Gross-Pitaevskii dynamics of Bose-Einstein condensates and superfluid turbulence

Fluid Dynamics Research

Volumn 33, Issue 5-6, 2003, Pages 509-544

  Abid, M ^a   Huepe, C ^b   Metens, S ^c   Nore, C ^d   Pham, C T ^e   Tuckerman, L S ^d   Brachet, M E ^e  

^a AIX MARSEILLE UNIVERSITÉ   (France)

^b UNIVERSITY OF CHICAGO   (United States)

^c UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^d UFR 919 Laboratoire d'Informatique Pour la Mécanique et les Sciences de l'Ingénieur   (France)

^e SORBONNE UNIVERSITÉ   (France)

Author keywords

Bifurcation and dynamics; Bose Einstein condensates; Branch following method; Exact results; Gross Pitaevskii equation; Superfluid turbulence

Indexed keywords

FLUID DYNAMICS; NONLINEAR EQUATIONS; SYSTEM STABILITY; TURBULENT FLOW; WAVE EQUATIONS;

LOW-TEMPERATURE SUPERFLOW; SUPERFLUID TURBULENCE;

GAS CONDENSATES;

BIFURCATION; DIRECT NUMERICAL SIMULATION; HYDRODYNAMICS; SUPERFLUID; TURBULENCE;

EID: 0345099329     PISSN: 01695983     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fluiddyn.2003.09.001     Document Type: Article

References (76)

