An introduction to quantum stochastic calculus:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1992
|
| Schriftenreihe: | Monographs in mathematics
Volume 85 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 290 Seiten |
| ISBN: | 3764326972 0817626972 |
Internformat
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| 245 | 1 | 0 | |a An introduction to quantum stochastic calculus |c K. R. Parthasarathy |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1992 | |
| 300 | |a XI, 290 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 7 | |a Stochastische processen |2 gtt | |
| 650 | 4 | |a Théorie quantique | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Quantum theory | |
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Datensatz im Suchindex
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| adam_text |
Contents
Preface IX
Chapter I
Events, Observables and States 1
1 From classical to quantum probability 1
2 Notational preliminaries 2
3 Finite dimensional quantum probability spaces 6
4 Observables in a simple quantum probability space 9
5 Variance and covariance 13
6 Dynamics in finite dimensional quantum probability spaces 18
7 Observables with infinite number of values and the
Hahn Hellinger Theorem 22
8 Probability distributions on 9 (3€) and Gleason's Theorem 31
9 Trace class operators and Schatten's Theorem 43
10 Spectral integration and Stone's Theorem on
the unitary representations of Uk 53
11 Basic notions of the theory of unbounded operators 60
12 Spectral integration of unbounded functions and
von Neumann's Spectral Theorem 65
13 Stone generators, characteristic functions and moments 73
14 Wigner's Theorem on the automorphisms of gP(X) 82
Chapter II
Observables and States in Tensor Products of Hilbert Spaces 91
15 Positive definite kernels and tensor products of Hilbert Spaces 91
16 Operators in tensor products of Hilbert Spaces 97
17 Symmetric and antisymmetric tensor products 105
18 Examples of discrete time quantum stochastic flows 111
19 The Fock Spaces 123
20 The Weyl Representation 134
21 Weyl Representation and infinitely divisible distributions 152
22 The symplectic group of 3€ and Shale's Theorem 162
23 Creation, conservation and annihilation operators in Ta{M) 172
Vm Contents
Chapter III
Stochastic Integration and Quantum Ito's Formula 179
24 Adapted processes 179
25 Stochastic integration with respect to creation,
conservation and annihilation processes 183
26 A class of quantum stochastic differential equations 207
27 Stochastic differential equations with infinite
degrees of freedom 221
28 Evans Hudson Flows 233
29 A digression on completely positive linear maps and
Stinespring's Theorem 250
30 Generators of quantum dynamical semigroups and
the Gorini, Kossakowski, Sudarshan, Lindblad Theorem 257
References 275
Index 283
Author Index 289 |
| any_adam_object | 1 |
| author | Parthasarathy, Kalyanapuram R. 1936- |
| author_GND | (DE-588)115641785 |
| author_facet | Parthasarathy, Kalyanapuram R. 1936- |
| author_role | aut |
| author_sort | Parthasarathy, Kalyanapuram R. 1936- |
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| dewey-full | 519.2 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-09-24T10:00:44Z |
| institution | BVB |
| isbn | 3764326972 0817626972 |
| language | English |
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| physical | XI, 290 Seiten |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Monographs in mathematics |
| series2 | Monographs in mathematics |
| spelling | Parthasarathy, Kalyanapuram R. 1936- (DE-588)115641785 aut An introduction to quantum stochastic calculus K. R. Parthasarathy Basel [u.a.] Birkhäuser 1992 XI, 290 Seiten txt rdacontent n rdamedia nc rdacarrier Monographs in mathematics Volume 85 Kwantummechanica gtt Mathematische fysica gtt Physique mathématique Physique mathématique ram Processus stochastiques Processus stochastiques ram Quanta, théorie des ram Stochastische processen gtt Théorie quantique Mathematische Physik Quantentheorie Mathematical physics Quantum theory Stochastic processes Quantentheorie (DE-588)4047992-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Quantentheorie (DE-588)4047992-4 s Erscheint auch als Online-Ausgabe 978-3-0348-8641-3 Monographs in mathematics Volume 85 (DE-604)BV000008284 85 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002895754&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Parthasarathy, Kalyanapuram R. 1936- An introduction to quantum stochastic calculus Monographs in mathematics Kwantummechanica gtt Mathematische fysica gtt Physique mathématique Physique mathématique ram Processus stochastiques Processus stochastiques ram Quanta, théorie des ram Stochastische processen gtt Théorie quantique Mathematische Physik Quantentheorie Mathematical physics Quantum theory Stochastic processes Quantentheorie (DE-588)4047992-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047992-4 (DE-588)4057630-9 (DE-588)4047989-4 |
| 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 K. R. Parthasarathy |
| title_fullStr | An introduction to quantum stochastic calculus K. R. Parthasarathy |
| title_full_unstemmed | An introduction to quantum stochastic calculus K. R. Parthasarathy |
| title_short | An introduction to quantum stochastic calculus |
| title_sort | an introduction to quantum stochastic calculus |
| topic | Kwantummechanica gtt Mathematische fysica gtt Physique mathématique Physique mathématique ram Processus stochastiques Processus stochastiques ram Quanta, théorie des ram Stochastische processen gtt Théorie quantique Mathematische Physik Quantentheorie Mathematical physics Quantum theory Stochastic processes Quantentheorie (DE-588)4047992-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Kwantummechanica Mathematische fysica Physique mathématique Processus stochastiques Quanta, théorie des Stochastische processen Théorie quantique Mathematische Physik Quantentheorie Mathematical physics Quantum theory Stochastic processes Stochastischer Prozess Quantenmechanik |
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