Universality in nonadiabatic behavior of classical actions in nonlinear models of Bose-Einstein condensates

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 76, Issue 2, 2007, Pages

  Itin, A P ^a,b   Watanabe, S ^a  

^a UNIVERSITY OF ELECTRO COMMUNICATIONS   (Japan)

^b Russian Academy of Sciences ^*  (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

HYDRODYNAMICS; MATHEMATICAL MODELS; NONLINEAR ANALYSIS; NUMERICAL METHODS;

BOSE-EINSTEIN CONDENSATES; NONLINEAR MODELS; RESONANCE PASSAGE; SEPARATRIX CROSSINGS;

BOSE-EINSTEIN CONDENSATION;

EID: 34548442934     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.026218     Document Type: Article

References (87)

1. P. Ehrenfest, Philos. Mag. PHMAA4 0031-8086 33, 500 (1917);
2. L. Navarro and E. Perez, Arch. Hist. Exact Sci. AHESAN 0003-9519 10.1007/s00407-005-0105-1 60, 209 (2006).
3. A. Einstein, Sitzungsber. K. Preuss. Akad. Wiss. SPAWAV 0371-196X 3, 18 (1925).
4. F. London, Nature (London) NATUAS 0028-0836 141, 632 (1938).
5. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science SCIEAS 0036-8075 10.1126/science.269.5221.198 269, 198 (1995).
6. K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.3969 75, 3969 (1995).
7. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.71.463 71, 463 (1999);
8. C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, England, 2001).
9. L. P. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Clarendon Press, Oxford, 2003)
10. A. M. Dykhne, Sov. Phys. JETP SPHJAR 0038-5646 11, 411 (1960).
11. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1976).
12. V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, Mathematical aspects of classical and celestial mechanics, Vol. 3 of Encyclopedia of Mathematical Sciences, 3rd ed. (Springer, Berlin, 2006).
13. A. V. Timofeev, Sov. Phys. JETP SPHJAR 0038-5646 48, 656 (1978).
14. J. R. Cary, D. F. Escande, and J. L. Tennyson, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.34.4256 34, 4256 (1986).
15. A. I. Neishtadt, Sov. J. Plasma Phys. SJPPDC 0360-0343 12, 568 (1986).
16. A. I. Neishtadt, PMM U.S.S.R. 51, 586 (1987).
17. J. R. Cary and R. T. Skodje, Physica D PDNPDT 0167-2789 10.1016/0167-2789(89)90086-9 36, 287 (1989);
18. D. L. Bruhwiler and J. R. Cary, Physica D PDNPDT 0167-2789 10.1016/0167-2789(89)90067-5 40, 265 (1989);
19. R. T. Skodje, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.461401 95, 7234 (1991).
20. A. P. Itin, A. I. Neishtadt, and A. A. Vasiliev, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(00)00039-7 141, 281 (2000).
21. A. I. Neishtadt and A. A. Vasiliev, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/12/2/010 12, 303 (1999);
22. D. L. Vainshtein, A. A. Vasiliev, and A. I. Neishtadt, Chaos CHAOEH 1054-1500 10.1063/1.166151 6, 67 (1996).
23. A. P. Itin, A. A. Vasiliev, and A. I. Neishtadt, J. Math. Sci. (N.Y.) JMTSEW 1072-3374 10.1007/s10958-005-0230-z 128, 2778 (2005);
24. also available in Russian: A. P. Itin, A. A. Vasiliev, and A. I. Neishtadt, Zap. Nauchn. Semin. POMI ZNSPEV 0136-1244 300, 173 (2003).
25. A. P. Itin, A. I. Neishtadt, and A. A. Vasiliev, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(01)00670-3 291, 133 (2001);
26. A. P. Itin and A. I. Neishtadt, Regular Chaotic Dyn. ZZZZZZ 8, 59 (2003);
27. A. P. Itin, Plasma Phys. Rep. PPHREM 1063-780X 10.1134/1.1494058 28, 592 (2002);
28. A. P. Itin, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2004.02.056 324, 159 (2004);
29. A. P. Itin, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.026601 67, 026601 (2003).
30. A. P. Itin, R. de la Llave, A. I. Neishtadt, and A. A. Vasiliev, Chaos CHAOEH 1054-1500 10.1063/1.1520070 12, 1043 (2002).
31. K. Dietz, J. Henkel, and M. Holthaus, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.45.4960 45, 4960 (1992).
32. Chaotic Dynamics and Transport in Quantum and Classical Systems, edited by, P. Collet, M. Courbage, S. Metens, G. M. Zaslavsky, and, A. I. Neishtadt, (Kluwer, Dordrecht, 2004);
33. G. M. Zaslavsky, Physics of Chaos in Hamiltonian Dynamics (Imperial College Press, London, 1998).
34. A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.4950 79, 4950 (1997).
35. O. Zobay and B. M. Garraway, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.033603 61, 033603 (2000).
36. J. Liu, L. Fu, B. Ou, S. Chen, D. Choi, B. Wu, and Q. Niu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.023404 66, 023404 (2002).
37. E. Pazy, I. Tikhonenkov, Y. B. Band, M. Fleischhaner, and A. Vardi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.170403 95, 170403 (2005);
38. I. Tikhonenkov, E. Pazy, Y. B. Band, M. Fleischhaner, and A. Vardi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.043605 73, 043605 (2006).
39. A. P. Itin, A. A. Vasiliev, and S. Watanabe (unpublished).
40. A. P. Itin (unpublished) (see also http://power1.pc.uec.ac.jp/~alx_it);
41. A. P. Itin, A. A. Vasiliev, G. Krishna, and S. Wantanabe, Physica D PDNPDT 0167-2789 232, 108 (2007).
42. Z. P. Karkuszewski, K. Sacha, and J. Zakrzewski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.061601 63, 061601 (R) (2001).
43. F. Kh. Abdullaev and R. A. Kraenkel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.023613 62, 023613 (2000).
