- 随机算子--量子光谱和动力学上的无序效应(英文版)(精)/美国数学会经典影印系列
- - 作者：(美)迈克尔·艾珍曼//(德)西蒙娜·沃泽尔|责编:和静
  - 出版社：高等教育
  - ISBN：9787040612165
  - 出版日期：2024/02/01
  - 页数：326
- 售价：54

内容大纲
本书介绍了关于量子光谱和动力学上无序效应的数学理论入门。涵盖的主题从自伴算子的谱和动力学的基本理论到这里通过分数矩量法提出的Anderson局域化，再到最近关于共振离域的结果。全书共有十七章，每章都集中于特定的数学主题或将理论与物理相关联的例证，例如量子Hall效应的影响。数学章节包括量子光谱和动力学的一般关系、遍历性及其含义、建立光谱和动力学局域化机制的方法、Green函数的应用和性质、它与本征函数关联子的关系、Herglotz-Pick函数的分数矩、树图算子的相图、共振离域、谱统计猜想及相关结果。此外，本书还包含作者在各自机构所开设课程的笔记，这些笔记被研究生和博士后研究人员广泛参考。
作者介绍
目录
Preface
Chapter 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 expression for the index
  14.4.Evaluating the charge transport index in a mobility gap
  14.5.Quantization of the Kubo-Streda-Hall conductancer
  14.6.The Connes area formula
  Notes
  Exercises
Chapter 15.Resonant Delocalization
  15.1.Quasi-modes and pairwise tunneling amplitude
  15.2.Delocalization through resonant tunneling
  15.3.Exploring the argument's
  Notes
  Exercises
Chapter 16.Phase Diagrams for Regular Tree Graphs
  16.1.Summary of the main results
  16.2.Recursion and factorization of the Green function
  16.3.Spectrum and DOS of the adjacency operator
  16.4.Decay of the Green function
  16.5.Resonant delocalization and localization
  Notes
  Exercises
Chapter 17.The Eigenvalue Point Process and a Conjectured Dichotomy
  17.1.Poisson statistics versus level repulsion
  17.2.Essential characteristics of the Poisson point processes
  17.3.Poisson statistics in finite dimensions in the localization regime
  17.4.The Minami bound and its CGK generalization
  17.5.Level statistics on finite tree graphs
  17.6.Regular trees as the large N limit of d-regular graphs
  Notes
  Exercises
Appendix A.Elements of Spectral Theory
  A.1.Hilbert spaces, self-adjoint linear operators, and their resolvents
  A.2.Spectral calculus and spectral types
  A.3.Relevant notions of convergence
  Notes
Appendix B.Herglotz-Pick Functions and Their Spectra
  B.1.Herglotz representation theorems
  B.2.Boundary function and its relation to the spectral measure
  B.3.Fractional moments of HP functions
  B.4.Relation to operator monotonicity
  B.5.Universality in the distribution of the values of random HP functions
Bibliography
Index

内容大纲

作者介绍

目录

同类热销排行榜

推荐书目