Quantum stochastic processes and noncommutative geometry:
The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2007
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| Schriftenreihe: | Cambridge tracts in mathematics
169 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 URL des Erstveröffentlichers |
| Zusammenfassung: | The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics |
| Beschreibung: | 1 Online-Ressource (x, 290 Seiten) |
| ISBN: | 9780511618529 |
| DOI: | 10.1017/CBO9780511618529 |
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| 505 | 8 | |a Introduction -- Preliminaries -- Quantum dynamical semigroups -- Hilbert modules -- Quantum stochastic calculus with bounded coefficients -- Dilation of quantum dynamical semigroups with bounded generator -- Quantum stochastic calculus with unbounded coefficients -- Dilation of quantum dynamical semigroups with unbounded generator -- Noncommutative geometry and quantum stochastic processes | |
| 520 | |a The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics | ||
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| 650 | 4 | |a Stochastic processes | |
| 650 | 4 | |a Quantum groups | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Sinha, Kalyan B. |
| author_facet | Sinha, Kalyan B. |
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| author_sort | Sinha, Kalyan B. |
| author_variant | k b s kb kbs |
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| bvnumber | BV043940978 |
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| contents | Introduction -- Preliminaries -- Quantum dynamical semigroups -- Hilbert modules -- Quantum stochastic calculus with bounded coefficients -- Dilation of quantum dynamical semigroups with bounded generator -- Quantum stochastic calculus with unbounded coefficients -- Dilation of quantum dynamical semigroups with unbounded generator -- Noncommutative geometry and quantum stochastic processes |
| ctrlnum | (ZDB-20-CBO)CR9780511618529 (OCoLC)850820993 (DE-599)BVBBV043940978 |
| 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 |
| doi_str_mv | 10.1017/CBO9780511618529 |
| format | Electronic eBook |
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| id | DE-604.BV043940978 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9780511618529 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349947 |
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| physical | 1 Online-Ressource (x, 290 Seiten) |
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| publishDate | 2007 |
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| publisher | Cambridge University Press |
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| spelling | Sinha, Kalyan B. Verfasser aut Quantum stochastic processes and noncommutative geometry Kalyan B. Sinha, Debashish Goswami Quantum Stochastic Processes & Noncommutative Geometry Cambridge Cambridge University Press 2007 1 Online-Ressource (x, 290 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 169 Introduction -- Preliminaries -- Quantum dynamical semigroups -- Hilbert modules -- Quantum stochastic calculus with bounded coefficients -- Dilation of quantum dynamical semigroups with bounded generator -- Quantum stochastic calculus with unbounded coefficients -- Dilation of quantum dynamical semigroups with unbounded generator -- Noncommutative geometry and quantum stochastic processes The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics Quantentheorie Stochastic processes Quantum groups Noncommutative differential geometry Quantum theory Stochastische Quantisierung (DE-588)4238900-8 gnd rswk-swf Quantengruppe (DE-588)4252437-4 gnd rswk-swf Nichtkommutative Differentialgeometrie (DE-588)4311174-9 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastische Quantisierung (DE-588)4238900-8 s Nichtkommutative Differentialgeometrie (DE-588)4311174-9 s DE-604 Stochastischer Prozess (DE-588)4057630-9 s Quantengruppe (DE-588)4252437-4 s Quantentheorie (DE-588)4047992-4 s Goswami, Debashish Sonstige oth Erscheint auch als Druck-Ausgabe 978-0-521-83450-6 https://doi.org/10.1017/CBO9780511618529 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Sinha, Kalyan B. Quantum stochastic processes and noncommutative geometry Introduction -- Preliminaries -- Quantum dynamical semigroups -- Hilbert modules -- Quantum stochastic calculus with bounded coefficients -- Dilation of quantum dynamical semigroups with bounded generator -- Quantum stochastic calculus with unbounded coefficients -- Dilation of quantum dynamical semigroups with unbounded generator -- Noncommutative geometry and quantum stochastic processes Quantentheorie Stochastic processes Quantum groups Noncommutative differential geometry Quantum theory Stochastische Quantisierung (DE-588)4238900-8 gnd Quantengruppe (DE-588)4252437-4 gnd Nichtkommutative Differentialgeometrie (DE-588)4311174-9 gnd Quantentheorie (DE-588)4047992-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4238900-8 (DE-588)4252437-4 (DE-588)4311174-9 (DE-588)4047992-4 (DE-588)4057630-9 |
| title | Quantum stochastic processes and noncommutative geometry |
| title_alt | Quantum Stochastic Processes & Noncommutative Geometry |
| title_auth | Quantum stochastic processes and noncommutative geometry |
| title_exact_search | Quantum stochastic processes and noncommutative geometry |
| title_full | Quantum stochastic processes and noncommutative geometry Kalyan B. Sinha, Debashish Goswami |
| title_fullStr | Quantum stochastic processes and noncommutative geometry Kalyan B. Sinha, Debashish Goswami |
| title_full_unstemmed | Quantum stochastic processes and noncommutative geometry Kalyan B. Sinha, Debashish Goswami |
| title_short | Quantum stochastic processes and noncommutative geometry |
| title_sort | quantum stochastic processes and noncommutative geometry |
| topic | Quantentheorie Stochastic processes Quantum groups Noncommutative differential geometry Quantum theory Stochastische Quantisierung (DE-588)4238900-8 gnd Quantengruppe (DE-588)4252437-4 gnd Nichtkommutative Differentialgeometrie (DE-588)4311174-9 gnd Quantentheorie (DE-588)4047992-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Quantentheorie Stochastic processes Quantum groups Noncommutative differential geometry Quantum theory Stochastische Quantisierung Quantengruppe Nichtkommutative Differentialgeometrie Stochastischer Prozess |
| url | https://doi.org/10.1017/CBO9780511618529 |
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