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Quantum stochastic processes and noncommutative geometry /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Quantum stochastic processes and noncommutative geometry // Kalyan B. Sinha, Debashish Goswami.
其他題名:	Quantum Stochastic Processes & Noncommutative Geometry
作者:	Sinha, Kalyan B.,
其他作者:	Goswami, Debashish,
面頁冊數:	1 online resource (x, 290 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Stochastic processes. -
電子資源:	https://doi.org/10.1017/CBO9780511618529
ISBN:	9780511618529 (ebook)

Quantum stochastic processes and noncommutative geometry /
Sinha, Kalyan B.,

Quantum stochastic processes and noncommutative geometry /Quantum Stochastic Processes & Noncommutative GeometryKalyan B. Sinha, Debashish Goswami. - 1 online resource (x, 290 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;169. - Cambridge tracts in mathematics ;203..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

ISBN: 9780511618529 (ebook)Subjects--Topical Terms:

528256
Stochastic processes.

LC Class. No.: QA274 / .G67 2007

Dewey Class. No.: 519.2/3

Quantum stochastic processes and noncommutative geometry /
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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.
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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