Quantum potential theory:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
|
| Schriftenreihe: | Lecture notes in mathematics
1954 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XI, 457 S. graph. Darst. 24 cm |
| ISBN: | 9783540693642 9783540693659 |
Internformat
MARC
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| 245 | 1 | 0 | |a Quantum potential theory |c Philippe Biane ... Ed.: Michael Schürmann ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XI, 457 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1954 | |
| 500 | |a Literaturangaben | ||
| 650 | 4 | |a Analyse fonctionnelle | |
| 650 | 4 | |a Processus de Markov | |
| 650 | 4 | |a Semi-groupes | |
| 650 | 4 | |a Théorie du potentiel | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Markov processes | |
| 650 | 4 | |a Potential theory (Mathematics) | |
| 650 | 4 | |a Semigroups | |
| 650 | 0 | 7 | |a Potenzialtheorie |0 (DE-588)4046939-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantenmechanik |0 (DE-588)4047989-4 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |y 2007 |z Greifswald |2 gnd-content | |
| 689 | 0 | 0 | |a Potenzialtheorie |0 (DE-588)4046939-6 |D s |
| 689 | 0 | 1 | |a Quantenmechanik |0 (DE-588)4047989-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Biane, Philippe |e Sonstige |4 oth | |
| 700 | 1 | |a Schürmann, Michael |d 1955- |e Sonstige |0 (DE-588)130828173 |4 oth | |
| 830 | 0 | |a Lecture notes in mathematics |v 1954 |w (DE-604)BV000676446 |9 1954 | |
| 856 | 4 | 2 | |u http://d-nb.info/989664546/04 |3 Inhaltsverzeichnis |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016756657 | ||
Datensatz im Suchindex
| _version_ | 1804138044373073920 |
|---|---|
| adam_text | Contents
Introduction
.................................................. 1
Potential
Theory in Classical Probability
.....................
З
Nicolas Privault
1
Introduction
.......................................... 3
2
Analytic Potential Theory
.............................. 4
3
Markov Processes
..................................... 24
4
Stochastic Calculus
.................................... 31
5
Probabilistic Interpretations
............................ 46
References
................................................. 58
Introduction to Random Walks
on
Noncommutative
Spaces
................................... 61
Philippe Biane
1
Introduction
.......................................... 61
2
Noncommutative
Spaces and Random Variables
........... 62
3
Quantum Bernoulli Random Walks
...................... 68
4
Bialgebras and Group Algebras
......................... 73
5
Random Walk on the Dual of SU(2)
..................... 76
6
Random Walks on Duals of Compact Groups
............. 80
7
The Case of SU(n)
.................................... 82
8
Choquet-Deny Theorem for Duals of Compact Groups
..... 87
9
The Martin Compactification of the Dual of SU(2)
........ 90
10
Central Limit Theorems for the Bernoulli Random Walk
... 94
11
The
Heisenberg
Group and the
Noncommutative
Brownian Motion
..................................... 100
12
Dilations for Noncompact Groups
....................... 106
13
Pitman s Theorem and the Quantum Group SUg(2)
....... 110
References
................................................. 114
Contents
viu
Interactions between Quantum Probability and Operator
117
Space Theory
.................................................
ll
Quanhua Xu
1
Introduction
..........................................11
2
Completely Positive Maps
..............................
H9
3
Concrete Operator Spaces and Completely
Bounded Maps
........................................12
4
Ruan s Theorem: Abstract Operator Spaces
..............126
5
Complex Interpolation and Operator Hubert Spaces
.......130
6
Vector-valued Noncommutative Z/p-spaces
................132
7
Noncommutative Khintchine Type Inequalities
............137
8
Embedding of OH into Noncommutative Li
..............156
References
.................................................158
Dirichlet Forms on Noncommutative Spaces
..................161
Fabio
Cipriani
1
Introduction
..........................................161
2
Dirichlet Forms on C*-algebras and KMS-symmetric
Semigroups
...........................................168
3
Dirichlet Forms in Quantum Statistical Mechanics
.........218
4
Dirichlet Forms and Differential Calculus on C*-algebras
. .. 224
5
Noncommutative Potential Theory and Riemannian
Geometry
............................................245
6
Dirichlet Forms and Noncommutative Geometry
..........259
7
Appendix
............................................265
8
List of Examples
......................................270
References
.................................................272
Applications of Quantum Stochastic Processes in Quantum
Optics
........................................................277
Luc
Bouten
1
Quantum Probability
..................................277
2
Conditional Expectations
...............................286
3
Quantum Stochastic Calculus
...........................290
4
Quantum Filtering
....................................298
References
.................................................306
Quantum Walks
..............................................309
Norio Konno
Part I: Discrete-Time Quantum Walks
1
Limit Theorems
......................................311
2
Disordered Case
......................................350
3
Reversible Cellular Automata
..........................357
4
Quantum Cellular Automata
...........................368
5
Cycle
...............................................377
6
Absorption Problems
..................................387
Contents ix
Part II: Continuous-Time Quantum Walks
7
One-Dimensional Lattice
..............................401
8
Tree
................................................410
9
Ułtrametric
Space
....................................420
10
Cycle
...............................................432
References
.................................................441
Index
.........................................................453
|
| adam_txt |
Contents
Introduction
. 1
Potential
Theory in Classical Probability
.
