ANALYSIS AND COMPUTATION FOR GROUND STATE SOLUTIONS OF BOSE-FERMI MIXTURES AT ZERO TEMPERATURE

作者：Cai Yongyong^*; Wang Hanquan

来源：SIAM Journal on Applied Mathematics, 2013, 73(2): 757-779.

DOI：10.1137/120873820

• coupled Gross-Pitaevskii equations
• Bose-Fermi mixtures
• gradient flow with discrete normalization
• numerical simulation
• ground state

Previous numerical studies on the ground state structure of Bose-Fermi mixtures mostly relied on Thomas-Fermi (TF) approximation for the Fermi gas. In this paper, we establish the existence and uniqueness of ground state solutions of Bose-Fermi mixtures at zero temperature for both a coupled Gross-Pitaevskii (GP) equations model and a model with TF approximation for fermions. To prove the uniqueness, the key is to estimate the L-infinity bounds of the ground state solution. By implementing an efficient method-gradient flow with discrete normalization with backward Euler finite difference discretization-to compute the coupled GP equations, we report extensive numerical results in one and two dimensions. The numerical experiments show that we can also extract many interesting phenomena without reference to TF approximation for the fermions. Finally, we numerically compare the ground state solutions for the coupled GP equations model and the model with TF approximation for fermions as well as for the model with TF approximations for both bosons and fermions.

• 出版日期2013
• 单位云南大学; 北京计算科学研究中心