Dissipation of energy and the loss of quantum coherence are the main hallmarks of open quantum systems, which refers to a system coupled to many degrees of freedom of an uncontrollable environment. Due to this coupling, the system gradually loses its quantum properties and behaves more "classical". On the other hand, in the regime of large quantum numbers, semiclassical theory helps to understand quantum systems using information about their classical limit, allowing to observe interference effects between classical trajectories. This thesis aims to use the semiclassical approach to study open quantum systems. In this work, a novel notion of temperature for strongly coupled systems is developed. as well as a semiclassical treatment of decoherence in classically chaotic systems. Further, a new approach to catch interference between dissipative classical trajectories is studied, which opens the possibility to observe path interference in quantum thermodynamics.

Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. From a mathematical point of view, it involves a large body of knowledge. Significant progress in the understanding of such systems has been made during the last decade. These books present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. In Volume I the Hamiltonian description of quantum open systems is discussed. This includes an introduction to quantum statistical mechanics and its operator algebraic formulation, modular theory, spectral analysis and their applications to quantum dynamical systems. Volume II is dedicated to the Markovian formalism of classical and quantum open systems. A complete exposition of noise theory, Markov processes and stochastic differential equations, both in the classical and the quantum context, is provided. These mathematical tools are put into perspective with physical motivations and applications. Volume III is devoted to recent developments and applications. The topics discussed include the non-equilibrium properties of open quantum systems, the Fermi Golden Rule and weak coupling limit, quantum irreversibility and decoherence, qualitative behaviour of quantum Markov semigroups and continual quantum measurements.

This book discusses the elementary ideas and tools needed for open quantum systems in a comprehensive manner. The emphasis is given to both the traditional master equation as well as the functional (path) integral approaches. It discusses the basic paradigm of open systems, the harmonic oscillator and the two-level system in detail. The traditional topics of dissipation and tunneling, as well as the modern field of quantum information, find a prominent place in the book. Assuming a basic background of quantum and statistical mechanics, this book will help readers familiarize with the basic tools of open quantum systems. Open quantum systems is the study of quantum dynamics of the system of interest, taking into account the effects of the ambient environment. It is ubiquitous in the sense that any system could be envisaged to be surrounded by its environment which could naturally exert its influence on it. Open quantum systems allows for a systematic understanding of irreversible processes such as decoherence and dissipation, of the essence in order to have a correct understanding of realistic quantum dynamics and also for possible implementations. This would be essential for a possible development of quantum technologies.

In this volume the fundamental theory of open quantum systems is revised in the light of modern developments in the field. A unified approach to the quantum evolution of open systems is presented by merging concepts and methods traditionally employed by different communities, such as quantum optics, condensed matter, chemical physics and mathematical physics. The mathematical structure and the general properties of the dynamical maps underlying open system dynamics are explained in detail. The microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions, is also discussed. Because of the step-by-step explanations, this work is a useful reference to novices in this field. However, experienced researches can also benefit from the presentation of recent results.

Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.

Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.

This monograph provides graduate students and also professional researchers aiming to understand the dynamics of open quantum systems with a valuable and self-contained toolbox. Special focus is laid on the link between microscopic models and the resulting open-system dynamics. This includes how to derive the celebrated Lindblad master equation without applying the rotating wave approximation. As typical representatives for non-equilibrium configurations it treats systems coupled to multiple reservoirs (including the description of quantum transport), driven systems and feedback-controlled quantum systems. Each method is illustrated with easy-to-follow examples from recent research. Exercises and short summaries at the end of every chapter enable the reader to approach the frontiers of current research quickly and make the book useful for quick reference.

Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.

This book presents four survey articles on various aspects of open quantum systems, specifically addressing quantum Markovian processes, Feller semigroups and nonequilibrium dynamics. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen, Germany. Starting from basic notions, the authors of these lecture notes accompany the reader on a journey up to the latest research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. Though the book is primarily addressed to graduate students, it will also be of interest to researchers.

Usually open quantum systems are considered to be under the influence of noise and therefore faulty. On the other hand, a controlled system is regarded as something stable and predictable. It is often neglected, that the two aspects are very closely related. A perfectly isolated quantum system will not be subject to environmental influences, but this makes it also impossible to interact with it in any manner. Controlling and measuring such a system is impossible and therefore of no technical relevance.Every system used in any technological device therefore must be in contact with its environment. The question, which is the starting point of this thesis is whether it is possible to not only control a system despite of its contact to some environment, but whether there are cases, where this interaction can be necessary, or at least helpful for certain control tasks.The first part of the thesis focuses on such a task, namely the purification of a qubit. Here the environment is essential, in order to serve as an entropy sink. The simplicity of the chosen model allowed us to derive the necessary time for the purification process analytically for arbitrary controls and interactions. This is helpful for architectures, where implementations of various configurations is possible.The second half of the thesis covers more methodogical work. In the example of the qubit reset, we see that the necessary time to perform the task is determined by the coupling between the system and environment. In order to perform such tasks fast, we have to develop a framework, which allows to analyse systems beyond the usual weak-coupling limit. There exists so far no general method for the propagation of such systems, which also allows for thermalisation. The surrogate Hamiltonian method is a promising candidate to capture dynamics beyond the weak-coupling limit and its extension, the stochastic surrogate Hamiltonian, allows for thermalisation. We expand the stochastic surrogate Hamiltonian by introducing a new method of performing stochastic swaps. This method is then tested on a simple example model.