| Chapter 1 Introduction | 第1-17页 |
| ·Bose-Einstein condensation | 第11页 |
| ·Historical efforts on the realization of Bose-Einstein condensation | 第11-13页 |
| ·Studies after the first realization of Bose-Einstein condensation | 第13-14页 |
| ·Schedule of this dissertation | 第14-17页 |
| Chapter 2 Effects of Trapping Potential and Spatial Dimensionality | 第17-51页 |
| ·Density of states and thermodynamic quantities of an ideal system | 第22-28页 |
| ·Density of states | 第22-25页 |
| ·Grand potential and other thermodynamic quantities | 第25-28页 |
| ·Thermodynamic properties of a degenerate ideal Bose gas | 第28-34页 |
| ·General expressions for an ideal Bose gas trapped in a generic power-law potential in n-dimensional space | 第28-29页 |
| ·Specific cases of the results presented in Sec. 2.2.1 | 第29-32页 |
| ·Tuning the critical temperature and adiabatic cooling | 第32-34页 |
| ·Two criteria concerning Bose-Einstein condensation | 第34-39页 |
| ·General criterion on BEC occurrence | 第34-36页 |
| ·General criterion on continuity of heat capacity at the critical temperature | 第36-39页 |
| ·Thermodynamic properties of an ideal Fermi gas | 第39-51页 |
| ·Introduction | 第39-40页 |
| ·Total number of particles and total energy of the system | 第40页 |
| ·Fermi energy, energy of the ground state, and chemical potential | 第40-41页 |
| ·Heat capacity of the system | 第41-42页 |
| ·Discussion | 第42-51页 |
| Chapter 3 Effects of Finite Particle Number | 第51-61页 |
| ·Bose-Einstein condensation of a finite number of particles trapped in any-dimensional space | 第55-61页 |
| ·Total particle number and density of states | 第55-58页 |
| ·Transition temperature | 第58-59页 |
| ·Condensate fraction at temperatures T < Tc | 第59-61页 |
| Chapter 4 Effects of Particle Interactions | 第61-77页 |
| ·Pseudopotential operator for hard-sphere interaction in any-dimensional space | 第63-68页 |
| ·Bose-Einstein condensation of a uniform imperfect Bose gas | 第68-77页 |
| ·Virial expansion of the equation of state | 第69-73页 |
| ·Effects of interactions on Bose-Einstein condensation | 第73-77页 |
| Chapter 5 Conclusions and Outlook | 第77-83页 |
| APPENDIXES | 第83-97页 |
| A. An n -dimensional sphere of radius R | 第85-88页 |
| B. Derivation of Equation (2.1.6) | 第88-91页 |
| C. Dirac δ-function in a space dimensionality n≥3 | 第91-93页 |
| D. On the Lame coefficients in spherical coordinates in n-dimensional space | 第93-95页 |
| E. List of selected papers | 第95-97页 |
| Bibliography | 第97-102页 |
