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.