© 2006

Open Quantum Systems II

The Markovian Approach

  • Stéphane Attal
  • Alain Joye
  • Claude-Alain Pillet

Part of the Lecture Notes in Mathematics book series (LNM, volume 1881)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Luc Rey Bellet
    Pages 1-39
  3. Luc Rey-Bellet
    Pages 41-78
  4. Stéphane Attal
    Pages 79-147
  5. Back Matter
    Pages 221-243

About this book


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.

In Volume I the Hamiltonian description of quantum open systems is discussed. This includes an introduction to quantum statistical mechanics and its operator algebraic formulation, modular theory, spectral analysis and their applications to quantum dynamical systems.

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.

Volume III is devoted to recent developments and applications. The topics discussed include the non-equilibrium properties of open quantum systems, the Fermi Golden Rule and weak coupling limit, quantum irreversibility and decoherence, qualitative behaviour of quantum Markov semigroups and continual quantum measurements.


Markov process Quantum dynamical systems algebra dynamical systems equation mathematical physics non-equilibrium statistical mechanics operator algebras quantum noises spectral theory stochastic differential equation

Editors and affiliations

  • Stéphane Attal
    • 1
  • Alain Joye
    • 2
  • Claude-Alain Pillet
    • 3
  1. 1.Institut Camille JordanUniversité Claude Bernard Lyon 1Villeurbanne CedexFrance
  2. 2.Institut FourierUniversité de Grenoble 1Saint-Martin d'Héres CedexFrance
  3. 3.CPT-CNRS, UMR 6207Université du Sud Toulon-VarLa Garde CedexFrance

Bibliographic information

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