Interacting Electrons: Theory and Computational Approaches (Hardcover)
暫譯: 互動電子:理論與計算方法 (精裝版)

Richard M. Martin, Lucia Reining, David M. Ceperley

  • 出版商: Cambridge
  • 出版日期: 2016-07-29
  • 售價: $1,350
  • 貴賓價: 9.8$1,323
  • 語言: 英文
  • 頁數: 840
  • 裝訂: Hardcover
  • ISBN: 0521871506
  • ISBN-13: 9780521871501
  • 下單後立即進貨 (約5~7天)

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商品描述

 

<內容簡介>

 

Recent progress in the theory and computation of electronic structure is bringing an unprecedented level of capability for research. Many-body methods are becoming essential tools vital for quantitative calculations and understanding materials phenomena in physics, chemistry, materials science and other fields. This book provides a unified exposition of the most-used tools: many-body perturbation theory, dynamical mean field theory and quantum Monte Carlo simulations. Each topic is introduced with a less technical overview for a broad readership, followed by in-depth descriptions and mathematical formulation. Practical guidelines, illustrations and exercises are chosen to enable readers to appreciate the complementary approaches, their relationships, and the advantages and disadvantages of each method. This book is designed for graduate students and researchers who want to use and understand these advanced computational tools, get a broad overview, and acquire a basis for participating in new developments.

>Provides extensive background and theory for each of the methods, which enables readers to understand capabilities as well as limitations, and how to avoid errors when making computations
>Designed to be accessible for beginners with non-technical introductory chapters for each method
>Chapters are complemented with exercises enabling students to master the theory by putting the tools to practical use

<章節目錄>

 

Preface
Part I. Interacting Electrons: Beyond the Independent-Particle Picture:
1. The many electron problem: introduction
2. Signatures of electron correlation
3. Concepts and models for interacting electrons
Part II. Foundations of Theory for Many-Body Systems:
4. Mean fields and auxiliary systems
5. Correlation functions
6. Many-body wavefunctions
7. Particles and quasi-particles
8. Functionals in many-particle physics
Part III. Many-Body Green's Function Methods:
9. Many-body perturbation theory: expansion in the interaction
10. Many-body perturbation theory via functional derivatives
11. The RPA and the GW approximation for the self-energy
12. GWA calculations in practice
13. GWA calculations: illustrative results
14. RPA and beyond: the Bethe-Salpeter equation
15. Beyond the GW approximation
16. Dynamical mean field theory
17. Beyond the single-site approximation in DMFT
18. Solvers for embedded systems
19. Characteristic hamiltonians for solids with d and f states
20. Examples of calculations for solids with d and f states
21. Combining Green's functions approaches: an outlook
Part IV. Stochastic Methods:
22. Introduction to stochastic methods
23. Variational Monte Carlo
24. Projector quantum Monte Carlo
25. Path integral Monte Carlo
26. Concluding remarks
Part V. Appendices: A. Second quantization
B. Pictures
C. Green's functions: general properties
D. Matsubara formulation for Green's functions for T ?= 0
E. Time-ordering, contours, and non-equilibrium
F. Hedin's equations in a basis
G. Unique solutions in Green's function theory
H. Properties of functionals
I. Auxiliary systems and constrained search
J. Derivation of the Luttinger theorem
K. Gutzwiller and Hubbard approaches
References
Index.

 

商品描述(中文翻譯)

內容簡介

最近在電子結構理論和計算方面的進展,為研究帶來了前所未有的能力。多體方法正成為量化計算和理解物理、化學、材料科學及其他領域材料現象的重要工具。本書提供了最常用工具的統一闡述:多體微擾理論、動態平均場理論和量子蒙特卡羅模擬。每個主題都以較少技術性的概述開始,以便廣泛讀者理解,隨後提供深入的描述和數學公式。實用指導、插圖和練習題的選擇使讀者能夠欣賞這些互補方法之間的關係,以及每種方法的優缺點。本書旨在幫助研究生和研究人員使用和理解這些先進的計算工具,獲得廣泛的概述,並為參與新發展奠定基礎。

- 提供每種方法的廣泛背景和理論,使讀者能夠理解其能力和限制,以及在進行計算時如何避免錯誤
- 設計為對初學者友好,為每種方法提供非技術性的入門章節
- 各章節配有練習題,使學生能夠通過實際應用工具來掌握理論

章節目錄

前言
第一部分:相互作用的電子:超越獨立粒子圖像:
1. 多電子問題:介紹
2. 電子相關性的特徵
3. 相互作用電子的概念和模型
第二部分:多體系統理論的基礎:
4. 平均場和輔助系統
5. 相關函數
6. 多體波函數
7. 粒子和準粒子
8. 多粒子物理中的泛函
第三部分:多體格林函數方法:
9. 多體微擾理論:在相互作用中的展開
10. 通過泛函導數的多體微擾理論
11. 自能的RPA和GW近似
12. 實踐中的GWA計算
13. GWA計算:示例結果
14. RPA及其以外:貝特-薩爾佩特方程
15. 超越GW近似
16. 動態平均場理論
17. DMFT中的單位點近似以外
18. 嵌入系統的求解器
19. 具有d和f態的固體的特徵哈密頓量
20. 具有d和f態的固體計算示例
21. 結合格林函數方法:展望
第四部分:隨機方法:
22. 隨機方法介紹
23. 變分蒙特卡羅
24. 投影量子蒙特卡羅
25. 路徑積分蒙特卡羅
26. 總結
第五部分:附錄:A. 第二量子化
B. 圖片
C. 格林函數:一般性質
D. Matsubara形式的格林函數(T ?= 0)
E. 時序、輪廓和非平衡
F. Hedin方程在基底中的表達
G. 格林函數理論中的唯一解
H. 泛函的性質
I. 輔助系統和約束搜索
J. Luttinger定理的推導
K. Gutzwiller和Hubbard方法
參考文獻
索引。