Asymptotic formula for the condensate wave function of a trapped Bose gas

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 5, 2000, Pages 556011-556012

  Margetis, Dionisios ^a  

^a HARVARD UNIVERSITY   (United States)

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EID: 0345850075     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. F. Dalfovo, L. Pitaevskii, and S. Stringari, Phys. Rev. A 54, 4213 (1996).
2. Handbook of Mathematical Functions, edited by M. Abramowitz and I.A. Stegun (Dover, New York, 1972), p. 446.
3. S.P. Hastings and J.B. Leod, Arch. Ration. Mech. Anal. 73, 31 (1980).
4. P.C.T. De Boer and G.S.S. Ludford, Plasma Phys. 17, 29 (1975).
5. C.M. Bender and S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978), pp. 419-479.
6. T.T. Wu, Phys. Rev. A 58, 1465 (1998).
7. -1/2, p being the equilibrium density, but C of course trivially reduces to zero. See T.T. Wu, J. Math. Phys. 2, 105 (1961). A precise description of the class of external potentials for which Eq. (1) makes sense is beyond the scope of this report.
8. P. Painlevé, Acta Math. 25, 1 (1902).
9. E.L. Ince, Ordinary Differential Equations (Dover, New York, 1956), p. 345.
10. In Ref. [3], the authors make use of the fact that the second Painlevé transcendent under condition (3) satisfies a linear integral equation. See, for instance, M.J. Ablowitz and H. Segur, Phys. Rev. Lett. 38, 1103 (1977).
11. D. Margetis, Ph.D. thesis, Harvard University, 1999 (unpublished).
12. D. Margetis, J. Math. Phys. 40, 5522 (1999).