Quantum Theory and Its Stochastic Limit / Edition 1

Quantum Theory and Its Stochastic Limit / Edition 1

by Luigi Accardi, Yun Gang Lu, Igor Volovich
     
 

The subject of this book is a new mathematical technique, the shastic 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 "shastic golden rules") which allow to

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Overview

The subject of this book is a new mathematical technique, the shastic 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 "shastic 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 shastic 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 shastic Schrödinger equation and the master equation. This monograph is well suited as a textbook in the emerging field of shastic limit techniques in quantum theory.

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Product Details

ISBN-13:
9783642075438
Publisher:
Springer Berlin Heidelberg
Publication date:
12/07/2010
Edition description:
Softcover reprint of hardcover 1st ed. 2002
Pages:
474
Product dimensions:
1.00(w) x 9.21(h) x 6.14(d)

Table of Contents

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 Shastic Limit.- 9. Functional Integral Approach to the Shastic Limit.- 10. Low-Density Limit: The Basic Idea.- 11. Six Basic Principles of the Shastic 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.

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