Quantum probability & related topics:
This volume contains several surveys of important developments in quantum probability. The new type of quantum central limit theorems, based on the notion of free independence rather than the usual Boson or Fermion independence is discussed. A surprising result is that the role of the Gaussian for t...
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c1991
|
| Schriftenreihe: | QP-PQ
v. VI |
| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | This volume contains several surveys of important developments in quantum probability. The new type of quantum central limit theorems, based on the notion of free independence rather than the usual Boson or Fermion independence is discussed. A surprising result is that the role of the Gaussian for this new type of independence is played by the Wigner distribution. This motivated the introduction of new type of quantum independent increments noise, the free noise and the corresponding stochastic calculus. A further generalization, the ϖ-noises, is discussed. The free stochastic calculus is shown to be able to fit naturally into the general representation free calculus. The basic free are shown to be realized as non-adapted stochastic integrals with respect to the usual Boson white noises. Quantum noise on the finite difference algebra is expressed in terms of the usual Boson white noises. A new quantum way of looking at classical stochastic flows, in particular diffusions on Riemannian Manifolds is explained. Quantum groups are discussed from the point of view of possible applications to quantum probability. The applications of quantum probability to physics are surveyed |
| Beschreibung: | vii, 523 p. ill |
| ISBN: | 9789814360203 |
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| spelling | Quantum probability & related topics managing editor, L. Accardi ; editorial board, A. Frigerio ... [et. al] Quantum probability and related topic Singapore World Scientific Pub. Co. c1991 vii, 523 p. ill txt rdacontent c rdamedia cr rdacarrier QP-PQ v. VI This volume contains several surveys of important developments in quantum probability. The new type of quantum central limit theorems, based on the notion of free independence rather than the usual Boson or Fermion independence is discussed. A surprising result is that the role of the Gaussian for this new type of independence is played by the Wigner distribution. This motivated the introduction of new type of quantum independent increments noise, the free noise and the corresponding stochastic calculus. A further generalization, the ϖ-noises, is discussed. The free stochastic calculus is shown to be able to fit naturally into the general representation free calculus. The basic free are shown to be realized as non-adapted stochastic integrals with respect to the usual Boson white noises. Quantum noise on the finite difference algebra is expressed in terms of the usual Boson white noises. A new quantum way of looking at classical stochastic flows, in particular diffusions on Riemannian Manifolds is explained. Quantum groups are discussed from the point of view of possible applications to quantum probability. The applications of quantum probability to physics are surveyed Quantum theory Probabilities Quantenstatistik (DE-588)4047991-2 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Quantenstatistik (DE-588)4047991-2 s 2\p DE-604 Accardi, L. 1947- Sonstige oth Frigerio, A. 1951- Sonstige oth Erscheint auch als Druck-Ausgabe 9789810206802 Erscheint auch als Druck-Ausgabe 9810206801 Erscheint auch als Druck-Ausgabe 9810207166 http://www.worldscientific.com/worldscibooks/10.1142/1415#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Quantum probability & related topics Quantum theory Probabilities Quantenstatistik (DE-588)4047991-2 gnd |
| subject_GND | (DE-588)4047991-2 (DE-588)4143413-4 |
| title | Quantum probability & related topics |
| title_alt | Quantum probability and related topic |
| title_auth | Quantum probability & related topics |
| title_exact_search | Quantum probability & related topics |
| title_full | Quantum probability & related topics managing editor, L. Accardi ; editorial board, A. Frigerio ... [et. al] |
| title_fullStr | Quantum probability & related topics managing editor, L. Accardi ; editorial board, A. Frigerio ... [et. al] |
| title_full_unstemmed | Quantum probability & related topics managing editor, L. Accardi ; editorial board, A. Frigerio ... [et. al] |
| title_short | Quantum probability & related topics |
| title_sort | quantum probability related topics |
| topic | Quantum theory Probabilities Quantenstatistik (DE-588)4047991-2 gnd |
| topic_facet | Quantum theory Probabilities Quantenstatistik Aufsatzsammlung |
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