The Analytical Solutions For1-D Spinor BEC Systems With Zeeman Terms

Spinor Bose-Einstein condensation (BEC) is one of the most important research topics in physics in recent years. Comparing with the scalar BEC, the frozen spin degree of freedom of the atoms are released, and rich novel behaviors of the spinor BECs related to the spin dynamics have been displayed. In the experiments, the ex-ternal magnetic field will separate the atoms with different spin degree of freedom due to the Zeeman effects, so Zeeman effects make deep influence to the spinor dynamics. Under the mean-field approximation, the spin-1and spin-2BEC with Zeeman effects are described by Gross-Pitaevskii systems with3and5components respectively. In this thesis for master’s degree, by using the Painleve direct truncation method, we present a variety of analytical solutions, including soliton-like solutions and periodic solutions, for the1-dimensional spin-1and spin-2BEC systems with Zeeman terms. These solutions will help to the further comprehension to the spinor dynamics.