An Introduction to Quantum Stochastic Calculus:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1992
|
| Schriftenreihe: | Monographs in Mathematics
85 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | "Elegantly written, with obvious appreciation for fine points of higher mathematics...most notable is [the] author's effort to weave classical probability theory into [a] quantum framework." – The American Mathematical Monthly "This is an excellent volume which will be a valuable companion both for those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students." – Mathematical Reviews An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito's correction formulae for Brownian motion and the Poisson process can be traced to communication relations or, equivalently, the uncertainty principle. Quantum stochastic interpretation enables the possibility of seeing new relationships between fermion and boson fields. Quantum dynamical semigroups as well as classical Markov semigroups are realized through unitary operator evolutions. The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level |
| Beschreibung: | 1 Online-Ressource (XI, 292 p) |
| ISBN: | 9783034886413 9783034897112 |
| DOI: | 10.1007/978-3-0348-8641-3 |
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| spelling | Parthasarathy, K. R. Verfasser aut An Introduction to Quantum Stochastic Calculus by K. R. Parthasarathy Basel Birkhäuser Basel 1992 1 Online-Ressource (XI, 292 p) txt rdacontent c rdamedia cr rdacarrier Monographs in Mathematics 85 "Elegantly written, with obvious appreciation for fine points of higher mathematics...most notable is [the] author's effort to weave classical probability theory into [a] quantum framework." – The American Mathematical Monthly "This is an excellent volume which will be a valuable companion both for those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students." – Mathematical Reviews An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito's correction formulae for Brownian motion and the Poisson process can be traced to communication relations or, equivalently, the uncertainty principle. Quantum stochastic interpretation enables the possibility of seeing new relationships between fermion and boson fields. Quantum dynamical semigroups as well as classical Markov semigroups are realized through unitary operator evolutions. The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Stochastischer Prozess (DE-588)4057630-9 s 1\p DE-604 Quantentheorie (DE-588)4047992-4 s 2\p DE-604 https://doi.org/10.1007/978-3-0348-8641-3 Verlag 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 | Parthasarathy, K. R. An Introduction to Quantum Stochastic Calculus Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Quantenmechanik (DE-588)4047989-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Quantentheorie (DE-588)4047992-4 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4057630-9 (DE-588)4047992-4 |
| title | An Introduction to Quantum Stochastic Calculus |
| title_auth | An Introduction to Quantum Stochastic Calculus |
| title_exact_search | An Introduction to Quantum Stochastic Calculus |
| title_full | An Introduction to Quantum Stochastic Calculus by K. R. Parthasarathy |
| title_fullStr | An Introduction to Quantum Stochastic Calculus by K. R. Parthasarathy |
| title_full_unstemmed | An Introduction to Quantum Stochastic Calculus by K. R. Parthasarathy |
| title_short | An Introduction to Quantum Stochastic Calculus |
| title_sort | an introduction to quantum stochastic calculus |
| topic | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Quantenmechanik (DE-588)4047989-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Quantentheorie (DE-588)4047992-4 gnd |
| topic_facet | Mathematics Distribution (Probability theory) Probability Theory and Stochastic Processes Mathematik Quantenmechanik Stochastischer Prozess Quantentheorie |
| url | https://doi.org/10.1007/978-3-0348-8641-3 |
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