文摘
英文文摘
Chapter1 Introduction
Chapter2 Squeezed Number State Solutions of Generalized Two-Mode Har-monic Oscillators Model
2.1 Introduction
2.2 so(3, 2) algebraic diagonalization of generalized two-mode oscillators model
2.2.1 so(3, 2) algebraic structure of generalized two-mode oscillators model
2.2.2 so(3, 2) algebraic diagonalization of the model
2.3 Statistical properties of extended su(1,1) squeezed number state
2.4 Conclusion and remarks
2.5 Appendix A
2.6 Appendix B
Bibliography
Chapter3 su(3) Algebraic Structure of the Cuprate Superconductors Model based on the Analogy with Atomic Nuclei
3.1 Introduction
3.2 The model and the reduced Hamiltonian of Iachello
3.3 The energy spectrum
3.3.1 The calculations of diagonalization
3.3.2 A special case: v2 = 0
3.3.3 The case of v2 ≠ 0
3.4 Conclusion
3.5 Appendix C
Bibliography
Chapter4 su(1, 2) Algebraic Structure of the XYZ Antiferromagnetic Model in Linear Spin-Wave Frame
4.1 Introduction
4.2 The model
4.2.1 XXZ antiferromagnetic model and su(1, 1) coherent states
4.2.2 XYZ antiferromagnetic model in linear spin-wave frame with an su(1, 2) algebraic structure
4.3 The diagonalization method and the energy spectrum
4.4 Conclusion and remarks
4.5 Appendix D
4.6 Appendix E
Bibliography
Chapter5 Superfluid-Mott Insulator Transition of Spin-2 Cold Bosons in an Optical Lattice in a Magnetic Field
5.1 Introduction
5.2 The generalized Bose-Hubbard model
5.3 The energy eigenvalues and the Mott ground states
5.4 Phase diagrams of superfluid-Mott insulator transition
5.5 Remarks and conclusion
5.6 Appendix F
Bibliography
List of Publications and Preprints
Acknowledgements
