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We study quantum dynamics of many-qubit systems strongly coupled to a quantized electromagnetic cavity mode, in the presence of decoherence and dissipation for both fermions and cavity photons. The analytic solutions are derived for a broad…
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the dynamics of entanglement for a system consisting of two uncoupled harmonic oscillators interacting with a…
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…
Thermodynamics entails a set of mathematical conditions on quantum Markovian dynamics. In particular, strict energy conservation between the system and environment implies that the dissipative dynamical map commutes with the unitary system…
An oscillator with stochastic frequency is discussed as a model for evaluating the quantum coherence properties of a physical system. It is found that the choice of jump statistics has to be considered with care if unphysical consequences…
Investigations of quantum and mesoscopic thermodynamics force one to answer two fundamental questions associated with the foundations of statistical mechanics: (i) how does macroscopic irreversibility emerge from microscopic reversibility?…
Nonequilibrium states of closed quantum many-body systems defy a thermodynamic description. As a consequence, constraints such as the principle of equal a priori probabilities in the microcanonical ensemble can be relaxed, which can lead to…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
Stochastic unravelings of Lindblad-type master equations, such as stochastic Schr\"odinger equations (SSEs), provide powerful tools to model open quantum systems and continuous measurement processes. The same master equation can be…
Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum trajectory'' techniques corresponding to continuous measurement schemes, which solve the master equation by…
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable entanglement for a system consisting of two independent harmonic oscillators…
We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes.…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
We show how random unitary dynamics arise from the coupling of an open quantum system to a static environment. Subsequently, we derive a master equation for the reduced system random unitary dynamics and study three specific cases:…
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…
By exploiting the complexity intrinsic to quantum dynamics, quantum technologies promise a whole host of computational advantages. One such advantage lies in the field of stochastic modelling, where it has been shown that quantum stochastic…
We consider the quantum-to-classical transition for macroscopic systems coupled to their environments. By applying Born's Rule, we are led to a particular set of quantum trajectories, or an unravelling, that describes the state of the…
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…
The study of the physical properties of open quantum systems is at the heart of many present investigations which aim to describe their dynamical evolution, on theoretical ground and through physical realizations. Here we develop a…
Quantum coherence, rooted in the superposition principle of quantum mechanics, is a crucial quantum resource. Various measures, operational interpretations, and generalizations of quantum coherence have been proposed. In recent years, its…