Analytical results for energy spectrum and eigenstates of a Bose-Einstein condensate in a Mott insulator state

作者：Wu Y^*; Yang XX

来源：Physical Review A, 2003, 68(1): 013608.

DOI：10.1103/PhysRevA.68.013608

We present a method to solve the model describing either a Bose-Einstein condensate (BEC) in a Mott-insulator state or a double-well BEC. We show that all the energy eigenvalues and eigenstates for an arbitrary (small or large) total atom number N can be explicitly expressed analytically in terms of a parameter lambda whose values are determined by the roots of the polynomials of the order of at most 1+int(N/2), with int(x) denoting x';s integer part. We also show that lambda';s explicit analytical expressions for Nless than or equal to7 can be readily obtained by a simple MATHEMATICA code. Besides, finding the roots of the polynomials of the order of at most 1+int(N/2) to give explicitly all the energy eigenvalues and eigenstates greatly simplifies the corresponding calculations, particularly when the total atom number N is large.

• 出版日期2003-7
• 单位华中科技大学; 中国科学院武汉物理与数学研究所