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The mathematics of open quantum systems = dissipative and non-unitary representations and quantum measurements /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The mathematics of open quantum systems/ Konstantin A. Makarov, Eduard Tsekanovskii.
其他題名:	dissipative and non-unitary representations and quantum measurements /
作者:	Makarov, Konstantin A.
其他作者:	Tsekanovskii, Eduard.
出版者:	Singapore :World Scientific, : c2022.,
面頁冊數:	1 online resource.
標題:	Quantum theory - Mathematics. -
電子資源:	https://www.worldscientific.com/worldscibooks/10.1142/12395#t=toc
ISBN:	9789811241239

The mathematics of open quantum systems = dissipative and non-unitary representations and quantum measurements /
Makarov, Konstantin A.

The mathematics of open quantum systemsdissipative and non-unitary representations and quantum measurements /[electronic resource] :Konstantin A. Makarov, Eduard Tsekanovskii. - Singapore :World Scientific,c2022. - 1 online resource.

Includes bibliographical references (p. 273-281) and index.

"This book presents new developments in the open quantum systems theory with emphasis on applications to the (frequent) measurement theory. In the first part of the book, the uniqueness theorems for the solutions to the restricted Weyl commutation relations braiding unitary groups and semi-groups of contractions are discussed. The major theme involves an intrinsic characterization of the simplest symmetric operator solutions to the Heisenberg uncertainty relations, the problem posed by Jørgensen and Muhly, followed by the proof of the uniqueness theorems for the simplest solutions to the restricted Weyl commutation relations. The detailed study of unitary invariants of the corresponding dissipative and symmetric operators opens up a look at the classical Stone-von Neumann uniqueness theorem from a new angle and provides an extended version of the uniqueness result relating various realizations of a differentiation operator on the corresponding metric graphs. The second part of the book is devoted to mathematical problems of the quantum measurements under continuous monitoring. Among the topics discussed are the complementarity of the Quantum Zeno effect and Exponential Decay scenario in frequent quantum measurements, and a rigorous treatment, within continuous monitoring paradigm, of the celebrated "double-slit experiment" where the renowned exclusive and interference measurement alternatives approach in quantum theory is presented in a way that is accessible for mathematicians. One of the striking applications of the generalized (1-stable) central limit theorem is the mathematical evidence of exponential decay of unstable states of the quantum pendulum under continuous monitoring"--

ISBN: 9789811241239Subjects--Topical Terms:

639940
Quantum theory
--Mathematics.

LC Class. No.: QC174.17.M4 / M35 2022

Dewey Class. No.: 530.1201/51542

The mathematics of open quantum systems = dissipative and non-unitary representations and quantum measurements /
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504 $a Includes bibliographical references (p. 273-281) and index.
520 $a "This book presents new developments in the open quantum systems theory with emphasis on applications to the (frequent) measurement theory. In the first part of the book, the uniqueness theorems for the solutions to the restricted Weyl commutation relations braiding unitary groups and semi-groups of contractions are discussed. The major theme involves an intrinsic characterization of the simplest symmetric operator solutions to the Heisenberg uncertainty relations, the problem posed by Jørgensen and Muhly, followed by the proof of the uniqueness theorems for the simplest solutions to the restricted Weyl commutation relations. The detailed study of unitary invariants of the corresponding dissipative and symmetric operators opens up a look at the classical Stone-von Neumann uniqueness theorem from a new angle and provides an extended version of the uniqueness result relating various realizations of a differentiation operator on the corresponding metric graphs. The second part of the book is devoted to mathematical problems of the quantum measurements under continuous monitoring. Among the topics discussed are the complementarity of the Quantum Zeno effect and Exponential Decay scenario in frequent quantum measurements, and a rigorous treatment, within continuous monitoring paradigm, of the celebrated "double-slit experiment" where the renowned exclusive and interference measurement alternatives approach in quantum theory is presented in a way that is accessible for mathematicians. One of the striking applications of the generalized (1-stable) central limit theorem is the mathematical evidence of exponential decay of unstable states of the quantum pendulum under continuous monitoring"-- $c Provided by publisher.
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