Perturbation Expansion for a Fermi Superfluid. I. Basic Formalism and Angular Momentum

Journal of the Physical Society of Japan

Volumn 65, Issue 5, 1996, Pages 1355-1372

  Kita, Takafumi ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

Angular momentum paradox of 3He A; Coordinate space formalism; Microscopic basis for the two fluid model; Theory of superconductivity

Indexed keywords

EID: 0030539445     PISSN: 00319015     EISSN: None     Source Type: Journal    
DOI: 10.1143/JPSJ.65.1355     Document Type: Article

References (54)

1. See the article by V. Ambegaokar: Superconductivity, ed. R. D. Parks (Dekker, New York, 1969) Vol. 1, p. 259 (Sec. IIC); see also the article by G. Rickayzen in that volume, especially eq. (50) and above in p. 81.
2. J. Bardeen, L. N. Cooper and J. R. Schrieffer: Phys. Rev. 108 (1957) 1175.
3. R. B. Laughlin: Phys. Rev. Lett. 60 (1988) 2677.
4. Z. Tešanović, M. Rasolt and L. Xing: Phys. Rev. B 43 (1991) 288.
5. N. N. Bogoliubov: Nuovo Cimento 7 (1958) 794; see also N. N. Bogoliubov, V. V. Tolmachev and D. V. Schirkov: A New Method in the Theory of Superconductivity (Consultants Bureau, New York, 1959).
6. N. N. Bogoliubov: Nuovo Cimento 7 (1958) 794; see also N. N. Bogoliubov, V. V. Tolmachev and D. V. Schirkov: A New Method in the Theory of Superconductivity (Consultants Bureau, New York, 1959).
7. J. G. Valatin: Nuovo Cimento 7 (1958) 843; see also J. G. Valatin: Mathematical Methods in Solid State and Superfluid Theory, ed. R. C. Clark and G. H. Derrick (Oliver and Boyd, Edinburgh, 1969) Sec. 5.
8. J. G. Valatin: Nuovo Cimento 7 (1958) 843; see also J. G. Valatin: Mathematical Methods in Solid State and Superfluid Theory, ed. R. C. Clark and G. H. Derrick (Oliver and Boyd, Edinburgh, 1969) Sec. 5.
9. R. Balian and N. R. Wertharmer: Phys. Rev. 131 (1963) 1553.
10. Y. Takada: Phys. Rev. B 37 (1988) 155.
11. L. P. Gor'kov: Zh. Eksp. Teor. Fiz. 34 (1958) 735, translation: Sov. Phys.-JETP 7 (1958) 505.
12. L. P. Gor'kov: Zh. Eksp. Teor. Fiz. 34 (1958) 735, translation: Sov. Phys.-JETP 7 (1958) 505.
13. G. M. ÉHashberg: Zh. Eksp. Teor. Fiz. 38 (1960) 966, translation: Sov. Phys.-JETP 11 (1960) 696.
14. G. M. ÉHashberg: Zh. Eksp. Teor. Fiz. 38 (1960) 966, translation: Sov. Phys.-JETP 11 (1960) 696.
15. Y. Nambu: Phys. Rev. 117 (1960) 648.
16. A. I. Larkin and A. B. Migdal: Zh. Eksp. Teor. Fiz. 44 (1963) 1703, translation: Sov. Phys.-JETP 17 (1963) 1146.
17. A. I. Larkin and A. B. Migdal: Zh. Eksp. Teor. Fiz. 44 (1963) 1703, translation: Sov. Phys.-JETP 17 (1963) 1146.
18. A. J. Leggett: Phys. Rev. 140 (1965) A1869.
19. L. P. Gor'kov: Zh. Eksp. Teor. Fiz. 36 (1959) 1918, translation: Sov. Phys.-JETP 9 (1959) 1364.
20. L. P. Gor'kov: Zh. Eksp. Teor. Fiz. 36 (1959) 1918, translation: Sov. Phys.-JETP 9 (1959) 1364.
