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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 |
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| Cite this article: |
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MA Zhong-Qi, C. N. Yang 2009 Chin. Phys. Lett. 26 120506 |
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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.
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05.30.Jp
67.85.-d
03.75.Hh
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Received: 19 October 2009
Published: 27 November 2009
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| PACS: |
05.30.Jp
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(Boson systems)
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67.85.-d
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(Ultracold gases, trapped gases)
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03.75.Hh
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(Static properties of condensates; thermodynamical, statistical, and structural properties)
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[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. |
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