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Quantum Theory and Its Stochastic Limit

  • Luigi Accardi
  • Igor Volovich
  • Yun Gang Lu

Table of contents

  1. Front Matter
    Pages I-XX
  2. Statement of the Problem and Simplest Models

    1. Front Matter
      Pages 1-1
    2. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 3-55
    3. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 57-84
    4. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 85-111
    5. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 113-151
    6. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 153-203
    7. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 205-218
    8. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 219-236
    9. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 237-246
    10. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 247-254
    11. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 255-260
    12. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 261-282
  3. Strongly Nonlinear Regimes

    1. Front Matter
      Pages 283-283
    2. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 285-350
    3. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 351-368
    4. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 369-390
  4. Estimates and Proofs

    1. Front Matter
      Pages 391-391
    2. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 393-451
    3. Luigi Accardi, Igor Volovich, Yun Gang Lu
      Pages 453-460
  5. Back Matter
    Pages 461-473

About this book

Introduction

The subject of this book is a new mathematical technique, the stochastic limit developed for solving nonlinear problems in quantum theory involving systems with infinitely many degrees of freedom (typically quantum fields or gases in the thermodynamic limit). This technique is condensed into some easily applied rules (called "stochastic golden rules") which allow to single out the dominating contributions to the dynamical evolution of systems in regimes involving long times and small effects. In the stochastic limit the original Hamiltonian theory is approximated using a new Hamiltonian theory which is singular. These singular Hamiltonians still define a unitary evolution and the new equations give much more insight into the relevant physical phenomena than the original Hamiltonian equations. Especially, one can explicitly compute multi-time correlations (e.g. photon statistics) or coherent vectors, which are beyond the reach of typical asymptotic techniques as well as deduce in the Hamiltonian framework the widely used stochastic Schrödinger equation and the master equation. This monograph is well suited as a textbook in the emerging field of stochastic limit techniques in quantum theory.

Keywords

Collection Phenomena Interacting Fock Space QED Quantum Noise Quantum Probability Stochastic Golden Rule Stochastic Limit correlation statistics

Authors and affiliations

  • Luigi Accardi
    • 1
  • Igor Volovich
    • 2
  • Yun Gang Lu
    • 3
  1. 1.Centro Vito Volterra, Facolta di EconomiaUniversità di RomaRomaItaly
  2. 2.Steklov Mathematical InstituteMoscow, GSP-1Russia
  3. 3.Dipartimento di MatematicaUniversità degli Studi di BariBariItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04929-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07543-8
  • Online ISBN 978-3-662-04929-7
  • Buy this book on publisher's site