21. C. de Dominicis and P. C. Martin: J. Math. Phys. 5 (1964) 14.
22. G. Eilenberger: Z. Phys. 190 (1966) 142.
23. P. G. de Gennes: Superconductivity of Metals and Alloys (Benjamin, New York, 1966) Chap. 5.
24. P. W. Anderson and P. Morel: Phys. Rev. 123 (1961) 1911.
25. M. C. Cross: J. Low Temp. Phys. 21 (1975) 525.
26. M. Ishikawa: Prog. Theor. Phys. 57 (1977) 1836.
27. A. J. Leggett and S. Takagi: Ann. Phys. 110 (1978) 353.
28. T. Kita: J. Phys. Soc. Jpn. 65 (1996) 664.
29. See, for example, P. R. Halmos: Finite-Dimensional Vector Spaces (Van Nostrand, Princeton, 1958) Secs. 72-85.
30. See, for example, A. L. Fetter and J. D. Walecka: Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971).
31. R. P. Feynman: Phys. Rev. 76 (1949) 769.
32. F. J. Dyson: Phys. Rev. 75 (1949) 1736.
33. T. Matsubara: Prog. Theoret. Phys. (Kyoto) 14 (1955) 351.
34. 1.
35. J. M. Luttinger and J. C. Ward: Phys. Rev. 118 (1960) 1417.
36. J. M. Luttinger: Phys. Rev. 119 (1960) 1153.
37. See, for example, I. M. Gelfand and S. V. Fomin: Calculus of Variations (Prentice-Hall, New Jersey, 1963).
38. In this respect, it is worth noting that the variational (effective) Hamiltonians of the variational formalisms 2, 3, 6, 8, 17) are so chosen as to make (γγ) vanish identically.
39. T. Kita: J. Phys. Soc. Jpn. 65 (1996) 1373.
40. On the concept of the off-diagonal long-range order, see, for example, C. N. Yang: Rev. Mod. Phys. 34 (1962) 694.
41. 3He - A, see, for example, A. J. Leggett: Rev. Mod. Phys. 47 (1975) 331; D. Vollhardt and P. Wölfle: The Superfluid Phases of Helium 3 (Taylor and Francis, London, 1990).
42. 3He - A, see, for example, A. J. Leggett: Rev. Mod. Phys. 47 (1975) 331; D. Vollhardt and P. Wölfle: The Superfluid Phases of Helium 3 (Taylor and Francis, London, 1990).
43. M. Ishikawa, K. Miyake and T. Usui: Prog. Theor. Phys. 63 (1980) 1083.
44. G. E. Volovik and V. P. Mineev: Zh. Eksp. Teor. Fiz. 81 (1981) 989, translation: Sov. Phys.-JETP 54 (1981) 524.
45. G. E. Volovik and V. P. Mineev: Zh. Eksp. Teor. Fiz. 81 (1981) 989, translation: Sov. Phys.-JETP 54 (1981) 524.
46. R. Combescot and T. Dombre: Phys. Rev. B 28 (1983) 5140.
47. J. Bardeen: Phys. Rev. Lett. 1 (1958) 399.
48. On flux quantization, see for example the article by A. L. Fetter and P. C. Hohenberg: Superconductivity, ed. R. D. Parks (Dekker, New York, 1969) Vol. 2, p. 853.
49. K. Miyake and T. Usui: Prog. Theoret. Phys. (Kyoto) 63 (1980) 711.
50. T. Kita: J. Phys. Soc. Jpn. 62 (1993) 3539.
51. H. E. Hall: Phys. Rev. Lett. 54 (1985) 205.
52. See, for example, L. D. Landau and E. M. Lifshitz: Fluid Mechanics (Pergamon, Oxford, 1959) Chap. XVI.
53. V. L. Ginzburg and L. D. Landau: Zh. Eksp. Teor. Fiz. 20 (1950) 1064.
54. A. J. Leggett and S. Takagi: Ann. Phys. 106 (1977) 79.