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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Physik & Astronomie Theoretische Physik Spectral Measures and Dynamics: Typical Behaviors
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Spectral Measures and Dynamics: Typical Behaviors
Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira (Broschiert, Englisch)
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Beschreibung
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 singularcontinuous 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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
29.10.2024
Sprache
Englisch
EAN
9783031382918
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Latin American Mathematics Series – UFSCar subseries
Sonderedition
Nein
Autor
Moacir Aloisio, Silas L. Carvalho, César R. de Oliveira
Seitenanzahl
246
Einbandart
Broschiert
Schlagwörter
mathematical physics, quantum mechanics, quantum theory, spectral analysis, elliptic equations, classical measure theory, fractals, quantum logic, singular continuous spectra, Hausdorff dimension, packing dimension, Wonderland theorem, average return probability, quasi ballistic dynamics, Schrödinger semigroups
Thema-Inhalt
PHU - Mathematische Physik
PBKL - Integralrechnung und -gleichungen
PHQ - Quantenphysik (Quantenmechanik und Quantenfeldtheorie)
PBKJ - Differentialrechnung und -gleichungen
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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