Open Quantum Systems I

Stéphane Attal (1) , Alain Joye (2) , Claude-Alain Pillet (3, 4, 5)

1 ICJ - Institut Camille Jordan
2 IF - Institut Fourier
3 CPT - E5 Physique statistique et systèmes complexes
4 FRUMAM - Fédération de Recherche des Unités de MAthématiques de Marseille
5 CPT - Centre de Physique Théorique - UMR 7332

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. 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.

Mots clés: spectral theory; Quantum dynamical systems; non-equilibrium statistical mechanics; operator algebras; quantum noises

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Physique Quantique [quant-ph]; Analyse fonctionnelle [math.FA]; Algèbres d'opérateurs [math.OA]; Probabilités [math.PR]; Systèmes dynamiques [math.DS]

Stéphane Attal, Alain Joye, Claude-Alain Pillet (Dir.). Open Quantum Systems I: The Hamiltonian approach. Springer/Lecture Notes in Mathematics 1880, pp.1-329, 2006, 978-3-540-30991-8. ⟨10.1007/b128449⟩. ⟨hal-01588821⟩