隨機運算元-量子光譜和動力學上的無序效應 9787040612165 Michael Aizenman Si
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物品所在地：中國大陸
原出版社：高等教育
物品所在地：中國大陸
原出版社：高等教育
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| *完成訂單後正常情形下約兩周可抵台。 *本賣場提供之資訊僅供參考，以到貨標的為正確資訊。 印行年月：202402*若逾兩年請先於私訊洽詢存貨情況，謝謝。 台灣(台北市)在地出版社，每筆交易均開具統一發票，祝您中獎最高1000萬元。 書名：隨機運算元-量子光譜和動力學上的無序效應 ISBN：9787040612165 出版社：高等教育 著編譯者：Michael Aizenman Si 叢書名：美國數學會經典影印系列 頁數：326 所在地：中國大陸 *此為代購商品 書號：1625879 可大量預訂，請先連絡。 【台灣高等教育出版社簡體書】 隨機運算元-量子光譜和動力學上的無序效應 787040612165 Michael Aizenman Si 內容簡介 本書介紹了關於量子光譜和動力學上無序效應的數學理論入門。涵蓋的主題從自伴運算元的譜和動力學的基本理論到這裏通過分數矩量法提出的Anderson局域化，再到最近關於共振離域的結果。全書共有十七章，每章都集中於特定的數學主題或將理論與物理相關聯的例證，例如量子Hall效應的影響。數學章節包括量子光譜和動力學的一般關係、遍歷性及其含義、建立光譜和動力學局域化機制的方法、Green函數的應用和性質、它與本徵函數關聯子的關係、Herglotz-Pick函數的分數矩、樹圖運算元的相圖、共振離域、譜統計猜想及相關結果。此外，本書還包含作者在各自機構所開設課程的筆記，這些筆記被研究生和博士后研究人員廣泛參考。目錄 PrefaceChapter 1 Introduction 1 1 The random Schr?dinger operator 1 2 The Anderson localization-delocalization transition 1 3 Interference， path expansions， and the Green function 1 4 Eigenfunction correlator and fractional moment bounds 1 5 Persistence of extended states versus resonant delocalization 1 6 The book's organization and topics not covered Chapter 2 General Relations Between Spectra and Dynamics 2 1 Infinite systems and their spectral decomposition 2 2 Characterization of spectra through recurrence rates 2 3 Recurrence probabilities and the resolvent 2 4 The RAGE theorem 2 5 A scattering perspective on the ac spectrum Notes Exercises Chapter 3 Ergodic Operators and Their Self-Averaging Properties 3 1 Terminology and basic examples 3 2 Deterministic spectra 3 3 Self-averaging of the empirical density of states 3 4 The limiting density of states for sequences of operators 3 5 Statistic mechanical significance of the DOS Notes Exercises Chapter 4 Density of States Bounds:Wegner Estimate and Lifshitz Tails 4 1 The Wegner estimate 4 2 DOS bounds for potentials of singular distributions 4 3 Dirichlet-Neumann bracketing 4 4 Lifshitz tails for random operators 4 5 Large deviation estimate 4 6 DOS bounds which imply localization Notes Exercises Chapter 5 The Relation of Green Functions to Eigenfunctions 5 1 The spectral fow under rank-one perturbations 5 2 The general spectral averaging principle 5 3 The Simon-Wolff criterion 5 4 Simplicity of the pure-point spectrum 5 5 Finite-rank perturbation theory 5 6 A zero-one boost for the Simon-Wolff criterion Notes Exercises Chapter 6 Anderson Localization Through Path Expansions 6 1 A random walk expansion 6 2 Feenberg's loop-erased expansion 6 3 A high-disorder localization bound 6 4 Factorization of Green functions Notes Exercises Chapter 7 Dynamical Localization and Fractional Moment Criteria 7 1 Criteria for dynamical and spectral localization 87 2 Finite-volume approximations 7 3 The relation to the Green function 7 4 The el-condition for localization Notes Exercises Chapter 8 Fractional Moments from an Analytical Perspective 8 1 Finiteness of fractional moments 8 2 The Herglotz-Pick perspective 8 3 Extension to the resolvent's off-diagonal elements 8 4 Decoupling inequalities Notes Exercises Chapter 9 Strategies for Mapping Exponential Decay 9 1 Three models with a common theme 9 2 Single-step condition: Subharmonicity and contraction arguments 9 3 Mapping the regime of exponential decay: The Hammersley stratagem 9 4 Decay rates in domains with boundary modes Notes Exercises Chapter 10 Localization at High Disorder and at Extreme Energies 10 1 Localization at high disorder 10 2 Localization at weak disorder and at extreme energies 10 3 The Combes-Thomas estimateux Notes Exercises Chapter 11 Constructive Criteria for Anderson Localization 11 1 Finite-volume localization criteriasolsC tnanoa 11 2 Localization in the bulk 11 3 Derivation of the finite-volume criteria 11 4 Additional implications Notes Exercises Chapter 12 Complete Localization in One Dimension 12 1 Weyl functions and recursion relations 12 2 Lyapunov exponent and Thouless relation 12 3 The Lyapunov exponent criterion for ac spectrum 12 4 Kotani theory 12 5 Implications for quantum wires 12 6 A moment-generating function 12 7 Complete dynamical localization Notes Exercises Chapter 13 Diffusion Hypothesis and the Green-Kubo-Streda Formula 13 1 The diffusion hypothesis 13 2 Heuristic linear response theory 13 3 The Green-Kubo-Streda formulas 13 4 Localization and decay of the two-point function Notes Exercises Chapter 14 Integer Quantum Hall Efect 14 1 Laughlin's charge pump 14 2 Charge transport as an index 14 3 A calculable expr 詳細資料或其他書籍請至台灣高等教育出版社查詢，查後請於PChome商店街私訊告知ISBN或書號，我們即儘速上架。 |
