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Quantum probability communications / / Stephane Attal, J.Martin Lindsay
| Quantum probability communications / / Stephane Attal, J.Martin Lindsay |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore ; ; London, : World Scientific, 2003 |
| Descrizione fisica | 1 online resource (294 p.) |
| Disciplina | 530.12 |
| Altri autori (Persone) |
LindsayJ. Martin
AttalS (Stephane) |
| Collana | QP-PQ |
| Soggetto topico |
Probabilities
Quantum theory Stochastic processes Markov processes |
| ISBN |
1-281-92814-3
9786611928148 981-277-542-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONTENTS; CONTENTS OF QPC XI; PREFACE for QPC Volumes XI & XII; INTEGRAL-SUM KERNEL OPERATORS; 0. INTRODUCTION; 1. FINITE POWER SETS; 1.1. Some products on F(Γ).; 1.2. Product functions.; 1.3. Guichardet Space.; 2. INTEGRAL-SUM CONVOLUTIONS; 2.1. Duality Transforms.; 2.2. Formal Derivation.; 2.3. Basic Estimate.; 3. QUANTUM WIENER INTEGRALS; 4. INTEGRAL-SUM KERNEL OPERATORS; 4.1. Basic Estimate.; 4.2. Uniqueness of the kernel.; 4.3. Reconstruction of kernel from operator.; 4.4. Algebras of integral-sum kernel operators.; 4.5. Four argument integral-sum kernels.; 4.6. Matrix-valued kernels.
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. 2.2.2. Definition of von Neumann algebras. |
| Record Nr. | UNINA-9910819476003321 |
| Singapore ; ; London, : World Scientific, 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Quantum probability communications [[electronic resource] ] : QP-PQ . Volume 11 / / managing editors, Stephane Attal, J. Martin Lindsay
| Quantum probability communications [[electronic resource] ] : QP-PQ . Volume 11 / / managing editors, Stephane Attal, J. Martin Lindsay |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | New Jersey, : World Scientific, c2003 |
| Descrizione fisica | 1 online resource (314 p.) |
| Disciplina | 530.12 |
| Altri autori (Persone) |
AttalS (Stephane)
LindsayJ. Martin |
| Collana | Quantum probability communications |
| Soggetto topico |
Probabilities
Quantum theory |
| ISBN |
1-281-92813-5
9786611928131 981-277-541-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""0. INTRODUCTION""""1. LARGE MATRICES""; ""2. FREE RANDOM VARIABLES""; ""3. FREE CONVOLUTION""; ""4. THEORY OF ADDITION OF FREE RANDOM VARIABLES""; ""5. SPEICHER'S COMBINATORIAL APPROACH TO FREENESS""; ""6. SOME FURTHER TOPICS""; ""ACKNOWLEDGMENT""; ""REFERENCES""; ""CONDITIONAL EXPECTATIONS ON VON NEUMANN ALGEBRAS""; ""0. INTRODUCTION""; ""1. THE NONCOMMUTATIVE CONDITIONAL EXPECTATION""; ""2. GENERALISED CONDITIONAL EXPECTATIONS""; ""3. CANONICAL STATE EXTENSIONS""; ""4. STOCHASTIC TRANSITIONS FOR VON NEUMANN ALGEBRAS""
""5. AN APPLICATION: MARKOVIANITY FOR STATES ON MUTUALLY COMMUTING VON NEUMANN ALGEBRAS""""REFERENCES""; ""CLASSICAL PROBABILITY THEORY AN OUTLINE OF STOCHASTIC INTEGRALS AND DIFFUSIONS""; ""First Lecture (One hour)""; ""BROWNIAN MOTIONS""; ""FURTHER READING""; ""Second Lecture (One hour)""; ""MARTINGALES""; ""FURTHER READING""; ""Third Lecture (One and a half hour)""; ""SEMIMARTINGALES AND STOCHASTIC INTEGRATION""; ""FURTHER READING""; ""Fourth Lecture (One and a half hour)""; ""THE CHANGE OF VARIABLE FORMULA; STOCHASTIC DIFFERENTIAL EQUATIONS""; ""FURTHER READING"" ""Fifth Lecture (One and a half hour)""""MARKOV PROCESSES, DIFFUSIONS AND FLOWS""; ""FURTHER READING""; ""Sixth Lecture (One and a half hour)""; ""ITERATED STOCHASTIC INTEGRALS, STRUCTURE EQUATIONS""; ""FURTHER READING""; ""ACKNOWLEDGEMENTS""; ""QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS""; ""0. INTRODUCTION""; ""1. QUANTUM STOCHASTIC CALCULUS""; ""2. TIME REVERSAL AND DUAL COCYCLES""; ""3. QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS""; ""4. MINIMAL QUANTUM DYNAMICAL SEMIGROUP""; ""5. THE RESOLVENT OF THE MINIMAL SEMIGROUP""; ""6. CONSERVATIVITY""; ""7. UNITARY SOLUTIONS"" ""8. INNER QUANTUM FLOWS"" |
| Record Nr. | UNINA-9910824440203321 |
| New Jersey, : World Scientific, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||