З
Nicolas Privault
1
Introduction
. 3
2
Analytic Potential Theory
. 4
3
Markov Processes
. 24
4
Stochastic Calculus
. 31
5
Probabilistic Interpretations
. 46
References
. 58
Introduction to Random Walks
on
Noncommutative
Spaces
. 61
Philippe Biane
1
Introduction
. 61
2
Noncommutative
Spaces and Random Variables
. 62
3
Quantum Bernoulli Random Walks
. 68
4
Bialgebras and Group Algebras
. 73
5
Random Walk on the Dual of SU(2)
. 76
6
Random Walks on Duals of Compact Groups
. 80
7
The Case of SU(n)
. 82
8
Choquet-Deny Theorem for Duals of Compact Groups
. 87
9
The Martin Compactification of the Dual of SU(2)
. 90
10
Central Limit Theorems for the Bernoulli Random Walk
. 94
11
The
Heisenberg
Group and the
Noncommutative
Brownian Motion
. 100
12
Dilations for Noncompact Groups
. 106
13
Pitman's Theorem and the Quantum Group SUg(2)
. 110
References
. 114
Contents
viu
Interactions between Quantum Probability and Operator
117
Space Theory
.
ll
'
Quanhua Xu
1
Introduction
.11 '
2
Completely Positive Maps
.
H9
3
Concrete Operator Spaces and Completely
Bounded Maps
.12"
4
Ruan's Theorem: Abstract Operator Spaces
.126
5
Complex Interpolation and Operator Hubert Spaces
.130
6
Vector-valued Noncommutative Z/p-spaces
.132
7
Noncommutative Khintchine Type Inequalities
.137
8
Embedding of OH into Noncommutative Li
.156
References
.158
Dirichlet Forms on Noncommutative Spaces
.161
Fabio
Cipriani
1
Introduction
.161
2
Dirichlet Forms on C*-algebras and KMS-symmetric
Semigroups
.168
3
Dirichlet Forms in Quantum Statistical Mechanics
.218
4
Dirichlet Forms and Differential Calculus on C*-algebras
. . 224
5
Noncommutative Potential Theory and Riemannian
Geometry
.245
6
Dirichlet Forms and Noncommutative Geometry
.259
7
Appendix
.265
8
List of Examples
.270
References
.272
Applications of Quantum Stochastic Processes in Quantum
Optics
.277
Luc
Bouten
1
Quantum Probability
.277
2
Conditional Expectations
.286
3
Quantum Stochastic Calculus
.290
4
Quantum Filtering
.298
References
.306
Quantum Walks
.309
Norio Konno
Part I: Discrete-Time Quantum Walks
1
Limit Theorems
.311
2
Disordered Case
.350
3
Reversible Cellular Automata
.357
4
Quantum Cellular Automata
.368
5
Cycle
.377
6
Absorption Problems
.387
Contents ix
Part II: Continuous-Time Quantum Walks
7
One-Dimensional Lattice
.401
8
Tree
.410
9
Ułtrametric
Space
.420
10
Cycle
.432
References
.441
Index
.453 |
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| id | DE-604.BV035088510 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:09:45Z |
| indexdate | 2024-07-09T21:21:56Z |
| institution | BVB |
| isbn | 9783540693642 9783540693659 |
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| physical | XI, 457 S. graph. Darst. 24 cm |
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| series2 | Lecture notes in mathematics |
| spelling | Quantum potential theory Philippe Biane ... Ed.: Michael Schürmann ... Berlin [u.a.] Springer 2008 XI, 457 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1954 Literaturangaben Analyse fonctionnelle Processus de Markov Semi-groupes Théorie du potentiel Functional analysis Markov processes Potential theory (Mathematics) Semigroups Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2007 Greifswald gnd-content Potenzialtheorie (DE-588)4046939-6 s Quantenmechanik (DE-588)4047989-4 s DE-604 Biane, Philippe Sonstige oth Schürmann, Michael 1955- Sonstige (DE-588)130828173 oth Lecture notes in mathematics 1954 (DE-604)BV000676446 1954 http://d-nb.info/989664546/04 Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016756657&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Quantum potential theory Lecture notes in mathematics Analyse fonctionnelle Processus de Markov Semi-groupes Théorie du potentiel Functional analysis Markov processes Potential theory (Mathematics) Semigroups Potenzialtheorie (DE-588)4046939-6 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4046939-6 (DE-588)4047989-4 (DE-588)1071861417 |
| title | Quantum potential theory |
| title_auth | Quantum potential theory |
| title_exact_search | Quantum potential theory |
| title_exact_search_txtP | Quantum potential theory |
| title_full | Quantum potential theory Philippe Biane ... Ed.: Michael Schürmann ... |
| title_fullStr | Quantum potential theory Philippe Biane ... Ed.: Michael Schürmann ... |
| title_full_unstemmed | Quantum potential theory Philippe Biane ... Ed.: Michael Schürmann ... |
| title_short | Quantum potential theory |
| title_sort | quantum potential theory |
| topic | Analyse fonctionnelle Processus de Markov Semi-groupes Théorie du potentiel Functional analysis Markov processes Potential theory (Mathematics) Semigroups Potenzialtheorie (DE-588)4046939-6 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Analyse fonctionnelle Processus de Markov Semi-groupes Théorie du potentiel Functional analysis Markov processes Potential theory (Mathematics) Semigroups Potenzialtheorie Quantenmechanik Konferenzschrift 2007 Greifswald |
| url | http://d-nb.info/989664546/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016756657&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT bianephilippe quantumpotentialtheory AT schurmannmichael quantumpotentialtheory |
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