1. Abid M. Brachet M. Maurer J. Nore C. Tabeling P. Experimental and numerical investigations of low-temperature superfluid turbulence Eur. J. Mech. B Fluids 17 4 1998 665-675
2. Anderson M.H. Ensher J.R. Matthews M.R. Wieman C.E. Cornell E.A. Observation of Bose-Einstein condensation in a dilute atomic vapor Science 269 1995 198
3. 4He without mutual friction J. Low Temp. Phys. 121 2000 405
4. Araki T. Tsubota M. Nemirovskii S.K. Energy spectrum of superfluid turbulence with no normal-fluid component Phys. Rev. Lett. 89 14 2002 1-4
5. 4He: answers and questions J. Low Temp. Phys. 93 1993 1031-1057
6. Barenghi, C.F., Donnelly, R.J., Vinen, W.F. (Eds.), 2001. Quantized Vortex Dynamics and Superfluid Turbulence, Lecture Notes in Physics.
7. Brachet M. Géométrie des structures à petite échelle dans le vortex de Taylor-Green C.R. Acad. Sci. 311 1990 775
8. Brachet M.E. Meiron D.I. Orszag S.A. Nickel B.G. Morf R.H. Frisch U. Small-scale structure of the Taylor-Green vortex J. Fluid Mech. 130 1983 411-452
9. Bradley C.C. Sackett C.A. Tollett J.J. Hulet R.G. Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions Phys. Rev. Lett. 75 9 1995 1687
10. Bradley C.C. Sackett C.A. Hulet R.G. Bose-Einstein condensation of lithium: observation of limited condensate number Phys. Rev. Lett. 78 6 1997 985
11. Bretin V. Rosenbush P. Chevy F. Shlyapnikov G.V. Dalibard J. Quadrupole oscillation of a single-vortex condensate: evidence for Kelvin modes Phys. Rev. Lett. 90 2003 100403
12. Dalfovo F. Giorgini S. Pitaevskii L.P. Stringari S. Theory of Bose-Einstein condensation in trapped gases Rev. Mod. Phys. 71 3 1999
13. Davis K.B. Mewes M.O. Adrews M.R. van Druten N.J. Durfee D.S. Kurn D.M. Ketterle W. Bose-Einstein condensation in a gas of sodium atoms Phys. Rev. Lett. 75 1995 3969
14. 4He at mK temperature Physica B 280 2000 43-44
15. Dodd R.J. Edwards M. Williams C.J. Clark C.W. Holland M.J. Ruprecht P.A. Burnett K. Role of attractive interactions on Bose-Einstein condensation Phys. Rev. A 54 1 1996 661
16. Domaradzki J. Liu W. Brachet M. An analysis of sugrid-scale interactions in numerically simulated isotropic turbulence Phys. Fluids A 5 1993 1747
17. Donnelly R.J. Quantized Vortices in Helium II 1991 Cambridge University Press Cambridge
18. Douady S. Couder Y. Brachet M.E. Direct observation of the intermittency of intense vorticity filaments in turbulence Phys. Rev. Lett. 67 1991 983
19. Fauve S. Laroche C. Castaing B. Pressure fluctuations in swirling turbulent flows J. Phys. II 3 1993 271
20. Frisch U. Turbulence, the Legacy of A.N. Kolmogorov 1995 Cambridge University Press Cambridge
21. Frisch T. Pomeau Y. Rica S. Transition to dissipation in a model of superflow Phys. Rev. Lett. 69 1992 1644
22. Gardiner C.W. Handbook of Stochastic Methods 1985 Springer Berlin
23. Gottlieb D. Orszag S.A. Numerical Analysis of Spectral Methods 1977 SIAM Philadelphia
24. Gross E.P. Structure of a quantized vortex in boson systems Nuovo Cimento 20 3 1961 454
25. Guckenheimer J. Holmes P. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields 1983 Springer Berlin
26. Hakim V. Nonlinear Schrödinger flow past an obstacle in one dimension Phys. Rev. E 55 3 1997 2835-2845
27. Huepe C. Brachet M.-E. Solutions de nucléation tourbillonnaires dans un modèle d'écoulement superfluide C.R. Acad. Sci. Paris 325 II 1997 195-202
28. Huepe C. Brachet M.E. Scaling laws for vortical nucleation solutions in a model of superflow Physica D 140 2000 126-140
29. Huepe C. Métens S. Dewel G. Borckmans P. Brachet M.-E. Decay rates in attractive Bose-Einstein condensates Phys. Rev. Lett. 82 2 1999 1616
30. Huepe C. Tuckerman L.S. Métens S. Brachet M.-E. Stability and decay rates of non-isotropic attractive Bose-Einstein condensates Phys. Rev. A 68 2003 023609
31. Ihas G.G. Avenel O. Aarts R. Salmelin R. Varoquaux E. Quantum nucleation of vortices in the flow of superfluid He-4 through an orifice Phys. Rev. Lett. 69 2 1992 327
32. Inouye S. Gupta S. Rosenband T. Chikkatur A.P. Görlitz A. Gustavson T.L. Leanhardt A.E. Pritchard D.E. Ketterle W. Observation of vortex phase singularities in Bose-Einstein condensates Phys. Rev. Lett. 87 2001 080402
33. Jones C.A. Roberts P.H. Motions in a Bose condensate: IV. axisymmetric solitary waves J. Phys. A 15 1982 2599
34. Kawatra M.P. Pathria R.K. Quantized vortices in imperfect Bose gas Phys. Rev. 151 1966 1
35. Kivotides D. Vassilicos J.C. Samuels D.C. Barenghi C.F. Kelvin waves cascade in superfluid turbulence Phys. Rev. Lett. 86 2001 3080-3083
36. Klein R. Majda A.J. Self-stretching of perturbed vortex filaments Physica D 53 1991 267
37. Koplik J. Levine H. Vortex reconnection in superfluid Helium Phys. Rev. Lett. 71 1993 1375-1378
38. Landau L. Lifchitz E. Fluid Mechanics 1980 Pergamon Press Oxford
