Quantum stochastics:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
New York, NY
Cambridge Univ. Press
2015
|
Ausgabe: | 1. publ. |
Schriftenreihe: | Cambridge series in statistical and probabilistic mathematics
[37] |
Schlagworte: | |
Online-Zugang: | Cover image Inhaltsverzeichnis |
Beschreibung: | Literaturverz. S. 397 - 406 |
Beschreibung: | XII, 412 S. |
ISBN: | 9781107069190 |
Internformat
MARC
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Datensatz im Suchindex
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adam_text | Titel: Quantum stochastics
Autor: Chang, Mou-Hsiung
Jahr: 2015
Contents
Preface
Introduction and Summary
1 Operator Algebras and Topologies
1.1 Complex Hilbert Spaces
1.2 Bounded Linear Operators on X
1.3 Spectral Theorem
1.4 Operator Topologies
1.5 Operator Algebras
1.6 Representations of Operator Algebras
1.7 Conclusion and Historical Notes
2 Quantum Probability
2.1 Bounded Linear Functionals
2.2 Quantum States
2.3 Quantum Observables
2.4 Quantum Probability Spaces
2.5 Quantum Measurements
2.6 Quantum Conditional Expectations
2.7 Conclusion and Historical Notes
3 Quantum Stochastic Calculus
3.1 Symmetrie Fock and Guichardet Spaces
3.2 Quantum Itö Integrals
3.3 Quantum Noises
3.4 Quantum Stochastic Integrals
3.5 Quantum Stochastic Calculus
3.6 Conclusion and Historical Notes
4 Quantum Stochastic Differential Equations
4.1 QSDE of Hudson-Parthasarathy Type
4.2 Conventions and Preliminaries
4.3 Stochastic Itö Formulae
4.4 Strong and Mild Solutions
page xi
1
8
8
13
25
30
32
36
49
50
52
63
67
69
74
78
80
81
81
89
98
109
115
118
119
119
121
125
128
vii
viii
Contents
4.5 Existence and Uniqueness 129
4.6 An Example by Fagnola and Wills [FWOO] 135
4.7 Unitary, Isometry, and Cocycle Properties 137
4.8 Approximating Solutions 143
4.9 A Solvable QSDE 150
4.10 Lyapunov Stability of QSDE 152
4.11 Conclusion and Historical Notes 159
5 Quantum Markov Semigroups 160
5.1 Semigroups of Bounded Linear Operators on Banach Spaces 161
5.2 Group of Unitary Operators 167
5.3 Linear Maps on A 173
5.4 Complete Positivity 175
5.5 Quantum Dynamical Semigroups 188
5.6 Lindblad Master Equation 198
5.7 Conclusion and Historical Notes 200
6 Minimal QDS 201
6.1 Construction of Minimal Quantum Dynamical Semigroups (QDSs) 201
6.2 The Resolvent of the Minimal Semigroup 213
6.3 Markovian t 0} 216
6.4 Conclusion and Historical Notes 223
7 Quantum Markov Processes 224
7.1 Quantum Markov Processes 225
7.2 Quantum Markov Cocycles 229
7.3 Weak Quantum Markov Flows (WQMF) 231
7.4 Construction of WQMF 234
7.5 Central Weak Markov Flows 251
7.6 Additional Results for [k.t, t 0} 256
7.7 Conclusion and Historical Notes 261
8 Strong Quantum Markov Processes 262
8.1 Quantum Stopping Times (QSTs) 263
8.2 Stopped Processes in Fock Spaces 271
8.3 Strong Quantum Markov Processes 286
8.4 Generalized Strong Quantum Markovian Properties 294
8.5 Martingale Problems 301
8.6 Lyapunov Stability 307
8.7 Conclusion and Historical Notes 312
9 Invariant Normal States 313
9.1 Prohorov Theorems 313
9.2 Invariances 317
9.3 Existence of Invariant States 318
Contents ix
9.4 Uniqueness of the Invariant State 325
9.5 F(ZXMCX), and-Affl) 329
9.6 Conclusion and Historical Notes 333
10 Recurrence and Transience 334
10.1 Subharmonic Projections 335
10.2 Reduced QMS 343
10.3 Potentials 345
10.4 Recurrence and Transience 357
10.5 Conclusion and Historical Notes 371
11 Ergodic Theory 372
11.1 Ergodicity 372
11.2 Lower Bounds and Mean Lower Bounds 388
11.3 Conclusion and Historical Notes 396
Bibliography
Index
397
407
|
any_adam_object | 1 |
author | Chang, Mou-Hsiung |
author_facet | Chang, Mou-Hsiung |
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author_sort | Chang, Mou-Hsiung |
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callnumber-first | Q - Science |
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ctrlnum | (OCoLC)904671536 (DE-599)BVBBV042185875 |
dewey-full | 519.2/3 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 519 - Probabilities and applied mathematics |
dewey-raw | 519.2/3 |
dewey-search | 519.2/3 |
dewey-sort | 3519.2 13 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
edition | 1. publ. |
format | Book |
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institution | BVB |
isbn | 9781107069190 |
language | English |
lccn | 014023639 |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027625021 |
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physical | XII, 412 S. |
publishDate | 2015 |
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series | Cambridge series in statistical and probabilistic mathematics |
series2 | Cambridge series in statistical and probabilistic mathematics |
spelling | Chang, Mou-Hsiung Verfasser aut Quantum stochastics Mou-Hsiung Chang 1. publ. New York, NY Cambridge Univ. Press 2015 XII, 412 S. txt rdacontent n rdamedia nc rdacarrier Cambridge series in statistical and probabilistic mathematics [37] Literaturverz. S. 397 - 406 MATHEMATICS / Probability & Statistics / General bisacsh Quantentheorie Stochastic processes Probabilities Quantum theory MATHEMATICS / Probability & Statistics / General Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Quantentheorie (DE-588)4047992-4 s Stochastik (DE-588)4121729-9 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Cambridge series in statistical and probabilistic mathematics [37] (DE-604)BV011442366 37 http://assets.cambridge.org/97811070/69190/cover/9781107069190.jpg Cover image HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027625021&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Chang, Mou-Hsiung Quantum stochastics Cambridge series in statistical and probabilistic mathematics MATHEMATICS / Probability & Statistics / General bisacsh Quantentheorie Stochastic processes Probabilities Quantum theory MATHEMATICS / Probability & Statistics / General Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Quantentheorie (DE-588)4047992-4 gnd Stochastik (DE-588)4121729-9 gnd |
subject_GND | (DE-588)4064324-4 (DE-588)4047992-4 (DE-588)4121729-9 |
title | Quantum stochastics |
title_auth | Quantum stochastics |
title_exact_search | Quantum stochastics |
title_full | Quantum stochastics Mou-Hsiung Chang |
title_fullStr | Quantum stochastics Mou-Hsiung Chang |
title_full_unstemmed | Quantum stochastics Mou-Hsiung Chang |
title_short | Quantum stochastics |
title_sort | quantum stochastics |
topic | MATHEMATICS / Probability & Statistics / General bisacsh Quantentheorie Stochastic processes Probabilities Quantum theory MATHEMATICS / Probability & Statistics / General Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Quantentheorie (DE-588)4047992-4 gnd Stochastik (DE-588)4121729-9 gnd |
topic_facet | MATHEMATICS / Probability & Statistics / General Quantentheorie Stochastic processes Probabilities Quantum theory Wahrscheinlichkeitsrechnung Stochastik |
url | http://assets.cambridge.org/97811070/69190/cover/9781107069190.jpg http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027625021&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV011442366 |
work_keys_str_mv | AT changmouhsiung quantumstochastics |