Spatially inhomogeneous superconducting and bosonic networks with emergent complex behaviors

International Journal of Modern Physics B

Volumn 21, Issue 12, 2007, Pages 1923-1949

  Mancini, F P ^a   Sodano, P ^a   Trombettoni, A ^b  

^a UNIVERSITY OF PERUGIA   (Italy)

^b SISSA   (Italy)

Author keywords

Bosonic and superconducting networks; Enhanced responses; Josephson effect

Indexed keywords

EID: 34250217815     PISSN: 02179792     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217979207037181     Document Type: Article

References (70)

1. N. Goldenfeld and L. Kadanoff, Science 284, 87 (1999).
2. E. Dagotto, Science 309, 257 (2005).
3. P. Xiong et al., Phys. Rev. Lett. 69, 3220 (1992).
4. E. Fradkin and S. A. Kivelson, Phys. Rev. 59, 8065 (1999).
5. S. A. Kivelson, E. Fradkin and V. J. Emery, Nature 393, 550 (1998).
6. E. Dagotto, T. Hotta and A. Moreo, Phys. Rep. 344, 1 (2001).
7. E. Dagotto, Nanoscale Phase Separation and Colossal Magnetoresistance (Springer- Verlag, Berlin, Germany, 2001).
8. V. J. Emery, S. A. Kivelson and J. M. Tranquada, Proc. Natl. Acad. Sci. U.S.A. 96, 8814 (1999).
9. J. Zaanen, Nature 404, 714 (2000) and references therein.
10. Ch. Renner et al., Phys. Rev. Lett. 80, 149 (1998).
11. M. Suzuki, T. Watanabe and A. Matsuda, Phys. Rev. Lett. 82, 5361 (1999).
12. T. Ekino et al., J. Low Temp. Phys. 117, 359 (1999).
13. S. A. Kivelson and E. Fradkin, Preprint cond-mat/0507459.
14. Yu. N. Ovchinnikov, S. A. Wolf and V. Z. Kresin, Phys. Rev. B 63, 064524 (2001).
15. P. W. Anderson, Science 177, 393 (1972).
16. J. E. Mooij and G. Schön, Physica B 152, 1 (1988).
17. H. A. Cerdeira and S. R. Shenoy, Physica B 222, 253 (1996).
18. R. Fazio and H. van der Zant, Phys. Rep. 355, 235 (2001).
19. O. Morsch and M. K. Oberthaler, Rev. Mod. Phys. 78, 179 (2006).
20. F. S. Cataliotti et al., Science 293, 843 (2001).
21. B. P. Anderson and M. Kasevich, Science 282, 1686 (1998).
22. E. Simánek, Inhomogeneous Superconductors (Oxford University Press, New York, 1994).
23. Y. Makhlin, G. Shoen and A. Shnirman, Rev. Mod. Phys. 73, 357 (2001).
24. P. G. de Gennes, C. R. Acad. Sci. Ser. B 292, 279 (1981).
25. P. G. de Gennes, C. R. Acad. Sci. Ser. B 292, 9 (1981).
26. S. Alexander, Phys. Rev. B 27, 1541 (1983).
27. H. J. Fink, A. Lopez and R. Maynard, Phys. Rev. B 26, 5237 (1982).
28. R. Rammal, T. C. Lubensky and G. Toulouse, Phys. Rev. B 27, 2820 (1983).
29. G. Deutscher and R. Rosembaum, Appl. Phys. Lett 27, 366 (1975).
30. G. Deutsher, I. Grave and S. Alexander, Phys. Rev. Lett. 48, 1497 (1982).
31. G. Deutscher et al., Phys. Rev. B 24, 6464 (1981).
32. J. Berger and J. Rubinstein (eds.), Connectivity and Superconductivity, Lecture Notes in Physics (Springer-Verlag, Berlin, 2000).
33. L. B. Ioffe et al., Nature 415, 503 (2002).
34. B. Doucot, M. V. Feigel'man and L. B. Ioffe, Phys. Rev. Lett. 90, 107003 (2003).
35. B. Doucot, L. B. Ioffe and J. Vidal, Phys. Rev. B 69, 107003 (2003).