44. P. V. Elyutin and A. N. Rogovenko, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.026610 63, 026610 (2001).
45. E. A. Ostrovskaya, Yu. S. Kivshar, M. Lisak, B. Hall, F. Cattani, and D. Anderson, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.031601 61, 031601 (R) (2000).
46. K. W. Mahmud, H. Perry, and W. P. Reinhardt, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.023615 71, 023615 (2005).
47. T. Miyakawa and P. Meystre, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.033624 71, 033624 (2005).
48. A. Vardi, V. A. Yurovsky, and J. R. Anglin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.063611 64, 063611 (2001).
49. G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.55.4318 55, 4318 (1997);
50. G. L. Salmond, C. A. Holmes, and G. J. Milburn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.033623 65, 033623 (2002);
51. A. P. Hines, R. H. McKenzie, and G. J. Milburn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.013609 67, 013609 (2003).
52. S. K. Adhikari, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.056704 63, 056704 (2001).
53. D. Ananikian and T. Bergeman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.013604 73, 013604 (2006).
54. J. Javanainen, M. Kostrun, Y. Zheng, A. Carmichael, U. Shrestha, P. Meinel, M. Mackie, O. Dannenberg, and K. A. Suominen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.200402 92, 200402 (2004).
55. J. Javanainen and M. Mackie, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.R3186 59, R3186 (1999).
56. E. Timmermans, P. Tommasini, R. Cote, M. Hussein, and A. Kerman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.2691 83, 2691 (1999);
57. E. Timmermans, P. Tommasini, R. Cote, M. Hussein, and A. Kerman, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(99)00025-3 315, 199 (1999).
58. R. A. Barankov and L. S. Levitov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.130403 93, 130403 (2004);
59. A. V. Andreev, V. Gurarie, and L. Radzihovsky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.130402 93, 130402 (2004);
60. J. Dukelsky, G. G. Dussel, C. Esebbag, and S. Pittel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.050403 93, 050403 (2004).
61. G. Santos, A. Tonel, A. Foerster, and J. Links, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.023609 73, 023609 (2006).
62. E. A. Yuzbashyan, B. L. Altshuler, V. B. Kuznetsov, and V. Z. Enolskii, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/36/003 38, 7831 (2005).
63. I. M. Lifshitz, A. A. Slutskin, and V. M. Nabutovskii, Sov. Phys. JETP SPHJAR 0038-5646 14, 669 (1962).
64. A. I. Neishtadt, Prikl. Mat. Mekh. PMAMAF 0032-8235 39, 1331 (1975).
65. A. A. Vasiliev, A. P. Itin, and A. I. Neishtadt, Regular Chaotic Dyn. ZZZZZZ 2, 21 (1997).
66. V. I. Arnold, Russ. Math. Surveys RMSUAF 0036-0279 10.1070/ rm1963v018n06ABEH001143 18, 85 (1963).
67. M. K. Oberthaler (private communication).
68. M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.010402 95, 010402 (2005).
69. A. Ishkhanyan, in Interactions in Ultracold Gases: From Atoms to Molecules, edited by, M. Weidemuller, and, K. Zimmermann, (Wiley-Vch, Berlin, 2003);
70. M. Mackie, ibid.
71. T. Koehler, K. Goral, and P. S. Julienne, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.78.1311 78, 1311 (2006).
72. C. A. Regal, Nature (London) NATUAS 0028-0836 10.1038/nature01738 424, 47 (2003).
73. K. E. Strecker, G. B. Partridge, and R. G. Hulet, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.080406 91, 080406 (2003).
74. J. Cubizolles, T. Bourdel, S. J. J. M. F. Kokkelmans, G. V. Shlyapnikov, and C. Salomon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.240401 91, 240401 (2003).
75. E. Hodby, S. T. Thompson, C. A. Regal, M. Greiner, A. C. Wilson, D. S. Jin, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.120402 94, 120402 (2005).
76. A. E. Leanhardt, A. Gorlitz, A. P. Chikkatur, D. Kielpinski, Y. Shin, D. E. Pritchard, and W. Ketterle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.190403 89, 190403 (2002);
77. Y. Kawaguchi, M. Nakahara, and T. Ohmi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.043605 70, 043605 (2004);
78. Y. Shin, C. Sanner, G. B. Jo, T. A. Pasquini, M. Saba, W. Ketterle, D. E. Pritchard, M. Vengalattore, and M. Prentiss, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.021604 72, 021604 (R) (2005);
79. A. P. Itin, T. Morishita, M. Satoh, O. I. Tolstikhin, and S. Watanabe, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.063615 73, 063615 (2006).
80. H. Saito and M. Ueda, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.040403 90, 040403 (2003);
81. F. K. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.013605 67, 013605 (2003);
82. A. P. Itin, T. Morishita, and S. Watanabe, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.033613 74, 033613 (2006).
83. R. Kanamoto, H. Saito, and M. Ueda, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.090404 94, 090404 (2005);
84. A. P. Itin and S. Watanabe (unpublished).
85. D. Witthaut, E. M. Graefe, and H. J. Korsch, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.063609 73, 063609 (2006);
86. E. M. Graefe and H. J. Korsch, arXiv: quant-ph/611010 (unpublished).
87. M. Holthaus and S. Stenholm, Eur. Phys. J. B PRLTAO 0031-9007 20, 451 (2001).