爱因斯坦凝聚体的动力学研究 外势场中玻色 英文版PDF电子书下载

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Chapter1 Theoretical models and methods 1

1.1Introduction to Bose-Einstein condensates 1

1.2The Gross-Pitaevskii mean-field models 3

1.2.1The continuous Gross-Pitaevskii equations 3

1.2.2The discrete Gross-Pitaevskiiequations 13

1.3Variational approximation approach 19

1.4Discrete modulational instablity analysis 22

1.5Prolongation structure technique 25

Bibliography 27

Chapter2 Variational approximation and modulational instability 30

2.1Variational approximation for continuous GP equations 30

2.1.1Variational approximation for the focusing NLS equation 30

2.1.2Collective excitations of a 3D BEC in a double-well trap 34

2.2Variational approximation for discrete Gross-Pitaevskii equations 37

2.3Discrete modulational instability of discrete Gross-Pitaevskii equations 41

Bibliography 45

Chapter3 Dynamics of BEC with time-and space-modulated nonlinearities 46

3.1Linear time-dependent Schrodinger equation with harmonic potential 47

3.2One-dimensional BECs with time- and space-modulated nonlinearities 49

3.2.1One-dimensional BEC with space-modulated nonlinearity 50

3.2.2Two-component BECs with spatiotemporally modulated nonlinearities 53

3.3Two-dimensional BEC with time- and space-modulated nonlinearities 71

3.3.1Quantized quasi-2D BEC with spatially modulated nonlinearity 71

3.3.2Quantized vortices in a rotating Bose-Einstein condensate 79

3.4Three-dimensional BEC with space-modulated nonlinearity 95

3.4.1 3D BEC in cylindrically symmetric potential 95

3.4.2 3D BEC in spherically symmetric potential 98

Bibliography 100

Chapter4 Dynamics of Bose-Einstein condensate with cubic-quintic nonlinearity 103

4.1The theoretical model and its solutions 105

4.2Stability of nonlinear matter waves in BEC with two-body interaction 109

4.3Stability of nonlinear matter waves in BEC with two- and three-body interactions 115

4.4The exact vortex soliton solutions of quasi-two dimensional GP equation 119

4.5Structures of the vortex solitons 121

Bibliography 126

Chapter5 Integrability and dynamics of a spin-1 Bose-Einstein condensate 127

5.1The theoretical model 127

5.2Integrability and matter-wave solitons in a spin-1 Bose-Einstein condensate 129

5.2.1Similarity transformation 130

5.2.2Prolongation structures of the three coupled NLS equation 131

5.3Matter-wave solitons in F＝1 spinor Bose-Einstein condensate 139

5.3.1Exact N-bright soliton solutions to the integrable case b2＝b0 139

5.3.2Exact N-bright soliton solutions to the integrable case b2＝0 141

Bibliography 152

Chapter6 Matter-wave solitons in a spin-1 BEC with time-modulated external potential 153

6.1The model 153

6.2Exact matter-wave soliton solutions 157

6.3Matter-wave solitons in a spin-1 BEC with time-dependent parameters 164

6.3.1Attractive harmonic potential with constant frequency 164

6.3.2Expulsive harmonic potential with time-dependent frequency 168

6.3.3Different choices of the condensate parameters 173

Bibliography 174

Chapter7 Dynamics and stability of the spin-1 BEC in a standing light wave 176

7.1Spin-1 BEC in a standing light wave 176

7.2Stationary solutions and linear stability analysis 179

7.2.1Exact stationary solutions of three-component GP equations 179

7.2.2Linear stability analysis 182

7.3Dynamics and stability 184

7.3.1Dynamics and stability of the stationary solutions 1～3 184

7.3.2Stability of the stationary solutions 4～5 189

7.3.3Stability of the stationary solutions 6～9 192

Bibliography 194

Chapter8 Summary and future prospects 196

8.1Summary 196

8.2Future prospects 199

编后记 202

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