| Description |
1 online resource (x, 290 pages). |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Cambridge tracts in mathematics ; 169
|
|
Cambridge tracts in mathematics ; 169.
|
| Bibliography |
Includes bibliographical references (pages 281-287) and index. |
| 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. |
| Summary |
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. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Stochastic processes.
|
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Stochastic processes. |
|
Quantum groups.
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Quantum groups. |
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Noncommutative differential geometry.
|
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Noncommutative differential geometry. |
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Quantum theory.
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Quantum theory. |
| Genre/Form |
Electronic books.
|
| Added Author |
Goswami, Debashish.
|
| Other Form: |
Print version: Sinha, Kalyan B. Quantum stochastic processes and noncommutative geometry. Cambridge ; New York : Cambridge University Press, 2007 9780521834506 0521834503 (DLC) 2006034088 (OCoLC)73742639 |
| ISBN |
9780511269974 (electronic book) |
|
0511269978 (electronic book) |
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9780521834506 (hardback) |
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0521834503 (hardback) |
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0511268378 (ebook ; ebrary) |
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9780511268373 (ebook ; ebrary) |
|
