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Quantum Probability Communications.
Lecture notes from a Summer School on Quantum Probability held at the University of Grenoble are collected in these two volumes of the QP-PQ series. The articles have been refereed and extensively revised for publication. It is hoped that both current and future students of quantum probability will...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore :
World Scientific Publishing Company,
2003.
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| Colección: | Qp-Pq: Quantum Probability & White Noise Analysis S.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- CONCLUSIONBIBLIOGRAPHICAL NOTES; REFERENCES; QUANTUM PROBABILITY APPLIED TO THE DAMPED HARMONIC OSCILLATOR; 1. THE FRAMEWORK OF QUANTUM PROBABILITY; 2. SOME QUANTUM MECHANICS; 3. CONDITIONAL EXPECTATIONS AND OPERATIONS; 4. SECOND QUANTISATION; 5. UNITARY DILATIONS OF SPIRALING MOTION; 6. THE DAMPED HARMONIC OSCILLATOR; REFERENCES; QUANTUM PROBABILITY AND STRONG QUANTUM MARKOV PROCESSES; 0. INTRODUCTION; I. Quantum Probability; 1. A COMPARATIVE DESCRIPTION OF CLASSICAL AND QUANTUM PROBABILITY; 2. THE ROLE OF TENSOR PRODUCTS OF HILBERT SPACES; 3. SOME BASIC OPERATORS ON FOCK SPACES
- 4. FROM URN MODEL TO CANONICAL COMMUTATION RELATIONSII. Quantum Markov Processes; 5. STOCHASTIC OPERATORS ON C*-ALGEBRAS; 6. STINESPRING'S THEOREM; 7. EXTREME POINTS OF THE CONVEX SET OF STOCHASTIC OPERATORS; 8. STINESPRING'S THEOREM IN TWO STEPS; 9. CONSTRUCTION OF A QUANTUM MARKOV PROCESS; 10. THE CENTRAL PART OF MINIMAL DILATION; 11. ONE PARAMETER SEMIGROUPS OF STOCHASTIC MAPS ON A C*-ALGEBRA; III. Strong Markov Processes; 12. NONCOMMUTATIVE STOP TIMES; 13. MARKOV PROCESS AT SIMPLE STOP TIMES; 14. MINIMAL MARKOV FLOW AT SIMPLE STOP TIMES
- 15. STRONG MARKOV PROPERTY OF THE MINIMAL FLOW FOR A GENERAL STOP TIME16. STRONG MARKOV PROPERTY UNDER A SMOOTHNESS CONDITION; 17. A QUANTUM VERSION OF DYNKIN'S LOCALIZATION FORMULA; ACKNOWLEDGEMENTS; REFERENCES; LIMIT PROBLEMS FOR QUANTUM DYNAMICAL SEMIGROUPS
- INSPIRED BY SCATTERING THEORY; 0. INTRODUCTION; 1. COMPARISON OF THE LARGE TIME BEHAVIOUR OF TWO SEMIGROUPS; 2. THE CLASSIFICATION OF STATES; 3. ERGODIC PROPERTIES OF QUANTUM DYNAMICAL SEMIGROUPS; 4. CONVERGENCE TOWARDS THE EQUILIBRIUM; ACKNOWLEDGEMENT; REFERENCES; A SURVEY OF OPERATOR ALGEBRAS; 0. COMPLEX BANACH ALGEBRAS
- 1. C*-ALGEBRAS1.1. Definition and first spectral properties.; 1.2. Adding a unit.; 1.3. First examples: abelian C*-aIgebras.; 1.4. Continuous functional calculus in C*-algebras.; 1.5. More examples: B(H) and its sub-C*-algebras.; 1.6. Order Structure, states, and t h e GNS construction.; 1.6.1. Positive elements and order in A.; 1.6.2. Dual order structure and states.; 1.6.3. GNS construction.; 2. VON NEUMANN ALGEBRAS; 2.1. Some topologies on B(H).; 2.1.1. Three natural topologies.; 2.1.2. The ideal L1(H); 2.2. von Neuman algebras.; 2.2.1. von Neumann bicommutant theorem.