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Spectral measures and dynamics = typical behaviors /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Spectral measures and dynamics/ by Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira.
其他題名:	typical behaviors /
作者:	Aloisio, Moacir.
其他作者:	de Oliveira, Cesar R.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	xi, 246 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Differential Equations. -
電子資源:	https://doi.org/10.1007/978-3-031-38289-5
ISBN:	9783031382895

Spectral measures and dynamics = typical behaviors /
Aloisio, Moacir.

Spectral measures and dynamicstypical behaviors /[electronic resource] :by Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira. - Cham :Springer International Publishing :2023. - xi, 246 p. :ill., digital ;24 cm. - Latin American mathematics series - UFSCar subseries,2524-6763. - Latin American mathematics series - UFSCar subseries..

Spectrum and Dynamics: Some Basic Concepts -- Part I Quantum Models: Correlation Dimension -- Fractal Measures and Dynamics -- Escaping Probabilities and Quasiballistic Dynamics -- Generalized Dimensions and Dynamics -- Part II Ergodic Theory and Semigroups: Generic Scales of Weak-Mixing -- Asymptotics of C0-Semigroups -- Generic Stability for Self-adjoint Semigroups -- References.

This book convenes and deepens generic results about spectral measures, many of them available so far in scattered literature. It starts with classic topics such as Wiener lemma, Strichartz inequality, and the basics of fractal dimensions of measures, progressing to more advanced material, some of them developed by the own authors. A fundamental concept to the mathematical theory of quantum mechanics, the spectral measure relates to the components of the quantum state concerning the energy levels of the Hamiltonian operator and, on the other hand, to the dynamics of such state. However, these correspondences are not immediate, with many nuances and subtleties discovered in recent years. A valuable example of such subtleties is found in the so-called "Wonderland theorem" first published by B. Simon in 1995. It shows that, for some metric space of self-adjoint operators, the set of operators whose spectral measures are singular continuous is a generic set (which, for some, is exotic) Recent works have revealed that, on top of singular continuity, there are other generic properties of spectral measures. These properties are usually associated with a number of different notions of generalized dimensions, upper and lower dimensions, with dynamical implications in quantum mechanics, ergodicity of dynamical systems, and evolution semigroups. All this opens ways to new and instigating avenues of research. Graduate students with a specific interest in the spectral properties of spectral measure are the primary target audience for this work, while researchers benefit from a selection of important results, many of them presented in the book format for the first time.

ISBN: 9783031382895

Standard No.: 10.1007/978-3-031-38289-5doiSubjects--Topical Terms:

681826
Differential Equations.

LC Class. No.: QA320 / .A46 2023

Dewey Class. No.: 515.7222

Spectral measures and dynamics = typical behaviors /
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520 $a This book convenes and deepens generic results about spectral measures, many of them available so far in scattered literature. It starts with classic topics such as Wiener lemma, Strichartz inequality, and the basics of fractal dimensions of measures, progressing to more advanced material, some of them developed by the own authors. A fundamental concept to the mathematical theory of quantum mechanics, the spectral measure relates to the components of the quantum state concerning the energy levels of the Hamiltonian operator and, on the other hand, to the dynamics of such state. However, these correspondences are not immediate, with many nuances and subtleties discovered in recent years. A valuable example of such subtleties is found in the so-called "Wonderland theorem" first published by B. Simon in 1995. It shows that, for some metric space of self-adjoint operators, the set of operators whose spectral measures are singular continuous is a generic set (which, for some, is exotic) Recent works have revealed that, on top of singular continuity, there are other generic properties of spectral measures. These properties are usually associated with a number of different notions of generalized dimensions, upper and lower dimensions, with dynamical implications in quantum mechanics, ergodicity of dynamical systems, and evolution semigroups. All this opens ways to new and instigating avenues of research. Graduate students with a specific interest in the spectral properties of spectral measure are the primary target audience for this work, while researchers benefit from a selection of important results, many of them presented in the book format for the first time.
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