Luigi Accardi, Yun Gang Lu, Igor Volovich

Quantum Theory and Its Stochastic Limit (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 474
• Erscheinungstermin: 14. März 2013
• Englisch
• ISBN-13: 9783662049297
• Artikelnr.: 53081557

Inhaltsangabe

1. Notations and Statement of the Problem.- 2. Quantum Fields.- 3. Those Kinds of Fields We Call Noises.- 4. Open Systems.- 5. Spin-Boson Systems.- 6. Measurements and Filtering Theory.- 7. Idea of the Proof and Causal Normal Order.- 8. Chronological Product Approach to the Stochastic Limit.- 9. Functional Integral Approach to the Stochastic Limit.- 10. Low-Density Limit: The Basic Idea.- 11. Six Basic Principles of the Stochastic Limit.- 12. Particles Interacting with a Boson Field.- 13. The Anderson Model.- 14. Field-Field Interactions.- 15. Analytical Theory of Feynman Diagrams.- 16. Term-by-Term Convergence.- References.

Rezensionen

From the reviews: MATHEMATICAL REVIEWS "The book is well written and covers many related problems; in particular, the section on filtering is worthy of mention. 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."

"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)