Spectral Measures and Dynamics: Typical Behaviors
暫譯: 光譜測度與動態：典型行為
Aloisio, Moacir, Carvalho, Silas L., de Oliveira, César R.
- 出版商: Springer
- 出版日期: 2024-10-29
- 售價: $5,510
- 貴賓價: 9.5 折 $5,235
- 語言: 英文
- 頁數: 246
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031382919
- ISBN-13: 9783031382918
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相關分類:
量子 Quantum
海外代購書籍(需單獨結帳)
相關主題
商品描述
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.
商品描述(中文翻譯)
本書匯集並深入探討有關譜測度的通用結果，其中許多結果至今仍散見於文獻中。內容從經典主題開始，如維納引理（Wiener lemma）、斯特里查茨不等式（Strichartz inequality）以及測度的分形維度基礎，逐步進入更高級的材料，其中一些是由作者自己發展的。
譜測度是量子力學數學理論中的一個基本概念，與量子態的組成部分有關，這些組成部分涉及哈密頓算符的能量水平，另一方面也與該狀態的動態有關。然而，這些對應關係並非立即顯現，近年來發現了許多細微之處和微妙之處。
這些微妙之處的一個寶貴例子是所謂的「仙境定理」（Wonderland theorem），該定理由B. Simon於1995年首次發表。它顯示，在某些自伴算符的度量空間中，譜測度為奇異連續的算符集合是一個通用集合（對某些人來說，這是異常的）。最近的研究顯示，除了奇異連續性之外，譜測度還具有其他通用性質。這些性質通常與多種不同的廣義維度概念、上維度和下維度相關，並在量子力學、動態系統的遍歷性以及演化半群中具有動態意義。所有這些為新的和引人入勝的研究途徑開辟了道路。
對於對譜測度的譜性質有特定興趣的研究生而言，本書是主要的目標讀者，而研究人員則可以從中獲益，因為書中呈現了許多重要結果，其中許多結果首次以書籍形式發表。
作者簡介
Silas L. Carvalho has earned his PhD in Physics at the University of São Paulo, Brazil, in 2010. From 2011 to 2013, he was an Adjunct Professor at the Federal University of São Paulo. Since then, Dr. Carvalho has been serving as an Adjunct Professor at the Math department of the Federal University of Minas Gerais. He develops research in Mathematical Physics, Ergodic Theory and Dynamical Systems, mainly in problems that involve fractal dimensions and measures. Some allied areas include Schrödinger and Dirac operators, quantum dynamics, and stability problems involving $C_0$-semigroups.
César R. de Oliveira is a Full Professor at the Math department of the Federal University of São Carlos, Brazil. His field of research is Mathematical Physics; more specifically, spectral theory of Schrödinger operators, the Aharonov-Bohm effect, and effective operators in systems with reduction of dimensions. He has spent extended research visits at the University of British Columbia, Canada, and Milan University, Italy. Dr. Oliveira has authored three books, including "Intermediate Spectral Theory and Quantum Dynamics" (Birkhäuser, 2009, ISBN 978-3-7643-8794-5).
作者簡介(中文翻譯)
莫艾西爾·阿洛伊西奧是巴西杰基廷霍尼亞和穆庫里山谷聯邦大學數學系的兼任教授。他於2019年在巴西米納斯吉拉斯聯邦大學獲得數學博士學位。他的研究興趣包括算子理論、數學物理和動態系統。一些相關領域包括薛丁格和狄拉克算子、量子（不）穩定性、動態局部化、抽象微分方程和算子代數。
西拉斯·L·卡瓦略於2010年在巴西聖保羅大學獲得物理學博士學位。從2011年到2013年，他是巴西聖保羅聯邦大學的兼任教授。自那時以來，卡瓦略博士一直在巴西米納斯吉拉斯聯邦大學數學系擔任兼任教授。他的研究領域包括數學物理、遍歷理論和動態系統，主要集中在涉及分形維度和測度的問題上。一些相關領域包括薛丁格和狄拉克算子、量子動力學，以及涉及 $C_0$-半群的穩定性問題。
塞薇爾·R·德·奧利維拉是巴西聖卡洛斯聯邦大學數學系的正教授。他的研究領域是數學物理；更具體地說，是薛丁格算子的譜理論、阿哈羅諾夫-博姆效應以及在降維系統中的有效算子。他曾在加拿大不列顛哥倫比亞大學和意大利米蘭大學進行過長期的研究訪問。奧利維拉博士著有三本書，包括《中級譜理論與量子動力學》（Birkhäuser, 2009, ISBN 978-3-7643-8794-5）。
