The present book provides a general framework for studying quantum and classical dynamical systems, both finite and infinite, conservative and dissipative. Special attention is paid to the use of statistical and geometrical techniques, such as multitime correlation functions, quantum dynamical entropy, and non-commutative Lyapunov exponents, for systems with a complex evolution. The material is presented in a concise but self-contained and mathematically friendly way with main ideas introduced and illustrated by numerous examples which are directly connected to the relevant physics.

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...