequilibrium steady state is of fundamental and practical importance for exploration and exploitation of open quantum systems. We establish a general equivalent…

We present a basic introduction to the dynamics of open quantum systems based on local-in-time master equations. We characterize the properties of time-local generators giving rise to legitimate completely positive trace preserving quantum…

We treat several key stochastic equations for non-Markovian open quantum system dynamics and present a formalism for finding solutions to them via canonical perturbation theory, without making the Born-Markov or rotating wave approximations…

The state-dependent diffusion, which concerns the Brownian motion of a particle in inhomogeneous media has been described phenomenologically in a number of ways. Based on a system-reservoir nonlinear coupling model we present a microscopic…

We study the asymptotic behavior of continuous-time, time-inhomogeneous Markovian quantum dynamics in a stationary random environment. Under mild faithfulness and eventually positivity-improving assumptions, the normalized evolution…

Motivated by networked systems in random environment and controlled hybrid stochastic dynamic systems, this work focuses on modeling and analysis of a class of switching diffusions consisting of continuous and discrete components. Novel…

Open quantum systems exhibit a range of novel out-of-equilibrium behavior due to the interplay between coherent quantum dynamics and dissipation. Of particular interest in these systems are driven, dissipative transitions, the emergence of…

Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the…

Semi-Markov processes represent a well known and widely used class of random processes in classical probability theory. Here, we develop an extension of this type of non-Markovian dynamics to the quantum regime. This extension is…

An asymmetric exclusion process comprising positive particles, negative particles and vacancies is introduced. The model is defined on a ring and the dynamics does not conserve the number of particles. We solve the steady state exactly and…

A completely positive master equation describing quantum dissipation for a Brownian particle is derived starting from microphysical collisions, exploiting a recently introduced approach to subdynamics of a macrosystem. The obtained equation…

We discuss dynamical response theory of driven-dissipative quantum systems described by Markovian Master Equations generating semi-groups of maps. In this setting thermal equilibrium states are replaced by non-equilibrium steady states and…

High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…

Any tripartite state which saturates the strong subadditivity relation for the quantum entropy is defined as the Markov state.A tripartite pure state describing an open system, its environment and their purifying system isa pure Markov…

We study a class of multipartite open quantum dynamics for systems of arbitrary number of qubits. The non-Markovian quantum master equation can involve arbitrary single or multipartite and time-dependent dissipative coupling mechanisms,…

We extend quantum trajectory theory to encompass the evolution of a large class of open quantum systems interacting with an environment at {arbitrary coupling strength}. Specifically, we prove that general time-local quantum master…

We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and…

The study of open quantum systems is important for fundamental issues of quantum physics as well as for technological applications such as quantum information processing. The interaction of a quantum system with it's environment is usually…

Abstract Simulating mixed-state evolution in open quantum systems is crucial for various chemical physics, quantum optics, and computer science applications. These simulations typically follow the Lindblad master equation dynamics. An…