Wave functions of the super-Tonks-Girardeau gas and the trapped one-dimensional hard-sphere Bose gas

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 81, Issue 6, 2010, Pages

  Girardeau, M D ^a   Astrakharchik, G E ^b  

^a UNIVERSITY OF ARIZONA   (United States)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BOSE GAS; CLUSTER STATE; COUPLING CONSTANTS; HARD-SPHERE; INTER-PARTICLE SEPARATION; METASTABILITIES; NEGATIVE VALUES; PARABOLIC CYLINDER; SCATTERING LENGTH; SUDDEN CHANGE; TONKS-GIRARDEAU GAS;

GASES; WAVE FUNCTIONS;

SPHERES;

EID: 77953749493     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.81.061601     Document Type: Article

References (30)

1. M. Olshanii, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.938 81, 938 (1998).
2. D. S. Petrov, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3745 85, 3745 (2000).
3. J. L. Roberts, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86. 4211 86, 4211 (2001).
4. T. Bergeman, M. G. Moore, and M. Olshanii, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.163201 91, 163201 (2003).
5. M. Girardeau, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1703687 1, 516 (1960).
6. B. Paredes, Nature NATUAS 0028-0836 10.1038/nature02530 429, 277 (2004).
7. T. Kinoshita, T. Wenger, and D. S. Weiss, Science SCIEAS 0036-8075 10.1126/science.1100700 305, 1125 (2004).
8. T. Cheon and T. Shigehara, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(98)00188-1 243, 111 (1998);
9. T. Cheon and T. Shigehara, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.2536 82, 2536 (1999).
10. M. D. Girardeau and M. Olshanii, e-print arXiv: cond-mat/0309396.
11. M. D. Girardeau, H. Nguyen, and M. Olshanii, Opt. Commun. OPCOB8 0030-4018 10.1016/j.optcom.2004.09.079 243, 3 (2004).
12. E. H. Lieb and W. Liniger, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.130.1605 130, 1605 (1963).
13. J. B. McGuire, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704156 5, 622 (1964).
14. G. E. Astrakharchik, D. Blume, S. Giorgini, and B. E. Granger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.030402 92, 030402 (2004).
15. M. T. Batchelor, M. Bortz, X. W. Guan, and N. Oelkers, J. Stat. Mech. PRLTAO 1742-5468 10.1088/1742-5468/2005/10/L10001 (2005) L10001.
16. G. E. Astrakharchik, J. Boronat, J. Casulleras, and S. Giorgini, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.190407 95, 190407 (2005).
17. E. Haller, M. Gustavsson, M. J. Mark, J. G. Danzl, R. Hart, G. Pupillo, and H.-C. Nägerl, Science SCIEAS 0036-8075 10.1126/science.1175850 325, 1224 (2009).
18. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic Press, New York, 1980), pp. 1058, 1064-1067.
19. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. II, pp. 1565-1567, 1641.
20. M. A. Cirone, J. Phys. B JPAPEH 0953-4075 10.1088/0953-4075/34/23/304 34, 4571 (2001).
21. S. Franke-Arnold, S. M. Barnett, G. Huyet, and C. Sailliot, Eur. Phys. J. D EPJDF6 1434-6060 10.1140/epjd/e2003-00036-6 22, 373 (2003);
22. their parameter a is related to g B by a = g B x osc.
23. E. Tempfli, S. Zöllner, and P. Schmelcher, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/10/10/103021 10, 103021 (2008).
24. M. D. Girardeau, E. M. Wright, and J. M. Triscari, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.033601 63, 033601 (2001).
25. M. D. Girardeau and E. M. Wright, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.010406 95, 010406 (2005).
26. M. D. Girardeau and A. Minguzzi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.080404 96, 080404 (2006).
27. F. Calogero, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1664820 10, 2191 (1969);
28. F. Calogero, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1664821 10, 2197 (1969);
29. B. Sutherland, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1665584 12, 246 (1971).
30. A similar calculation for an untrapped system on a ring was carried out by S. Chen, L. Guan, X. Yin, Y. Hao, and X. W. Guan, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.031609 81, 031609 (R) (2010). The energy E TG following Eq. (5) of that paper is not a hard-sphere energy but instead the energy of point particles with λ □ 1 (strong Lieb-Liniger repulsion).