Self-consistent perturbation expansion for Bose-Einstein condensates satisfying Goldstone's theorem and conservation laws

Physical Review B - Condensed Matter and Materials Physics

Volumn 80, Issue 21, 2009, Pages

  Kita, Takafumi ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954691782     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.214502     Document Type: Article

References (60)

1. P. W. Anderson, Basic Notions of Condensed Matter Physics (Benjamin-Cummings, Menlo Park, 1984).
2. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Westview Press, Boulder, 1995).
3. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961). 10.1103/PhysRev.122.345
4. J. Goldstone, Nuovo Cimento 19, 154 (1961) 10.1007/BF02812722
5. J. Goldstone, A. Salam, and S. Weinberg, Phys. Rev. 127, 965 (1962). 10.1103/PhysRev.127.965
6. L. D. Landau, Zh. Eksp. Teor. Fiz. 30, 1058 (1956)
7. [L. D. Landau, Sov. Phys. JETP 3, 920 (1957)]
8. L. D. Landau, Zh. Eksp. Teor. Fiz. 32, 59 (1957)
9. [L. D. Landau, Sov. Phys. JETP 5, 101 (1957)].
10. G. Baym and C. Pethick, Landau Fermi-Liquid Theory (John Wiley & Sons, New York, 1991).
11. E. Kaxiras, Atomic and Electronic Structure of Solids (Cambridge University Press, Cambridge, 2003).
12. A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, Englewood Cliffs, NJ, 1963).
13. A. J. Leggett, Phys. Rev. 140, A1869 (1965) 10.1103/PhysRev.140.A1869
14. A. J. Leggett, Phys. Rev. 147, 119 (1966). 10.1103/PhysRev.147.119
15. G. Baym, Phys. Rev. 127, 1391 (1962). 10.1103/PhysRev.127.1391
16. L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1962).
17. J. M. Luttinger and J. C. Ward, Phys. Rev. 118, 1417 (1960). 10.1103/PhysRev.118.1417
18. J. M. Luttinger, Phys. Rev. 119, 1153 (1960). 10.1103/PhysRev.119.1153
19. L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964)
20. [L. V. Keldysh, Sov. Phys. JETP 20, 1018 (1965)].
21. K. C. Chou, Z. B. Su, B. L. Hao, and L. Yu, Phys. Rep. 118, 1 (1985). 10.1016/0370-1573(85)90136-X
22. J. Rammer and H. Smith, Rev. Mod. Phys. 58, 323 (1986). 10.1103/RevModPhys.58.323
23. C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, 2008).
24. L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford University Press, Oxford, 2003).
25. A. Griffin, T. Nikuni, and E. Zaremba, Bose-Condensed Gases at Finite Temperatures (Cambridge University Press, Cambridge, 2009).
26. M. R. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995). 10.1126/science.269.5221.198
27. N. M. Hugenholtz and D. Pines, Phys. Rev. 116, 489 (1959). 10.1103/PhysRev.116.489
28. N. N. Bogoliubov, J. Phys. (USSR) 9, 23 (1947).
29. P. C. Hohenberg and P. C. Martin, Ann. Phys. (N.Y.) 34, 291 (1965). 10.1016/0003-4916(65)90280-0
30. A. Griffin, Phys. Rev. B 53, 9341 (1996). 10.1103/PhysRevB.53.9341
31. S. K. Ma and C. W. Woo, Phys. Rev. 159, 165 (1967). 10.1103/PhysRev.159. 165
32. P. Szépfalusy and I. Kondor, Ann. Phys. (N.Y.) 82, 1 (1974). 10.1016/0003-4916(74)90330-3
33. V. K. Wong and H. Gould, Ann. Phys. (N.Y.) 83, 252 (1974). 10.1016/0003-4916(74)90198-5
34. A. Griffin, Excitations in a Bose-Condensed Liquid (Cambridge University Press, Cambridge, 1993).
35. J. Gavoret and P. Noziéres, Ann. Phys. (N.Y.) 28, 349 (1964). 10.1016/0003-4916(64)90200-3
36. T. Kita, J. Phys. Soc. Jpn. 74, 1891 (2005) 10.1143/JPSJ.74.1891
37. T. Kita, J. Phys. Soc. Jpn. 74, 3397 (E) (2005). 10.1143/JPSJ.74.3397 (Pubitemid 41810962)
38. T. Kita, J. Phys. Soc. Jpn. 75, 044603 (2006). 10.1143/JPSJ.75.044603 (Pubitemid 43543153)
39. R. P. Feynman, Phys. Rev. 94, 262 (1954) 10.1103/PhysRev.94.262
40. R. P. Feynman and M. Cohen, Phys. Rev. 102, 1189 (1956). 10.1103/PhysRev.102.1189
41. E. Feenberg, Theory of Quantum Fluids (Academic, New York, 1969).
42. D. M. Ceperley, Rev. Mod. Phys. 67, 279 (1995). 10.1103/RevModPhys.67.279
43. J. M. Cornwall, R. Jackiw, and E. Tomboulis, Phys. Rev. D 10, 2428 (1974). 10.1103/PhysRevD.10.2428
44. J. Berges, Phys. Rev. D 70, 105010 (2004). 10.1103/PhysRevD.70.105010
45. G. Baym and G. Grinstein, Phys. Rev. D 15, 2897 (1977). 10.1103/PhysRevD.15.2897
46. Yu. B. Ivanov, F. Riek, and J. Knoll, Phys. Rev. D 71, 105016 (2005) 10.1103/PhysRevD.71.105016
47. Yu. B. Ivanov, F. Riek, H. van Hees, and J. Knoll, Phys. Rev. D 72, 036008 (2005). 10.1103/PhysRevD.72.036008 (Pubitemid 41493403)
48. S. T. Beliaev, Zh. Eksp. Teor. Fiz. 34, 417 (1958)
49. [S. T. Beliaev, Sov. Phys. JETP 7, 289 (1958)].
50. E. P. Gross, Nuovo Cimento 20, 454 (1961). 10.1007/BF02731494
51. L. P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961)
52. [L. P. Pitaevskii, Sov. Phys. JETP 13, 451 (1961)].
53. C. de Dominicis and P. C. Martin, J. Math. Phys. 5, 14 (1964). 10.1063/1.1704062
54. N. V. Popov, Functional Integrals and Collective Excitations (Cambridge University Press, Cambridge, 1987), Sec..
55. T. Kita, J. Phys. Soc. Jpn. 68, 3740 (1999). 10.1143/JPSJ.68.3740
56. T. Kita, J. Phys. Soc. Jpn. 75, 114005 (2006). 10.1143/JPSJ.75.114005
57. See, e.g., The Physics of Liquid and Solid Helium, edited by, K. H. Bennemann, and, J. B. Ketterson, (John Wiley & Sons, New York, 1976), Part I.
58. T. Kita, J. Phys. Soc. Jpn. 65, 1373 (1996). 10.1143/JPSJ.65.1373
59. A. L. Fetter, Ann. Phys. (N.Y.) 70, 67 (1972). 10.1016/0003-4916(72) 90330-2
60. N. Fukushima, Y. Ohashi, E. Taylor, and A. Griffin, Phys. Rev. A 75, 033609 (2007). 10.1103/PhysRevA.75.033609 (Pubitemid 46474044)