量子圖導論格雷戈里.伯科拉科 9787040612608 【台灣高等教育出版社】

Name: 量子圖導論 格雷戈里.伯科拉科 9787040612608 【台灣高等教育出版社】
Brand: abooksthep
Price: 859.0 TWD
Availability: InStock

圖書均為代購，正常情形下，訂後約兩周可抵台。
物品所在地：中國大陸
原出版社：高等教育

NT$859

商品編號:

供貨狀況: 尚有庫存

加入最愛

商品介紹

*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：量子圖導論
ISBN：9787040612608
出版社：高等教育
著編譯者：格雷戈里.伯科拉科
頁數：270
所在地：中國大陸 *此為代購商品
書號：1624952
可大量預訂，請先連絡。

內容簡介

「量子圖」被認為是一維複合體，並配備了微分運算元（「Hamilton運算元」）。當人們考慮各種波通過類似於圖的薄鄰域的准一維（例如「中等尺度」或「納米尺度」）系統傳播時，量子圖在數學、物理、化學和工程中自然而然地作為簡化模型出現。至少從20世紀30年代開始，有關量子圖的研究已經出現，從那時起，量子圖技術已經成功地應用於數學物理、一般數學及其應用的各個領域。例如，動力系統理論、控制理論、量子混沌、Anderson局域化、微電子學、光子晶體、物理化學、納米科學、超導理論等。量子圖提出了許多非平凡的數學挑戰，這使得它們成為數學家鍾愛的對象。量子圖的研究彙集了來自圖論、組合學、數學物理、偏微分方程和譜理論等領域的工具和直覺。本書全面介紹了這個主題，收集了主要的概念和技術。它還包括對當前量子圖研究和應用狀況的概述。

Preface
Introduction
Chapter 1 Operators on Graphs Quantum graphs
1 1 Main graph notions and notation
1 2 Difference operators Discrete Laplace operators
1 3 Metric graphs
1 4 Differential operators on metric graphs Quantum graphs
1 4 1 Vertex conditions Finite graphs
1 4 2 Scale invarianee
1 4 3 Quadratic form
1 4 4 Examples of vertex conditions
1 4 5 Infinite graphs
1 4 6 Non-local vertex conditions
1 5 Further remarks and references
Chapter 2 Quantum Graph Operators Special Topics
2 1 Quantum graphs and scattering matrices
2 1 1 Scattering on vertices
2 1 2 Bond scattering matrix and the secular equation
2 2 First order operators and scattering matrices
2 3 Factorization of quantum graph Hamiltonians
2 4 Index of quantum graph operators
2 5 Dependence on vertex conditions
2 5 1 Variations in the edge lengths
2 6 Magnetic SchrSdinger operator
2 7 Further remarks and references
Chapter 3 Spectra of Quantum Graphs
3 1 Basic spectral properties of compact quantum graphs
3 1 1 Discreteness of the spectrum
3 1 2 Dependence on the vertex conditions
3 1 3 Eigenfunction dependence
3 1 4 An Hadamard-type formula
3 1 5 Generic simplicity of the spectrum
3 1 6 Eigenvalue bracketing
3 1 7 Dependence on the coupling constant at a vertex
3 2 The Shnol' theorem
3 3 Generalized eigenfunctions
3 4 Failure of the unique continuation property Scars
3 5 The ubiquitous Dirichlet-to-Neumann map
3 5 1 DtN map for a single edge
3 5 2 DtN map for a compact graph with a "boundary
3 5 3 DtN map for a single vertex boundary
3 5 4 DtN map and the secular equation
3 5 5 DtN map and number of negative eigenvalues
3 6 Relations between quantum and discrete graph spectra
3 7 Trace formulas
3 7 1 Secular equation
3 7 2 Weyl's law
3 7 3 Derivation of the trace formula
3 7 4 Expansion in terms of periodic orbits
3 7 5 Other formulations of the trace formula
3 8 Further remarks and references
Chapter 4 Spectra of Periodic Graphs
4 1 Periodic graphs
4 2 Floquet-Bloch theory
4 2 1 Floquet transform on combinatorial periodic graphs
4 2 2 Floquet transform of periodic difference operators
4 2 3 Floquet transform on quantum periodic graphs
4 2 4 Floquet transform of periodic operators
4 3 Band-gap structure of spectrum
4 3 1 Discrete case
4 3 2 Quantum graph case
4 3 3 Floquet transform in Sobolev classes
4 4 Absence of the singular continuous spectrum
4 5 The point spectrum
4 6 Where do the spectral edges occur
4 7 Existence and location of spectral gaps
4 8 Impurity spectra
4 9 Further remarks and references
Chapter 5 Spectra of Quantum Graphs Special Topics
5 1 Resonant gap opening
5 1 1 "Spider" decorations
5 2 Zeros of eigenfunctions and nodal domains
5 2 1 Some basic results
5 2 2 Bounds on the nodal count
5 2 3 Nodal count for special types of graphs
5 2 4 Nodal deficiency and Morse indices
5 3 Spectral determinants of quantum graphs
5 4 Scattering on quantum graphs
5 5 Further remarks and references
Chapter 6 Quantum Chaos on Graphs
6 1 Classical "motion" on graphs
6 2 Spectral statistics and random matrix theory
6 2 1 Form factor of a unitary matrix
6 2 2 Random matrices
6 3 Spectral statistics of graphs
6 4 Periodic orbit expansions
6 4 1 On time-reversal invariance
6 4 2 Diagonal approximation
6 4 3 The simplest example of an off-diagonal term
6 5 Further remarks and references
Chapter 7 Some Applications and Generalizations
7 1 Inverse problems
7 1 1 Can one hear the shape of a quantum graph
7 1 2 Quantum graph isospectrality
7 1 3 Can one count the shape of a graph
7 1 4 Inverse scattering
7
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。