玻色-愛因斯坦凝聚中的量化渦旋及其動力學

內(nèi)容概要

玻色-愛因斯坦凝聚中的量化渦旋及其動力學（英文版）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(shù)值方法來求得靜態(tài)的Gross-Pitaevskii方程（組）的數(shù)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(tài)的Gross-Pitaevskii方程（組）的數(shù)值解；并用所求得的數(shù)值解來分別模擬玻色-愛因斯坦凝聚體的基態(tài)與動力學，特別是揭示了基態(tài)中的渦旋現(xiàn)象及渦旋運動規(guī)律。玻色-愛因斯坦凝聚中的量化渦旋及其動力學（英文版）提出的高效數(shù)值方法可以為人們利用計算機研究玻色-愛因斯坦凝聚現(xiàn)象提供理論方法，加深人們對第五種物質(zhì)-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(zhì)現(xiàn)象的各種規(guī)律，以便更好地使之在國民經(jīng)濟建設中發(fā)揮作用。玻色-愛因斯坦凝聚中的量化渦旋及其動力學（英文版）提出的高效數(shù)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(xiàn)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(shù)值求解問題等。玻色-愛因斯坦凝聚中的量化渦旋及其動力學（英文版）在在描述理論和數(shù)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(shù)學的簡化過程；這些讓讀者既領悟到了數(shù)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(xiàn)象。

書籍目錄

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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