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The paper shortly presents the role of Stochastic Processes Theory in the present day Quantum Theory, and the relation to Operational Quantum Physics. The dynamics of an open quantum system is studied on a usual example from Quantum Optics,…

We investigate the transport of a single excitation through a chain of weakly coupled subunits. At both ends the chain is exposed to baths which are incorporated by means of a master equation in Lindblad form. This master equation is solved…

We consider a two-dimensional quantum control system evolving under an entropy-increasing irreversible dynamics in the semigroup form. Considering a phenomenological approach to the dynamics, we show that the accessibility property of the…

We study the evolution of an open quantum system using a Langevin unravelling of the density matrix evolution over matrix product states. As the strength of coupling to and temperature of the environment is increased, we find a transition…

We give sufficient conditions for the existence of positive travelling wave solutions for multi-dimensional autonomous reaction-diffusion systems with distributed delay. To prove the existence of travelling waves, we give an abstract…

Steady-state manifolds of open quantum systems, such as decoherence-free subspaces and noiseless subsystems, are of great practical importance to the end of quantum information processing. Yet, it is a difficult problem to find steady-state…

The mean evolution of an open quantum system in continuous time is described by a time continuous semigroup of quantum channels (completely positive and trace-preserving linear maps). Baumgartner and Narnhofer presented a general…

In the classical domain, it is well-known that divisibility does not imply that a stochastic process is Markovian. However, for quantum processes, divisibility is often considered to be synonymous with Markovianity. We show that completely…

We study a general class of translation invariant quantum Markov evolutions for a particle on $\bbZ^d$. The evolution consists of free flow, interrupted by scattering events. We assume spatial locality of the scattering events and…

We consider a closed quantum system subject to a stochastic resetting process. The generic expression for the resulting density operator is formulated for arbitrary resetting dynamics, fully characterised by the distribution of times…

During the last ten years, the studies on non-Markovian open system dynamics has become increasingly popular and having contributions from diverse set of research communities. This interest has arisen due to fundamental problematics how to…

These notes are a short introduction to the mathematical theory of open quantum systems. They are meant to serve as an entry point into a broad research area which has applications across the quantum sciences dealing with systems subjected…

Non-Markovian dynamics is studied for two interacting quibts strongly coupled to a dissipative bosonic environment. For the first time, we have derived the non-Markovian quantum state diffusion (QSD) equation for the coupled two-qubit…

Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of…

A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular…

A prominent tool to study the dynamics of open quantum systems is the reduced density matrix. Yet, approaching open quantum systems by means of state vectors has well known computational advantages. In this respect, the physical meaning of…

"Quantum mechanics must be regarded as open systems. On one hand, this is due to the fact that, like in classical physics, any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a…

The reduced density matrix that characterises the state of an open quantum system is a projection from the full density matrix of the quantum system and its environment, and there are many full density matrices consistent with a given…

We investigate dissipation-driven topological phase transitions in one-dimensional quantum open systems governed by the Lindblad equation with linear dissipation operators, which ensure the density matrix retains its Gaussian form…

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…