玻色：愛因斯坦凝聚中的量化渦旋及其動力學（簡體書）

《玻色：愛因斯坦凝聚中的量化渦旋及其動力學》的特點與獨到之處是我們設計了一種模守恒且能量遞減的數值方法來求得靜態的Gross-Pitaevskii方程（組）的數值解；我們也設計了一種高精度且快速的方法-時間分裂譜方法來求解動態的Gross-Pitaevskii方程（組）的數值解;并用所求得的數值解來分別模擬玻色-愛因斯坦凝聚體的基態與動力學，特別是揭示了基態中的渦旋現象及渦旋運動規律。《玻色：愛因斯坦凝聚中的量化渦旋及其動力學》提出的高效數值方法可以為人們利用計算機研究玻色-愛因斯坦凝聚現象提供理論方法，加深人們對第五種物質-玻色-愛因斯坦凝聚體的理解，最終使人們更方便掌握這種物質現象的各種規律，以便更好地使之在國民經濟建設中發揮作用。《玻色：愛因斯坦凝聚中的量化渦旋及其動力學》提出的高效數值方法使用方便，不僅僅只可以用在研究玻色-愛因斯坦凝聚現象，還可以推廣應用到其它科學問題之中：例如一般能量泛函在有限制性條件下的求極值計算問題、具有守恒率的偏微分方程（組）的數值求解問題等。本書在在描述理論和數值方法過程中深入淺出，從簡單到復雜，循序漸進。既有深奧的理論說明，又有詳細的算法推導過程；既有原始的物理模型，又有數學的簡化過程；這些讓讀者既領悟到了數值模擬的具體過程，又了解了玻色-愛因斯坦凝聚這一極低溫度的物理現象。

Preface
Chapter 1 Introduction
1.1 Brief history of Bose-Einstein condensation
1.2 Quantized vortex states in BEC
1.3 Review on numerical methods for stationary states
1.4 Review on numerical methods for the time-dependent GPE
1.5 Scope of this book

Chapter 2 Stationary states for rotating BEC
2.1 GPE in a rotational frame
2.1.1 Dimensionless GPE
2.1.2 Reduction to two dimensions
2.2 Stationary states
2.2.1 Semiclassical scaling and geometrical optics
2.2.2 Ground state
2.2.3 Approximate ground state
2.2.4 Excited states
2.2.5 Critical angular velocity in symmetric trap
2.3 Numerical methods for stationary states
2.3.1 Gradient flow with discrete normalization
2.3.2 Energy diminishing
2.3.3 Continuous normalized gradient fiow
23.4 Fully numerical discretization
2.4 Numerical results
2.4.1 Initial data for computing ground state
2.4.2 Results in 2D
2.4.3 Results in 3D
2.4.4 Critical angular velocity
2.4.5 Numerical verification for dimension reduction
2.4.6 Errors of the TF approximation
2.4.7 Spurious numerical ground states when
2.5 Conclusion

Chapter 3 Dynamics of rotating BEC
3.1 Some properties of the GPE
3.2 A TSSP method for the GPE
3.2.1 Time-splitting
3.2.2 Discretization in 2D
3.2.3 Discretization in 3D
3.2.4 Stability
3.3 Numerical results
3.3.1 Accuracy test
3.3.2 Dynamics of a vortex lattice in rotating BEC
3.3.3 Generation of giant vortex in rotating BEC
3.4 Conclusion N

Chapter 4 Applications to stationary states of rotating two-component BEC
4.1 The time-dependent coupled GPEs
4.1.1 Dimensionless coupled GPEs
4.1.2 Reduction to two dimensions
4.1.3 Semiclassical scaling
4.2 Stationary states
4.2.1 Ground state
4.2.2 Symmetric and central vortex states
4.2.3 Numerical methods for the stationary states
4.2.4 Numerical results for the stationary states
4.3 Conclusion

Chapter 5 Applications to dynamics of rotating two-component BEC
5.1 Some properties of the coupled GPEs
5.2 A TSSP method for the coupled GPEs
5.2.1 Time-splitting
5.2.2 Discretization in 2D
5.2.3 Stability
5.3 Numerical results for the dynamics
5.4 Conclusion

Chapter 6 Application into ground state of spinor BEC
6.1 A continuous normalized gradient flow
6.1.1 Euler-Lagrange equations
6.1.2 A continuous normalized gradient flow
6.2 Normalization and magnetization conservative and energy diminishing numerical scheme
6.2.1 Semi-discretization in time
……
Chapter 7 Applications to dynamics of spinor F=1BEC
Chapter 8 Concluding remarks and future work
Bibliography