Theory of elementary excitations in unstable Bose-Einstein condensates and the instability of sonic horizons

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 67, Issue 3, 2003, Pages

  Leonhardt, U ^a   Kiss, T ^a,b,c   Ohberg P ^a,d  

^a UNIVERSITY OF ST ANDREWS   (United Kingdom)

^b WIGNER RESEARCH CENTRE FOR PHYSICS   (Hungary)

^c UNIVERSITY OF PÉCS   (Hungary)

^d UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ATOMIC PHYSICS; EIGENVALUES AND EIGENFUNCTIONS; FLUID DYNAMICS; HAMILTONIANS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS;

BOGOLIUBOV-DE GENNES EQUATION; GROSS-PITAEVSKII EQUATION; HYDRODYNAMIC INSTABILITY; UNSTABLE BOSE-EINSTEIN CONDENSATE;

QUANTUM THEORY;

EID: 0038193934     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (39)

1. R. Courant and K.O. Friedrichs, Supersonic Flow and Shock Waves (Wiley, New York, 1967).
2. L.D. Landau and E.M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1982).
3. F. Dalfovo, S. Giorgini, L.P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999).
4. C. Raman, M. Köhl, R. Onofrio, D.S. Durfee, C.E. Kuklewicz, Z. Hadzibabic, and W. Ketterle, Phys. Rev. Lett. 83, 2502 (1999)
5. S. Inouye, S. Gupta, T. Rosenband, A.P. Chikkatur, A. Görlitz, T.L. Gustavson, A.E. Leanhardt, D.E. Pritchard, and W. Ketterle, Phys. Rev. Lett. 87, 080402 (2001).
6. S. Sinha and Y. Castin, Phys. Rev. Lett. 87, 190402 (2001).
7. L.J. Garay, J.R. Anglin, J.I. Cirac, and P. Zoller, Phys. Rev. Lett. 85, 4643 (2000).
8. L.J. Garay, J.R. Anglin, J.I. Cirac, and P. Zoller, Phys. Rev. A 63, 023611 (2001).
9. L.J. Garay, in Artificial Black Holes, edited by M. Novello, M. Visser, and G.E. Volovik (World Scientific, Singapore, 2002).
10. C. Barcelo, S. Liberati, and M. Visser, e-print arXiv:gr-qc/0110036
11. M. Sakagami and A. Ohashi, Prog. Theor. Phys. 107, 1267 (2002).
12. U. Leonhardt, T. Kiss, and P. Öhberg, e-print arXiv:cond-mat/02111464.
13. One of the most spectacular unstable Bose-Einstein condensates is the Bose nova, see E.A. Donley, N.R. Claussen, S.L. Cornish, J.L. Roberts, E.A. Cornell, and C.E. Wieman, Nature (London) 412, 295 (2001). Here a condensate collapses due to a change from repulsive to attractive atom-atom interaction, induced by a Feshbach resonance. Our theory can be easily modified to describe the initial stage of a collapsing condensate with attractive interactions.
14. G. Kang, Phys. Rev. D55, 7563 (1997), and references therein
15. S.A. Fulling, Aspects of Quantum Field Theory in Curved Spacetime (Cambridge University Press, Cambridge, 1989)
16. B. Schroer and J.A. Swieca, Phys. Rev. D 2, 2938 (1970).
17. V.A. Yurovsky, Phys. Rev. A 65, 033605 (2002).
18. A.L. Fetter, Ann. Phys. (N.Y.) 70, 67 (1972)
19. A.L. Fetter, Phys. Rev. A 53, 4245 (1996).
20. S. Stringari, Phys. Rev. Lett. 77, 2360 (1996)
21. M. Fliesser, A. Csordás, P. Szépfalusy, and R. Graham, Phys. Rev. A 56, R2533 (1997)
22. P. Öhberg, E.L. Surkov, I. Tittonen, S. Stenholm, M. Wilkens, and G.V. Shlyapnikov, ibid. 56, R3346 (1997).
23. W.G. Unruh, Phys. Rev. Lett. 46, 1351 (1981)
24. M. Visser, Class. Quantum Grav. 15, 1767 (1998).
25. For a wave equation of sound in fluids with vorticity see S.E.P. Bergliaffa, K. Hibberd, M. Stone, and M. Visser, e-print cond-mat/0106255.
26. A. Csordás, R. Graham, and P. Szépfalusy, Phys. Rev. A 57, 4669 (1998).
27. M.J. Ablowitz and A.S. Fokas, Complex Variables (Cambridge University Press, Cambridge, 1997)
28. R.B. Dingle, Asymptotic Expansions: Their Derivation and Interpretation (Academic, London, 1973)
29. W.H. Furry, Phys. Rev. 71, 360 (1947).
30. S.M. Hawking, Nature (London) 248, 30 (1974)
31. S.M. Hawking, Commun. Math. Phys. 43, 199 (1975).
32. R. Brout, S. Massar, R. Parentani, and Ph. Spindel, Phys. Rep. 260, 329 (1995).
33. The issue is related to the trans-Planckian problem of black holes, see G.t. Hooft, Nucl. Phys. B 256, 727 (1985)
34. T. Jacobson, Phys. Rev. D 44, 1731 (1991)
35. W.G. Unruh; Phys. Rev. D 51, 2827 (1995)
36. R. Brout, S. Massar, R. Parentani, and Ph. Spindel, Phys. Rev. D 52, 4559 (1995). The healing length ξ [3] plays the role of the Planck length.
37. S. Corley, Phys. Rev. D 57, 6280 (1998).
38. S. Corley and T. Jacobson, Phys. Rev. D 59, 124011 (1999).
39. U. Leonhardt, T. Kiss, and P. Ohberg, e-print gr-qc/0211069.