36. B. Doucot et al., Phys. Rev. B 71, 024505 (2005).
37. X. G. Wen and Q. Niu, Phys. Rev. B 41, 9377 (1990).
38. X. G. Wen, Phys. Rev. Lett. 90, 016803 (2003).
39. C. C. Abilio et al., Phys. Rev. Lett. 83, 5102 (1999).
40. J. Vidal, R. Mosseri and B. Doucot, Phys. Rev. Lett. 81, 5888 (1998).
41. I. V. Protopopov and M. V. Feigel'man, Phys. Rev. B 70, 184519 (2004).
42. I. V. Protopopov and M. V. Feigel'man, cond-mat/0510766.
43. P. Silvestrini, R. Russo, V. Corato, B. Ruggiero, C. Granata, S. Rombetto, M. Russo, M. Cirillo, A. Trombettoni and P. Sodano, cond-mat/0512478.
44. P. Sodano, A. Trombettoni, P. Silvestrini, R. Russo and B. Ruggiero, New J. Phys. 8, 327 (2006).
45. L. P. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford University Press, Oxford, 2003).
46. M. K. Oberthaler and T. Pfau, J. Phys.: Condens. Matter 15, R233 (2003).
47. R. Roth and K. Burnett, Phys. Rev. A 68, 023604 (2003).
48. I. Brunelli, G. Giusiano, F. P. Mancini, P. Sodano and A. Trombettoni, J. Phys. B 37, S275 (2004).
49. M. Albiez, R. Gati, J. Foiling, S. Hunsmann, M. Cristiani and M. K. Oberthaler, Phys. Rev. Lett. 95, 010402 (2005).
50. A. Smerzi, S. Fantoni, S. Giovanazzi and S. R. Shenoy, Phys. Rev. Lett. 79, 4950 (1997).
51. F. Harary, Graph Theory (Addison-Wesley, Reading, 1969).
52. R. Burioni, D. Cassi, I. Meccoli, M. Rasetti, S. Regina, P. Sodano and A. Vezzani, Europhys. Lett. 52, 251 (2000).
53. R. Burioni, D. Cassi, M. Rasetti, P. Sodano and A. Vezzani, J. Phys. B 34, 4697 (2001).
54. G. Giusiano, F. P. Mancini, P. Sodano and A. Trombettoni, Int. J. Mod. Phys. B 18, 691 (2004).
55. P. G. de Gennes, Superconductivity of Metals and Alloys (Addison-Wesley, Manlo Park, USA, 1989).
56. B. Abeles, Phys. Rev. B 15, 2828 (1997).
57. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998).
58. F. P. Mancini, P. Sodano and A. Trombettoni, to appear in Eleventh Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors, Vietri sul Mare, Italy, Oct 2006, cond-mat/0612388.
59. V. Ambegaokar and A. Baratoff, Phys. Rev. Lett. 10, 486 (1963).
60. V. Ambegaokar and A. Baratoff, Phys. Rev. Lett. 11, 104 (1963).
61. This approximation holds for f ≫ 1 and it is in very good agreement with the results of a numerical evaluation of the integral (4.63).
62. A. O. Caldeira and A. J. Leggett, Ann. Phys. (N.Y.) 149, 374 (1983).
63. M. H. Devoret et al., Phys. Rev. Lett. 64, 1824 (1990).
64. S. M. Girvin et al., Phys. Rev. Lett. 64, 3183 (1990).
65. G. Schön and A. D. Zaikin, Phys. Rep. 198, 237 (1990).
66. A. Schmid, J. Low Temp. Phys. 49, 609 (1982).
67. L. I. Glazman and A. I. Larkin, Phys. Rev. Lett. 79, 3736 (1997).
68. D. Giuliano and P. Sodano, Nucl. Phys. B 711, 480 (2005).
69. P. Buonsante, R. Burioni, D. Cassi and A. Vezzani, Phys. Rev. B 66, 094207 (2002).
70. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (National Bureau of Standards, Washington, D.C., 1964).