玻色-爱因斯坦凝聚中的量化涡旋及其动力学

出版时间：2012-5  出版社：科学出版社  作者：王汉权  页数：134  字数：409000  

内容概要

玻色-爱因斯坦凝聚中的量化涡旋及其动力学（英文版）的特点与独到之处是我们设计了一种模守恒且能量递减的数值方法来求得静态的Gross-Pitaevskii方程（组）的数值解；我们也设计了一种高精度且快速的方法-时间分裂谱方法来求解动态的Gross-Pitaevskii方程（组）的数值解；并用所求得的数值解来分别模拟玻色-爱因斯坦凝聚体的基态与动力学，特别是揭示了基态中的涡旋现象及涡旋运动规律。玻色-爱因斯坦凝聚中的量化涡旋及其动力学（英文版）提出的高效数值方法可以为人们利用计算机研究玻色-爱因斯坦凝聚现象提供理论方法，加深人们对第五种物质-玻色-爱因斯坦凝聚体的理解，最终使人们更方便掌握这种物质现象的各种规律，以便更好地使之在国民经济建设中发挥作用。玻色-爱因斯坦凝聚中的量化涡旋及其动力学（英文版）提出的高效数值方法使用方便，不仅仅只可以用在研究玻色-爱因斯坦凝聚现象，还可以推广应用到其它科学问题之中：例如一般能量泛函在有限制性条件下的求极值计算问题、具有守恒率的偏微分方程（组）的数值求解问题等。玻色-爱因斯坦凝聚中的量化涡旋及其动力学（英文版）在在描述理论和数值方法过程中深入浅出，从简单到复杂，循序渐进。既有深奥的理论说明，又有详细的算法推导过程；既有原始的物理模型，又有数学的简化过程；这些让读者既领悟到了数值模拟的具体过程，又了解了玻色-爱因斯坦凝聚这一极低温度的物理现象。

书籍目录

PrefaceChapter 1 Introduction1.1 Brief history of Bose-Einstein condensation1.2 Quantized vortex states in BEC1.3 Review on numerical methods for stationary states1.4 Review on numerical methods for the time-dependent GPE1.5 Scope of this bookChapter 2 Stationary states for rotating BEC2.1 GPE in a rotational frame2.1.1 Dimensionless GPE2.1.2 Reduction to two dimensions2.2 Stationary states2.2.1 Semiclassical scaling and geometrical optics2.2.2 Ground state2.2.3 Approximate ground state2.2.4 Excited states2.2.5 Critical angular velocity in symmetric trap2.3 Numerical methods for stationary states2.3.1 Gradient flow with discrete normalization2.3.2 Energy diminishing2.3.3 Continuous normalized gradient flow2.3.4 Fully numerical discretization2.4 Numerical results2.4.1 Initial data for computing ground state2.4.2 Results in 2D2.4.3 Results in 3D2.4.4 Critical angular velocity2.4.5 Numerical verification for dimension reduction2.4.6 Errors of the TF approximation2.4.7 Spurious numerical ground states when |Ω|≥γxy=12.5 ConclusionChapter 3 Dynamics of rotating BEC3.1 Some properties of the GPE3.2 A TSSP method for the GPE3.2.1 Time-splitting3.2.2 Discretization in 2D3.2.3 Discretization in 3D3.2.4 Stability3.3 Numerical results3.3.1 Accuracy test3.3.2 Dynamics of a vortex lattice in rotating BEC3.3.3 Generation of giant vortex in rotating BEC3.4 ConclusionChapter 4 Applications to stationary states of rotating two-component BEC4.1 The time-dependent coupled GPEs4.1.1 Dimensionless coupled GPEs4.1.2 Reduction to two dimensions4.1.3 Semiclassical scaling4.2 Stationary states4.2.1 Ground state4.2.2 Symmetric and central vortex states4.2.3 Numerical methods for the stationary states4.2.4 Numerical results for the stationary states4.3 ConclusionChapter 5 Applications to dynamics of rotating two-component BEC5.1 Some properties of the coupled GPEs5.2 A TSSP method for the coupled GPEs5.2.1 Time-splitting5.2.2 Discretization in 2D5.2.3 Stability5.3 Numerical results for the dynamics5.4 ConclusionChapter 6 Application into ground state of spinor BEC6.1 A continuous normalized gradient flow6.1.1 Euler-Lagrange equations6.1.2 A continuous normalized gradient flow6.2 Normalization and magnetization conservative and energy diminishing numerical scheme6.2.1 Semi-discretization in time6.2.2 A fully discretized method6.3 Numerical results6.3.1 Choice of initial data and energy diminishing6.3.2 Accuracy test6.3.3 Applications6.4 ConclusionChapter 7 Applications to dynamics of spinor F=1 BEC7.1 The generalized Gross-Pitaevskii equations7.2 A TSSP method for the generalized GPEs7.2.1 Time-splitting7.2.2 Discretization in 2D7.2.3 Stability7.3 Numerical results7.3.1 Accuracy tests7.3.2 Generation of vortices7.3.3 Dynamics of a vortex lattice7.4 ConclusionChapter 8 Concluding remarks and future workBibliography

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