玻色-爱因斯坦凝聚中的量化涡旋及其动力学

所属分类:力学  
出版时间:2012-5   出版时间: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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