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Quantum Theory and Its Stochastic Limit

Authors: Accardi, Luigi, Lu, Yun Gang, Volovich, Igor

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  • ISBN 978-3-662-04929-7
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About this book

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.

Reviews

"The authors have produced a very important and detailed book on the subject of the stochastic limit of quantum field theory. In particular, they formulate the stochastic limit in the framework of an algebraic central limit theory using the sort of scaling limits encountered in quantum transport phenomena. [...] The book is well written and covers many related problems [...] The audience will be mathematical and theoretical physicists. The authors are to be congratulated for showing the power and range of application of quantum probability to quantum physics." (Mathematical Reviews 2003h)


Table of contents (16 chapters)

Table of contents (16 chapters)

Buy this book

eBook 117,69 €
price for Spain (gross)
  • ISBN 978-3-662-04929-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 166,39 €
price for Spain (gross)
  • ISBN 978-3-540-41928-0
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 145,78 €
price for Spain (gross)
  • ISBN 978-3-642-07543-8
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Quantum Theory and Its Stochastic Limit
Authors
Copyright
2002
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-04929-7
DOI
10.1007/978-3-662-04929-7
Hardcover ISBN
978-3-540-41928-0
Softcover ISBN
978-3-642-07543-8
Edition Number
1
Number of Pages
XX, 474
Topics

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