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"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…
We study the dynamics of states perturbatively expanded about a harmonic system of loop quantum cosmology, exhibiting a bounce. In particular, the evolution equations for the first and second order moments of the system are analyzed. These…
Quantum dynamics of the density operator in the framework of a single probability vector is analyzed. In this framework quantum states define a proper convex quantum subset in an appropriate simplex. It is showed that the corresponding…
This paper is devoted to the description of the evolution of states of quantum many-particle systems within the framework of a one-particle density operator, which enables to construct the kinetic equations in scaling limits in the presence…
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the…
The notion of "closed systems" in Quantum Mechanics is discussed. For this purpose, we study two models of a quantum-mechanical system $P$ spatially far separated from the "rest of the universe" $Q$. Under reasonable assumptions on the…
Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the…
Proper management of resources whose arrival and consumption are subject to environmental randomness is an intrinsic process in both natural and artificial systems. This phenomenon can be modeled as a queuing process whose arrival…
We consider the description of quantum noise within the framework of the standard Copenhagen interpretation of quantum mechanics applied to a composite system environment setting. Averaging over the environmental degrees of freedom leads to…
Dissipationless localized bound states of open quantum systems are significantly robust to decoherence and have potential applications in quantum technologies. In this work, the decoherence dynamics and dissipationless localized bound…
Quantum heat engines have undergone extensive studies over the last two decades. Simultaneously, the studies of the applications of stochastic resetting in various fields are on the rise. We explore the effect of stochastic resetting on the…
Stochastic unravelings represent a useful tool to describe the dynamics of open quantum systems and standard methods, such as quantum state diffusion (QSD), call for the complete positivity of the open-system dynamics. Here, we present a…
We study non-equilibrium dynamics of integrable and non-integrable closed quantum systems whose unitary evolution is interrupted with stochastic resets, characterized by a reset rate $r$, that project the system to its initial state. We…
We first introduce and discuss density operator interpretations of quantum theory as a special case of a more general class of interpretations, giving special attention to a version that we call the `atomic version'. We then review some…
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…
In this survey the possible approaches to the description of the evolution of states of quantum many-particle systems by means of the possible modifications of the density operator which kernel known as density matrix are considered. In…
The dynamics of open quantum systems is often solved by stochastic unravellings where the average over the state vector realizations reproduces the density matrix evolution. We focus on quantum jump descriptions based on the rate operator…
We consider Markovian open quantum systems subject to stochastic resetting, which means that the dissipative time evolution is reset at randomly distributed times to the initial state. We show that the ensuing dynamics is non-Markovian and…
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…
We design several examples of constrained, symmetric quantum circuit dynamics that generate non-equilibrium steady states. The qubit networks maintain local memory of the initial conditions and display inhomogeneous subsystem dynamics over…