Open Quantum Systems I

The Hamiltonian Approach

  • Stéphane Attal
  • Alain Joye
  • Claude-Alain Pillet
Part of the Lecture Notes in Mathematics book series (LNM, volume 1880)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Claude-Alain Pillet
    Pages 107-182
  3. Marco Merkli
    Pages 183-233
  4. Vojkan Jakšić
    Pages 235-312
  5. Back Matter
    Pages 313-333

About this book

Introduction

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.

Keywords

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'Hères CedexFrance
  3. 3.CPT-CNRS, UMR 6207Université du Sud Toulon-VarLa Garde CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/b128449
  • Copyright Information Springer 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-30991-8
  • Online ISBN 978-3-540-33922-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692