Open quantum systems. The Primas lectures. (Q847991)

The book originates from two courses given by Hans Primas at the ETH Zürich in the early 80s, aiming to give a general theoretical introduction to spectroscopy, providing a background in signal theory of thermal quantum systems. The book is divided into six chapters: 1) Information thermostatics; 2) Statistical operators for the description of open quantum systems; 3) Dynamics of open quantum systems; 4) Linear response of thermal quantum systems; 5) First example: a simple nuclear resonance experiment; 6) Second example: Fermi's golden rule and Einstein's transition probabilities. The book is concerned with an introduction to fundamental ideas of open quantum systems theory, having in mind applications relevant for spectroscopy. After considering Jaynes' information-theoretic approach to the derivation of canonical ensembles, the authors introduce the notion of statistical operator and use it for the description of an open system, taking as benchmark dynamics the one given by the Karplus-Schwinger equation. Linear response theory is treated in detail, paying great attention to the mathematical background of complex analysis. Examples considering the dynamics of a two-level system are discussed in detail, also considering the Bloch equations and their connection to the theory of quantum dynamical semigroups. A critical discussion of Fermi's golden rule, considering in particular Einstein's transition probabilities for spontaneous and stimulated emission, closes the book. The topics are presented in a fresh, direct style, and despite the original lectures are by now 30 years old, many aspects of the presentation are quite modern. The authors pursue throughout a critical attitude, discussing at length possible controversial conceptual issues, clearly stating their own standpoint. A non-trivial feature is the broad range of interests covered, indeed the presentation is at many points very close to real-life experimental situations. At the same time great attention is paid to the connection with the relevant mathematics, e.g., in the treatment of linear response theory, or in considering the notion of complete positivity for quantum dynamical evolutions. Each chapter is closed by exercises which, according to the authors, could be solved using a program such as \texttt{Matlab}.