Well suited as a textbook in the emerging field of stochastic limit, which is a new mathematical technique developed for solving nonlinear problems in quantum theory.
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Editorial Reviews
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"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)
From the Back Cover
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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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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boson field, polynomial interactions, complementary material, universality class principle, conjugated vertices, stochastic resonance principle, stochastic golden rule, operator transport coefficient, same stochastic limit, quantum transport coefficient, double integral lemma, noncrossing pair partition, photon splitting cascades, first vanishing theorem, iterated series solution, normal ordering theorem, iterated series expansion, generalized susceptivities, quantum white noise, interacting commutation relations, annihilation block, second vanishing theorem, stochastic limit approach, rescaled fields, noncrossing diagrams Key Phrases - Capitalized Phrases (CAPs): (learn more)
Particles Interacting, Open Systems, Analytical Theory of Feynman Diagrams, Spin-Boson Systems, Quantum Fields, Chronological Product Approach, Field-Field Interactions, Canonical Forms, The Anderson Model, The Factorization Theorem, Time-Ordered Product Approach, Term Theorem, The Vanishing of the Crossing Diagrams, Low-Density Limit, The Second Multiple-Simplex Theorem, The Connected Component Theorem, The Quantum Transport Coefficient, The Filtering Problem, Fermi Fock, Theory of Distributions, The Fermi Block Theorem, Generalized White Noises, Multiplicative Coupling, Non-Time-Consecutive Terms, Gauge-Invariant Case Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
boson field, polynomial interactions, complementary material, universality class principle, conjugated vertices, stochastic resonance principle, stochastic golden rule, operator transport coefficient, same stochastic limit, quantum transport coefficient, double integral lemma, noncrossing pair partition, photon splitting cascades, first vanishing theorem, iterated series solution, normal ordering theorem, iterated series expansion, generalized susceptivities, quantum white noise, interacting commutation relations, annihilation block, second vanishing theorem, stochastic limit approach, rescaled fields, noncrossing diagrams Key Phrases - Capitalized Phrases (CAPs): (learn more)
Particles Interacting, Open Systems, Analytical Theory of Feynman Diagrams, Spin-Boson Systems, Quantum Fields, Chronological Product Approach, Field-Field Interactions, Canonical Forms, The Anderson Model, The Factorization Theorem, Time-Ordered Product Approach, Term Theorem, The Vanishing of the Crossing Diagrams, Low-Density Limit, The Second Multiple-Simplex Theorem, The Connected Component Theorem, The Quantum Transport Coefficient, The Filtering Problem, Fermi Fock, Theory of Distributions, The Fermi Block Theorem, Generalized White Noises, Multiplicative Coupling, Non-Time-Consecutive Terms, Gauge-Invariant Case Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
10
books
cite this book:
See all 10 books citing this book
- Quantum Probability and Infinite-Dimensional Analysis: Proceedings of the Conference, Burg (Spreewald), Germany, 15-20 March 2001 (Qptpq Quantum Probability and White Noise Analysis, 15) by W. Freudenberg on page 27, page 56, and page 74
- Fundamental Aspects of Quantum Physics: Proceedings of the Japan-Italy Joint Workshop on Quantum Open Systems, Quantum Chaos and Quantum Measurement : ... Probability and White Noise Analysis, 17) by Quantum Chaos and Japan-Italy Joint Workshop on Quantum Open Systems on page 23
- Proceedings of the International Conference on Stochastic Analysis and Applications: Hammamet, 2001 by Sergio Albeverio on page 182
- The Physics of Communication: Proceedings of the Xxii Solvay Conference on Physics Delphi Lamia, Greece 24 - 29 November 2001 by I. Antoniou on page 173
- Non-Commutativity, Infinite Dimensionality and Probability at the Crossroads: Proceedings of the Rims Workshop on Infinite-Dimensional Analysis and ... Quantum Probability & White Noise Analysis) by Obata Nobuaki on page 94
See all 10 books citing this book
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