In this text the authors develop quantum dynamics of open systems for a wide class of irreversible processes starting from the concept of completely positive semigroups. This unified approach makes the material easily accessible to non-specialists and provides an easy access to practical applications. Written for graduate students, the book presents a wealth of useful examples; in particular, models of unstable and N-level systems are treated systematically and in considerable detail including new types of generated Bloch-equations. The general theory is extensively summarized from abstract dynamical maps to those obtained by a reduction of Hamiltonian dynamics under a Markovian approximation. Various methods of determining semigroup generators and the corresponding master equations are discussed including time-dependent and nonlinear generators. Further topics treated are a generalized H-theorem, quantum detailed balance and return to equilibrium, discrete quantum Boltzmann equation, nonlinear Schro dinger equation, spin relaxation by spin waves, entropy production and its generalization by a measure of irreversibiblity. In this text the authors develop quantum dynamics of open systems for a wide class of irreversible processes starting from the concept of completely positive semigroups. This unified approach makes the material easily accessible to non-specialists and provides an easy access to practical applications. Written for graduate students, the book presents a wealth of useful examples; in particular, models of unstable and N-level systems are treated systematically and in considerable detail including new types of generated Bloch-equations. The general theory is extensively summarized from abstract dynamical maps to those obtained by a reduction of Hamiltonian dynamics under a Markovian approximation. Various methods of determining semigroup generators and the corresponding master equations are discussed including time-dependent and nonlinear generators. Further topics treated are a generalized H-theorem, quantum detailed balance and return to equilibrium, discrete quantum Boltzmann equation, nonlinear Schrödinger equation, spin relaxation by spin waves, entropy production and its generalization by a measure of irreversibiblity Contents: General Theory and Applications to Unstable Particles: General Theory: Introduction. Completely positive dynamical semigroups. Hamiltonian models and Markovian approximation. Extensions of the formalism. A system of N 2-level atoms Quantum Dynamical Semigroups for Unstable Particles: Introduction. Damped and Pumped Quantum Harmonic Oscillator. Models of unstable particles Appendices References N-Level Systems and Applications to Spectroscopy: Introduction. General structure of quantum Markovian master equations for N-level systems. Two-level systems: Generalized magnetic or optical Bloch-equations. Three-level systems. Comparison with common versions of master equations. Open quantum systems with non-constant relaxation in time-dependent external fields. Determination of relaxation parameters from first principles. Entropy and irreversibility. Conclusion Appendices References. Reinvigorated by advances and insights, in particular from the active fields of quantum information and computing, the quantum theory of irreversible processes has recently attracted growing attention. This volume introduces the very basic concepts of semigroup dynamics of open quantum systems and reviews a variety of modern applications. The present book, originally published as Vol. 286 (1987) in Lecture in Physics, has been newly typeset, revised and corrected and also expanded to include a review on recent developments
