Spinless Bosons in a 1D Harmonic Trap with Repulsive Delta Function Interparticle Interaction I: General Theory
MA Zhong-Qi1, C. N. Yang2,3
1Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 1000492Institute for Advanced Study, Tsinghua University, Beijing 1000843Institute of Theoretical Physics, The Chinese University of Hong Kong, Hong Kong
Spinless Bosons in a 1D Harmonic Trap with Repulsive Delta Function Interparticle Interaction I: General Theory
MA Zhong-Qi1, C. N. Yang2,3
1Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 1000492Institute for Advanced Study, Tsinghua University, Beijing 1000843Institute of Theoretical Physics, The Chinese University of Hong Kong, Hong Kong
摘要In these two papers, we solve the N body 1D harmonically trapped spinless Boson problem with repulsive δ function interaction in the limit N→∞. The general theory is given in paper I and the numerical solutions will be given in paper II.
Abstract：In these two papers, we solve the N body 1D harmonically trapped spinless Boson problem with repulsive δ function interaction in the limit N→∞. The general theory is given in paper I and the numerical solutions will be given in paper II.
(Static properties of condensates; thermodynamical, statistical, and structural properties)
引用本文:
MA Zhong-Qi;C. N. Yang;. Spinless Bosons in a 1D Harmonic Trap with Repulsive Delta Function Interparticle Interaction I: General Theory[J]. 中国物理快报, 2009, 26(12): 120506-120506.
MA Zhong-Qi, C. N. Yang,. Spinless Bosons in a 1D Harmonic Trap with Repulsive Delta Function Interparticle Interaction I: General Theory. Chin. Phys. Lett., 2009, 26(12): 120506-120506.
[1] Olshanii M 1998 Phys. Rev. Lett. 81 938 G\"{orlitz A et al 2001 Phys. Rev. Lett. 87130402 Moritz H et al 2003 Phys. Rev. Lett. 91 250402 St\"{oferle T et al 2004 Phys. Rev. Lett. 92130403 and reference therein [2] Bloch I et al 2008 Rev. Mod. Phys. 80 885 [3] Guan L et al 2009 Phys. Rev. Lett. 102 160402 Yang C N 2009 Chin. Phys. Lett. 26 120504. Wewill follow the notation $\{N-M,M\$ in this paper for the symmetryof space wave functions. [4] Lieb E H and Liniger W 1963 Phys. Rev. 1301605 [5] You Y Z 2009 Chin. Phys. Lett. (submitted) NoticeYou's $f$ and $\alpha$ are related to $\zeta$ and $\beta$ of thepresent paper by $f=2\zeta /\beta^2$ and $\alpha =1/\beta$, wherethe factor 2 comes from a comparison of You's Hamiltonian with ours.
2009, Vol. 26 
