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...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
2007.
|
| Schriftenreihe: | Cambridge tracts in mathematics ;
169. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| 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 resource (x, 290 pages) |
| Bibliographie: | Includes bibliographical references (pages 281-287) and index. |
| ISBN: | 9780511269974 0511269978 9780521834506 0521834503 0511268378 9780511268373 9780511618529 0511618522 |
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| 505 | 0 | |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. | |
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| 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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| author | Sinha, Kalyan B. (Kalyan Bidhan), 1944- |
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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. |
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| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:07Z |
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| isbn | 9780511269974 0511269978 9780521834506 0521834503 0511268378 9780511268373 9780511618529 0511618522 |
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| spelling | Sinha, Kalyan B. (Kalyan Bidhan), 1944- https://id.oclc.org/worldcat/entity/E39PCjGgFkgy3wTTt7VTKyHMxC Quantum stochastic processes and noncommutative geometry / Kalyan B. Sinha, Debashish Goswami. Cambridge ; New York : Cambridge University Press, 2007. 1 online resource (x, 290 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge tracts in mathematics ; 169 Includes bibliographical references (pages 281-287) and index. 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. Print version record. 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. Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Quantum groups. http://id.loc.gov/authorities/subjects/sh90005801 Noncommutative differential geometry. http://id.loc.gov/authorities/subjects/sh97004788 Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Processus stochastiques. Groupes quantiques. Géométrie différentielle non commutative. Théorie quantique. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Noncommutative differential geometry fast Quantum groups fast Quantum theory fast Stochastic processes fast Goswami, Debashish. http://id.loc.gov/authorities/names/n2006078380 Print version: Sinha, Kalyan B. Quantum stochastic processes and noncommutative geometry. Cambridge ; New York : Cambridge University Press, 2007 9780521834506 0521834503 (DLC) 2006034088 (OCoLC)73742639 Cambridge tracts in mathematics ; 169. http://id.loc.gov/authorities/names/n42005726 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=185828 Volltext |
| spellingShingle | Sinha, Kalyan B. (Kalyan Bidhan), 1944- Quantum stochastic processes and noncommutative geometry / Cambridge tracts in mathematics ; 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. Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Quantum groups. http://id.loc.gov/authorities/subjects/sh90005801 Noncommutative differential geometry. http://id.loc.gov/authorities/subjects/sh97004788 Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Processus stochastiques. Groupes quantiques. Géométrie différentielle non commutative. Théorie quantique. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Noncommutative differential geometry fast Quantum groups fast Quantum theory fast Stochastic processes fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85128181 http://id.loc.gov/authorities/subjects/sh90005801 http://id.loc.gov/authorities/subjects/sh97004788 http://id.loc.gov/authorities/subjects/sh85109469 https://id.nlm.nih.gov/mesh/D013269 https://id.nlm.nih.gov/mesh/D011789 |
| title | Quantum stochastic processes and 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 | Stochastic processes. http://id.loc.gov/authorities/subjects/sh85128181 Quantum groups. http://id.loc.gov/authorities/subjects/sh90005801 Noncommutative differential geometry. http://id.loc.gov/authorities/subjects/sh97004788 Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Stochastic Processes https://id.nlm.nih.gov/mesh/D013269 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Processus stochastiques. Groupes quantiques. Géométrie différentielle non commutative. Théorie quantique. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Noncommutative differential geometry fast Quantum groups fast Quantum theory fast Stochastic processes fast |
| topic_facet | Stochastic processes. Quantum groups. Noncommutative differential geometry. Quantum theory. Stochastic Processes Quantum Theory Processus stochastiques. Groupes quantiques. Géométrie différentielle non commutative. Théorie quantique. MATHEMATICS Probability & Statistics Stochastic Processes. Noncommutative differential geometry Quantum groups Quantum theory Stochastic processes |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=185828 |
| work_keys_str_mv | AT sinhakalyanb quantumstochasticprocessesandnoncommutativegeometry AT goswamidebashish quantumstochasticprocessesandnoncommutativegeometry |