在未來三年中，我計劃研究低維量子系統的量子相變問題，著眼於和冷原子系統實驗的相關性，我將以研究玻色系統的量子相變為主，並專注於底下幾個子題： A. ㄧ維 Feshbach resonant atom-molecule system 在 optical lattice 下之相圖與相變。 B. ㄧ維 boson system 在 optical lattice 中出現 supersolid 之可能性。 C. 二維及三維 boson Hubbard model 中的 supersolid phase. D. Multi-component BEC 系統中的量子相變行為及其和 dilute quantum gas critical point 之關聯。 In this three-year research project, I plane to study the quantum phase transition problems in low dimensional quantum mechanical many body systems. With an eye on the possible relations and implications on (from) experiments, I will mainly concentrate on the study of the quantum phase transitions in Boson systems and quantum spin systems. In particular, I will focus in the following research topics: A. The phase and phase transitions of a one-dimensional Feshbach resonant atom-molecule system in an optical lattice. B. The study of the possible supersolid phases in a generalized one-dimensional Boson Hubbard model. C. The lattice supersolid phase and the relating phase transitions to superfluid or Mott insulating states in two and three dimensional boson Hubbard model. D. The quantum phase transitions in multi-component bose or fermion systems and their relations to the dilute quantum gas fixed point.
