Preface
前言
Chapter 1 Overview
概述
1.1 Orientation
研究方向
1.2 An experiment—ballistic expansion
一个实验——弹道展开
1.3 One dimension versus two or three dimensions
一维与二维或三维
1.4 Quantum mechanics
量子力学
1.5 The essence of the Bethe ansatz
贝脱方案的实质
1.6 A simple example—the 1/r2 potential
一个简单的例子——1/r2势
1.7 References and history
参考文献和历史事件
Chapter 2 Integrability and Nondiffraction
可积性和非衍射
2.1 What does it mean to say that a system is integrable
一个系统可积意味着什么
2.2 Scattering without diffraction
无衍射效应的散射
2.3 Proof of integrability for the hyperbolic potential
双曲势可积性的证明
2.4 The δ-function potentia
δ函数势
2.5 Adding periodic boundary conditions
添加周期性边界条件
2.6 This is not a low-density approximation
这不是低密度近似
Chapter 3 Techniques
技巧
3.1 Our fundamental equation
基本方程
3.2 The ground state
基态
3.3 Response of the ground state
基态的响应
3.4 Excitations near the ground state
基态附近的激发
3.5 Zero-temperature thermodynamics
零温热力学
3.6 Finite temperature thermodynamics
有限温度热力学
3.7 The inverse-square potential—an example
一个例子——平方反比势
Chapter 4 The Classical Limit
经典极限
4.1 Classical diffraction—pictures from an exhibition
图片展示——经典衍射
4.2 The classical limit
经典极限
4.3 Classical system at zero temperature
零温时的经典系统
4.4 The inverse-square limit—example 1
例1——平方反比极限
4.5 The Toda limit—example 2
例2——户田极限
4.6 Solitons and constant profile solutions
孤子和形状不变解
Chapter 5 Groundstate Wavefunctions of Product Form
乘积形式的基态波函数
5.1 An ansatz for the ground state wavefunction
基态波函数的假设
5.2 Excited states for the trigonometric case
三角问题的激发态
5.3 Ground state correlations for the trigonometric case
三角问题中的基态关联
Chapter 6 The Heisenberg-Ising Model
海森伯-伊辛模型
6.1 The model and its symmetries
模型及其对称性
6.2 Bethe′s ansatz
贝脱方案
6.3 The dilute limit M＜＜N
低密度极限M＜＜N
6.4 A change of variables
变量的改变
6.5 The ground state
基态
6.6 Perturbations and excitations of the ground state
基态的微扰和激发
6.7 Zero-temperature thermodynamics
零温热力学
6.8 The low-density limit and complex solutions
低密度极限和复杂解
6.9 Further results
进一步的结果
Chapter 7 Consistency
一致性
7.1 How can we show integrability
如何证明可积性
7.2 How can we show non-integrability
如何证明不可积性
7.3 Consistency conditions
一致性条件
7.4 Solution to consistency conditions
一致性条件的解
7.5 Periodic and twisted boundary conditions
周期性边界条件和扭曲的边界条件
7.6 Eigenvectors of the transfer matrix，two-components
转移矩阵的本征矢，二分量
7.7 Eigenvectors of the transfer matrix: multicomponent system
转移矩阵的本征矢，多分量系统
7.8 The constructive approach
构造法
Chapter 8 Exchange Models
交换模型
8.1 Hyperbolic exchange models
双曲交换模型
8.2 Integrability
可积性
8.3 The two-body phase shifts
二体相移
8.4 The inverse-square exchange potential
平方反比交换势
8.5 The δ-function potential
δ 函数势
Chapter 9 The Sinh-Cosh Model
双曲正弦-双曲余弦模型
9.1 The sinh-cosh potential
双曲正弦-双曲余弦势
9.2 Integrability
可积性
9.3 The two-body problem
二体问题
9.4 Phase shifts
相移
9.5 Spin waves
自旋波
9.6 Solution and results for zero temperature and zero spin/charge
零温和零自旋/电荷的解和结论
Chapter 10 Exchange Lattice Systems by Freezing
冻结的交换晶格系统
10.1 Freezing continuum models to give lattice models
从连续模型的冻结到晶格模型
10.2 Review of the continuum exchange model
连续交换模型的回顾
10.3 The limit λ→∞
λ→∞极限
10.4 The first order equation
一阶方程
10.5 The densities ρ(x) and e(x)
密度ρ(x) 和e(x)
10.6 Results for the nearest-neighbor model
最近邻模型的结果
10.7 Results for the hyperbolic model
双曲模型的结果
10.8 The inverse-square lattice at finite temperature
有限温度的平方反比晶格
Chapter 11 The Hubbard Model
赫伯德模型
11.1 The model and its symmetries
模型及其对称性
11.2 Bethe′s ansatz
贝脱方案
11.3 The repulsive case
排斥情况
11.4 The attractive case
吸引情况
11.5 Excitations at the symmetric point
对称点的激发
Appendix A Some Two-Body Problems
几个二体问题
A.1 The two-body problem
二体问题
A.2 The potential v(r)=cδ(r)
v(r)=cδ(r) 势
A.3 The potential v(r)=λ(λ-1)/r2
v(r)=λ(λ-1)/r2势
A.4 The potential v(r)=λ(λ-1)/sin h2r
v(r)=λ(λ-1)/sin h2r势
A.5 The potential v(r)=-λ(λ-1)/cos h2r
v(r)=-λ(λ-1)/cos h2r势
A.6 Combination potentials
混合势
Appendix B Representations
表象
B.1 The permutation group
置换群
B.2 The twisted permutation group
扭曲的置换群
B.3 Two ways to write the Bethe ansatz
贝脱方案的两种表述
B.4 Two-body scattering
二体散射
B.5 The consistency conditions
一致性条件
B.6 Representations
表象
B.7 Twisted boundary conditions
扭曲的边界条件
B.8 Realizations
实现
Bibliography
文献目录
Index
索引 |
