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Quantum Stochastic Processes and Noncommutative Geometry

Quantum Stochastic Processes and Noncommutative Geometry

£79.00

Part of Cambridge Tracts in Mathematics

  • Date Published: January 2007
  • availability: In stock
  • format: Hardback
  • isbn: 9780521834506

£ 79.00
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  • 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.

    • This book is the first to describe how the mathematical constructions of noncommutative geometry and quantum stochastic structures are related
    • Contains many unique features, e.g. discussion of calculus with unbounded operator coefficients
    • Accessible to a wide range of graduate students and researchers
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    Product details

    • Date Published: January 2007
    • format: Hardback
    • isbn: 9780521834506
    • length: 300 pages
    • dimensions: 235 x 162 x 20 mm
    • weight: 0.561kg
    • availability: In stock
  • Table of Contents

    1. Introduction
    2. Preliminaries
    3. Quantum dynamical semigroups
    4. Hilbert modules
    5. Quantum stochastic calculus with bounded coefficients
    6. Dilation of quantum dynamical semigroups with bounded generator
    7. Quantum stochastic calculus with unbounded coefficients
    8. Dilation of quantum dynamical semigroups with unbounded generator
    9. Noncommutative geometry and quantum stochastic processes
    Bibliography
    Index.

  • Authors

    Kalyan B. Sinha, Indian Statistical Institute, New Delhi
    Kalyan Sinha is a Distinguished Scientist in the Statistics-Mathematics Unit at the Indian Statistical Institute, New Dehli.

    Debashish Goswami, Indian Statistical Institute, Kolkata
    Debashish Goswami is an Assistant Professor in the Statistics-Mathematics Unit at the Indian Statistical Institute, Kolkata.

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