39. Leadbeater M. Samuels D.C. Barenghi C.F. Adams C.S. Decay of superfluid turbulence via Kelvin-wave radiation Phys. Rev. A 67 2003 015601
40. Lund F. Defect dynamics for the nonlinear Schrödinger equation derived from a variational principle Phys. Rev. Lett. A 159 1991 245
41. Madison K.W. Chevy F. Wohlleben W. Dalibard J. Vortex formation in a stirred Bose-Einstein condensate Phys. Rev. Lett. 84 2000 806-809
42. Mamun C. Tuckerman L. Asymmetry and Hopf bifurcation in spherical Couette flow Phys. Fluids 7 1 1995 80
43. Matthews M.R. Anderson B.P. Haljan P.C. Hall D.S. Wieman C.E. Cornell E.A. Vortices in a Bose-Einstein condensate Phys. Rev. Lett. 83 1999 2498-2501
44. Maurer J. Tabeling P. Local investigation of superfluid turbulence Europhys. Lett. 43 1 1998 29-34
45. Neu J.C. Vortices in complex scalar fields Physica D 43 1990 385
46. Nore C. Brachet M. Fauve S. Numerical study of hydrodynamics using the nonlinear Schrödinger equation Physica D 65 1993 154-162
47. Nore C. Abid M. Brachet M. Simulation numérique d'écoulements cisaillés tridimensionnels à l'aide de l'équation de Schrödinger non linéaire C.R. Acad. Sci. 319 II 7 1994 733
48. Nore C. Abid M. Brachet M. Decaying Kolmogorov turbulence in a model of superflow Phys. Fluids 9 9 1997 2644
49. Nore C. Abid M. Brachet M.E. Kolmogorov turbulence in low-temperature superflows Phys. Rev. Lett. 78 20 1997 3896-3899
50. Nore C. Huepe C. Brachet M.E. Subcritical dissipation in three-dimensional superflows Phys. Rev. Lett. 84 10 2000 2191
51. Nozières P. Pines D. The Theory of Quantum Liquids 1990 Addison-Wesley New York
52. Ogawa S.I. Tsubota M. Hattori Y. Study of reconnection and acoustic emission of quantized vortices in superfluid by the numerical analysis of the Gross-Pitaevskii equation J. Phys. Soc. Japan 71 2002 813
53. Pham C.-T. Brachet M. Dynamical scaling laws in two types of extended Hamiltonian systems at dissipation onset Physica D 163 2002 129-147
54. Pitaevskii L.P. Vortex lines in an imperfect Bose gas Sov. Phys.-JETP 13 2 1961 451
55. Pomeau Y. Rica S. Model of superflow with rotons Phys. Rev. Lett. 71 2 1993 247
56. Press W. Teukolsky S. Vetterling W. Flannery B. Numerical Recipees in Fortran 1994 Cambridge Univesity Press Cambridge
57. Raman C. Köhl M. Onofrio R. Durfee D.S. Kuklewicz C.E. Hadzibabic Z. Ketterle W. Evidence for a critical velocity in a Bose-Einstein condensed gas Phys. Rev. Lett. 83 13 1999 2502
58. Roberts, P.H., Berloff, N.G., 2001. The nonlinear Schrödinger equation as a model of superfluidity. In: Barenghi, C.F., Donnelly, R.J., Vinen, W.F. (Eds.), Quantized Vortex Dynamics and Superfluid Turbulence, Lecture Notes in Physics. Springer, Berlin, pp. 235-256.
59. Rosenbush, P., Bretin, V., Dalibard, J., 2002. Dynamics of a single vortex line in a Bose-Einstein condensate. Phys. Rev. Lett. 89, 200403-1.
60. Ruprecht P.A. Holland M.J. Burnett K. Edwards M. Time-dependent solution of the nonlinear Schrödinger equation for Bose-condensed trapped neutral atoms Phys. Rev. A 51 6 1995 4704
61. Sackett C.A. Stoof H.T.C. Hulet R.G. Growth and collapse of a Bose-Einstein condensate with attractive interactions Phys. Rev. Lett. 80 10 1998 2031
62. 4He: line-line and line-boundary interactions Phys. Rev. B 31 1985 5782
63. Seydel R. From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis 1988 Elsevier New York
64. Shi H. Zheng W.-M. Bose-Einstein condensation in an atomic gas with attractive interactions Phys. Rev. A 55 4 1997 2930
65. Spiegel E.A. Fluid dynamical form of the linear and nonlinear Schrödinger equations Physica D 1 1980 236
66. Stoof H.T.C. Macroscopic quantum tunneling of a Bose condensate J. Stat. Phys. 87 1997 1353
67. Svistunov B.V. Superfluid turbulence in the low-temperature limit Phys. Rev. B 52 1995 3647
68. Taylor G.I. Green A.E. Mechanism of the production of small eddies from large ones Proc. Soc. Lond. A 158 1937 499
69. Tsuzuki T. Nonlinear waves in the Pitaevskii-Gross equation J. Low Temp. Phys. 4 4 1971
70. Ueda M. Leggett A.J. Macroscopic quantum tunneling of a Bose-Einstein condensate with attractive interaction Phys. Rev. Lett. 80 8 1998 1576
71. van der Vorst H. Bi-cgstab: a fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems SIAM J. Sci. Stat. Comput. 13 1992 631
72. Vinen, W.F., 2001. Decay of turbulence at a very low temperature: the radiation of sound from a Kelvin wave on a quantized vortex. Phys. Rev. B 64, 134520-1.
73. Vinen W.F. Niemela J.J. Quantum turbulence J. Low Temp. Phys. 128 2002 167-231
74. Wilks J. The Properties of Liquid and Solid Helium 1967 Clarendon Press Oxford
75. Zakharov V.E. Shabat A.B. Interaction between solitons in a stable medium Sov. Phys.-JETP 37 5 1973 823-828
76. Zocchi G. Tabeling P. Maurer J. Willaime H. Measurement of the scaling of the dissipation at high Reynolds numbers Phys. Rev. E 50 1994 3693