Pair Correlations in a Finite-Temperature 1D Bose Gas

Physical Review Letters

Volumn 91, Issue 4, 2003, Pages

  Kheruntsyan, K V ^a   Gangardt, D M ^b   Drummond, P D ^a   Shlyapnikov, G V ^b,c,d  

^a UNIVERSITY OF QUEENSLAND   (Australia)

^b LABORATOIRE KASTLER BROSSEL   (France)

^c FOM INSTITUTE AMOLF   (Netherlands)

^d KURCHATOV INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CALCULATIONS; CORRELATION METHODS; FERMI LEVEL; FREE ENERGY; HAMILTONIANS; HIGH ENERGY PHYSICS; INTEGRAL EQUATIONS; IONIZATION OF GASES; ONE DIMENSIONAL; VAPORS;

BOSE GAS; FERMIONIZATION; HELLMANN-FEYNMAN THEOREM; PAIR CORRELATIONS; PERIODIC BOUNDARY CONDITION; PHOTOASSOCIATION; YANG-YANG EQUATION;

GAS DYNAMICS;

EID: 4243680114     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.91.040403     Document Type: Article

References (25)

1. A. Görlitz et al, Phys. Rev. Lett.10.1103/PhysRevLett.87.130402 87, 130402 (2001);
2. F. Schreck et al, Phys. Rev. Lett.10.1103/PhysRevLett.87.080403 87, 080403 (2001);
3. M. Greiner et al, Phys. Rev. Lett.10.1103/PhysRevLett.87.160405 87, 160405 (2001).
4. D.C. Mattis, The Many-Body Problem: An Encyclopedia of Exactly Solved Models in 1D (World Scientific, Singapore, 1994).
5. M.D. Girardeau, J. Math. Phys. (N.Y.) 1, 516 (1960);
6. M.D. GirardeauPhys. Rev. 139, B500 (1965).
7. E.H. Lieb and W. Liniger, Phys. Rev.10.1103/PhysRev.130.1605 130, 1605 (1963);
8. E.H. Lieb, Phys. Rev.10.1103/PhysRev.130.1616 130, 1616 (1963).
9. C.N. Yang and C.P. Yang, J. Math. Phys. (N.Y.) 10, 1115 (1969).
10. V.N. Popov, Functional Integrals in Quantum Field Theory and Statistical Physics (Reidel, Dordrecht, 1983).
11. H.B. Thacker, Rev. Mod. Phys.10.1103/RevModPhys.53.253 53, 253 (1981).
12. V.E. Korepin, N.M. Bogoliubov, and A.G. Izergin, Quantum Inverse Scattering Method and Correlation Functions (Cambridge University Press, Cambridge, England, 1993).
13. Yu. Kagan, B.V. Svistunov, and G.V. Shlyapnikov, JETP Lett.JTPLA2 42, 209 (1985);
14. Yu. KaganB.V. SvistunovG.V. ShlyapnikovJETP Lett.48, 56 (1988).
15. D.M. Gangardt and G.V. Shlyapnikov, Phys. Rev. Lett.10.1103/PhysRevLett.90.010401 90, 010401 (2003).
16. F.D.M. Haldane, Phys. Rev. Lett.10.1103/PhysRevLett.47.1840 47, 1840 (1981).
17. M. Olshanii, Phys. Rev. Lett.10.1103/PhysRevLett.81.938 81, 938 (1998).
18. H. Hellmann, Z. Phys. 85, 180 (1933);
19. R.P. Feynman, Phys. Rev.10.1103/PhysRev.56.340 56, 340 (1939).
20. N.D. Mermin and H. Wagner, Phys. Rev. Lett.10.1103/PhysRevLett.17.1133 17, 1133 (1966);
21. P.C. Hohenberg, Phys. Rev.10.1103/PhysRev.158.383 158, 383 (1967).
22. D.S. Petrov, G.V. Shlyapnikov, and J.T.M. Walraven, Phys. Rev. Lett.10.1103/PhysRevLett.85.3745 85, 3745 (2000).
23. Similar results for the crossover GP/DQ regime have been obtained using a classical field approximation in Y. Castin et al, J. Mod. Opt.10.1080/095003400750039627 47, 2671 (2000).
24. For an axially trapped nonuniform gas with a large number of particles, the peak density can be used for determining the lower bound on the local interaction parameter (Formula presented). In this case, one can also use the local density approximation such that our results give the local pair correlation at different positions from the trap center. Work on this problem is currently in progress: K.V. Kheruntsyan, D.M. Gangardt, P.D. Drummond, and G.V. Shlyapnikov (to be published).
25. For the 3D gas, this result requires the grand canonical description [see, e.g., R.M. Ziff, G.E. Uhlenbeck, and M. Kac, Phys. Rep. 32, 169 (1977)], while in 1D and 2D it is valid for any choice of the ensemble.