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＜電子ブック＞
Spectral Measures and Dynamics: Typical Behaviors / by Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira
(Latin American Mathematics Series – UFSCar subseries. ISSN:25246763)

版	1st ed. 2023.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2023
本文言語	英語
大きさ	XI, 246 p. 1 illus. in color : online resource
著者標目	*Aloisio, Moacir author Carvalho, Silas L author de Oliveira, César R author SpringerLink (Online service)
件　名	LCSH:Mathematical physics LCSH:Measure theory LCSH:Quantum physics LCSH:Differential equations FREE:Mathematical Physics FREE:Measure and Integration FREE:Quantum Physics FREE:Differential Equations
一般注記	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 ageneric 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 HTTP:URL=https://doi.org/10.1007/978-3-031-38289-5

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