Quantum Stochastic Calculus Using Infinitesimals

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Quantum Stochastic Calculus Using Infinitesimals

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Author : Martin Leitz-Martini
language : en
Publisher:
Release Date : 2001

Quantum Stochastic Calculus Using Infinitesimals written by Martin Leitz-Martini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.

Stochastic Calculus With Infinitesimals

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Author : Frederik S. Herzberg
language : en
Publisher: Springer
Release Date : 2012-11-06

Stochastic Calculus With Infinitesimals written by Frederik S. Herzberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-06 with Mathematics categories.

Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.

Quantum Stochastics And Information

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Author : V. P. Belavkin
language : en
Publisher: World Scientific
Release Date : 2008

Quantum Stochastics And Information written by V. P. Belavkin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.

Quantum stochastic calculus has become an indispensable tool in modern quantum physics, its effectiveness being illustrated by recent developments in quantum control which place the calculus at the heart of the theory. Quantum statistics is rapidly taking shape as an intrinsically quantum counterpart to classical statistics, motivated by advances in quantum engineering and the need for better statistical inference tools for quantum systems. This volume contains a selection of regulear research articles and reviews by leading researchers in quantum control, quantum statistics, quantum probability and quantum information. The selection offers a unified view of recent trends in quantum stochastics, highlighting the common mathematical language of Hilbert space operators, and the deep connections between classical and quantum stochastic phenomena.

An Introduction To Quantum Stochastic Calculus

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Author : K.R. Parthasarathy
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

An Introduction To Quantum Stochastic Calculus written by K.R. Parthasarathy and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

"Elegantly written, with obvious appreciation for fine points of higher mathematics...most notable is [the] author's effort to weave classical probability theory into [a] quantum framework." – The American Mathematical Monthly "This is an excellent volume which will be a valuable companion both for those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students." – Mathematical Reviews An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito's correction formulae for Brownian motion and the Poisson process can be traced to communication relations or, equivalently, the uncertainty principle. Quantum stochastic interpretation enables the possibility of seeing new relationships between fermion and boson fields. Quantum dynamical semigroups as well as classical Markov semigroups are realized through unitary operator evolutions. The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level.

Quantum Probability And Related Topics

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Author : Luigi Accardi
language : en
Publisher: World Scientific
Release Date : 1994

Quantum Probability And Related Topics written by Luigi Accardi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

Quantum Probability and Related Topics is a series of volumes whose goal is to provide a picture of the state of the art in this rapidly growing field where classical probability, quantum physics and functional analysis merge together in an original synthesis which, for 20 years, has been enriching these three areas with new ideas, techniques and results.

Quantum Probability And Related Topics Qp Pq Volume Ix

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Author : Luigi Accardi
language : en
Publisher: World Scientific
Release Date : 1994-12-16

Quantum Probability And Related Topics Qp Pq Volume Ix written by Luigi Accardi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-16 with Mathematics categories.

Quantum Probability and Related Topics is a series of volumes whose goal is to provide a picture of the state of the art in this rapidly growing field where classical probability, quantum physics and functional analysis merge together in an original synthesis which, for 20 years, has been enriching these three areas with new ideas, techniques and results.

Quantum Engineering With Quantum Optics

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Author : Joseph Alan Kerckhoff
language : en
Publisher: Stanford University
Release Date : 2011

Quantum Engineering With Quantum Optics written by Joseph Alan Kerckhoff and has been published by Stanford University this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.

Despite initial set backs in the 1980s, the prospect for large scale integration of optical devices with high spatial-density and low energy consumption for information applications has grown steadily in the past decade. At the same time these advances have been made towards classical information processing with integrated optics, largely in an engineering context, a broad physics community has been pursuing quantum information processing platforms, with a heavy emphasis on optics-based networks. But despite these similarities, the two communities have exchanged models and techniques to a very limited degree. The aim of this thesis is to provide examples of the advantages of an engineering perspective to quantum information systems and quantum models to systems of interest in optical engineering, in both theory and experiment. I present various observations of ultra-low energy optical switching in a cavity quantum electrodynamical (cQED) system containing a single emitter. Although such devices are of interest to the engineering community, the dominant, classical optical models used in the field are incompatible with several photon, ultra-low energy devices like these that evince a discrete Hilbert space and are perturbed by quantum fluctuations. And in complement to this, I also propose a nanophotonic/cQED approach to building a self-correcting quantum memory, simply "powered" by cw laser beams and motivated by the conviction that for quantum engineering to be a viable paradigm, quantum devices will have to control themselves. Intuitive in its operation, this network represents a coherent feedback network in which error correction occurs entirely "on-chip, " without measurement, and is modeled using a flexible formalism that suggests a quantum generalization of electrical circuit theory.

Quantum Probability And Applications V

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Author : Luigi Accardi
language : en
Publisher: Springer
Release Date : 2006-11-14

Quantum Probability And Applications V written by Luigi Accardi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Science categories.

These proceedings of the workshop on quantum probability held in Heidelberg, September 26-30, 1988 contains a representative selection of research articles on quantum stochastic processes, quantum stochastic calculus, quantum noise, geometry, quantum probability, quantum central limit theorems and quantum statistical mechanics.

Stochastic Analysis And Mathematical Physics

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Author : A.B. Cruzeiro
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Stochastic Analysis And Mathematical Physics written by A.B. Cruzeiro and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This volume represents the outgrowth of an ongoing workshop on stochastic analysis held in Lisbon. The nine survey articles in the volume extend concepts from classical probability and stochastic processes to a number of areas of mathematical physics. It is a good reference text for researchers and advanced students in the fields of probability, stochastic processes, analysis, geometry, mathematical physics, and physics. Key topics covered include: nonlinear stochastic wave equations, completely positive maps, Mehler-type semigroups on Hilbert spaces, entropic projections, and many others.

Quantum Probability And Related Topics Volume Viii

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Author : Luigi Accardi
language : en
Publisher: World Scientific
Release Date : 1993-09-30

Quantum Probability And Related Topics Volume Viii written by Luigi Accardi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-09-30 with Mathematics categories.

Quantum Probability and Related Topics is a series of volumes based on material discussed at the various QP conferences. It aims to provide an update on the rapidly growing field of classical probability, quantum physics and functional analysis.