The Bogoliubov-de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry

Annals of Physics

Volumn 324, Issue 12, 2009, Pages 2522-2547

  Correa, Francisco ^a   Dunne, Gerald V ^b   Plyushchay, Mikhail S ^a  

^a UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

^b UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Bogoliubov de Gennes system; Integrable systems; Nonlinear symmetries; Supersymmetric quantum mechanics

Indexed keywords

EID: 70350704806     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2009.06.005     Document Type: Article

References (89)

1. de Gennes P.G. Superconductivity of Metals and Alloys (1989), Addison-Wesley, Redwood City
2. V. Schön, M. Thies, 2D model field theories at finite temperature and density, in: M. Shifman (Ed.), At the Frontier of Particle Physics, vol. 3, World Scientific. [arXiv:hep-th/0008175].
3. Thies M. J. Phys. A 39 (2006) 12707 [arXiv:hep-th/0601049].
4. Basar G., and Dunne G.V. Phys. Rev. Lett. 100 (2008) 200404 [arXiv:0803.1501 [hep-th]]
5. Basar G., and Dunne G.V. Phys. Rev. D 78 (2008) 065022 [arXiv:0806.2659 [hep-th]]
6. 2 model. [arXiv:0903.1868 [hep-th]].
7. Gross D.J., and Neveu A. Phys. Rev. D 10 (1974) 3235
8. Dashen R.F., Hasslacher B., and Neveu A. Phys. Rev. D 12 (1975) 2443
9. Neveu A., and Papanicolaou N. Commun. Math. Phys. 58 (1978) 31
10. Klimenko K.G. Z. Phys. C 37 (1988) 457
11. Feinberg J., and Zee A. Generalized supersymmetric quantum mechanics and reflectionless fermion bags in 1 + 1 dimensions. In: Olshanetsky M., et al. (Ed). Multiple Facets of Quantization and Supersymmetry (2002), World Scientific hep-th/0109045
12. Feinberg J. Ann. Phys. 309 (2004) 166 [arXiv:hep-th/0305240]
13. Jackiw R., and Rebbi C. Phys. Rev. D 13 (1976) 3398
14. Niemi A.J., and Semenoff G.W. Phys. Rep. 135 (1986) 99
15. Peierls R. The Quantum Theory of Solids (1955), Oxford
16. Belokolos E.D., et al. Algebro-Geometric Approach to Nonlinear Integrable Equations (1994), Springer, Berlin
17. Brazovskii S.A., Gordynin S.A., and Kirova N.N. Pis. Zh. Eksp. Teor. Fiz. 31 (1980) 486 [JETP Lett. 31 (1980) 456]
18. Pis. Zh. Eksp. Teor. Fiz. 33 (1981) 6 [JETP Lett. 33 (1981) 4]
19. Brazovskii S.A., Kirova N.N., and Matveenko S.I. Zh. Eksp. Teor. Fiz. 86 (1984) 743 [Sov. Phys. JETP 59 (1984) 434]
20. Horovitz B. Phys. Rev. Lett. 46 (1981) 742
21. Campbell D.K., and Bishop A.R. Nucl. Phys. B 200 (1982) 297
22. Heeger A.J., Kivelson S., Schrieffer J.R., and Su W.P. Rev. Mod. Phys. 60 (1988) 781
23. Eilenberger G. Z. Phys. 214 (1968) 195
24. Bar-Sagi J., and Kuper C.G. Phys. Rev. Lett. 28 (1972) 1556
25. Buzdin A.I., and Tugushev V.V. Zh. Eksp. Teor. Fiz. 85 (1983) 735 [Sov. Phys. JETP 58 (1983) 428]
26. Buzdin A.I., and Polonskii S.V. Zh. Eksp. Teor. Fiz. 93 (1987) 747 [Sov. Phys. JETP 66 (1988) 422]
27. Kosztin I., Kos S., Stone M., and Leggett A.J. Phys. Rev. B 58 (1998) 9365
28. Kos S., and Stone M. Phys. Rev. B 59 (1999) 9545
29. Machida K., and Nakanishi H. Phys. Rev. B 30 (1984) 122
30. Mertsching J., and Fischbeck H.J. Phys. Status Solidi B 103 (1981) 783
31. Su Z.b., and Sakita B. Phys. Rev. Lett. 56 (1986) 780
32. Giorgini S., Pitaevskii L.P., and Stringari S. Rev. Mod. Phys. 80 (2008) 1215
33. Andrianov A.A., Ioffe M.V., and Spiridonov V.P. Phys. Lett. A 174 (1993) 273 [arXiv:hep-th/9303005]
34. Klishevich S.M., and Plyushchay M.S. Nucl. Phys. B 606 (2001) 583 [arXiv:hep-th/0012023]
35. Gorkov L.P. Zh. Eksp. Teor. Fiz. 34 (1958) 735 [Sov. Phys. JETP 7 (1958) 505]
36. Dickey L.A. Soliton Equations and Hamiltonian Systems (1991), World Scientific, Singapore
37. Das A. Integrable Models (1989), World Scientific, Singapore
38. Gesztesy F., and Holden H. Soliton Equations and Their Algebro-Geometric Solutions (2003), Cambridge University Press
39. Kapusta J. Finite Temperature Field Theory (1989), Cambridge University Press
40. Waxman D. Ann. Phys. 241 (1995) 285
41. Perelomov A.M. Ann. Inst. H. Poincare 24 (1976) 161
42. Perelomov A.M., and Zeldovich Y. Quantum Mechanics: Selected Topics (1998), World Scientific, Singapore
43. Ablowitz M.J., Kaup D.J., Newell A.C., and Segur H. Stud. Appl. Math. 53 (1974) 249
44. Lax P.D. Commun. Pure Appl. Math. 21 (1968) 467
45. Gesztesy F., and Weikard R. Acta Math. 181 (1998) 63
46. Bull. Am. Math. Soc. 35 (1998) 271
47. Smirnov A.O. Sb. Math. 186 (1995) 1213
48. Plyushchay M.S. Ann. Phys. 245 (1996) 339 [arXiv:hep-th/9601116]
49. Int. J. Mod. Phys. A 15 (2000) 3679 [arXiv:hep-th/9903130]
50. Correa F., and Plyushchay M.S. Ann. Phys. 322 (2007) 2493 [arXiv:hep-th/0605104]
51. J. Phys. A 40 (2007) 14403 [arXiv:0706.1114 [hep-th]]
52. Correa F., Nieto L.M., and Plyushchay M.S. Phys. Lett. B 644 (2007) 94 [arXiv:hep-th/0608096]
53. Witten E. Nucl. Phys. B 188 (1981) 513
54. Cooper F., Khare A., and Sukhatme U. Phys. Rep. 251 (1995) 267 [arXiv:hep-th/9405029]
55. Grant A.K., and Rosner J.L. J. Math. Phys. 35 (1994) 2142 [arXiv:hep-th/9304139]
56. Matveev V.B., and Salle M.A. Darboux Transformations and Solitons (1991), Springer, Berlin
57. G. Dunne, H. Gies, K. Klingmuller, K. Langfeld. [arXiv:0903.4421 [hep-th]].
58. Dunne G.V., and Feinberg J. Phys. Rev. D 57 (1998) 1271 [arXiv:hep-th/9706012]
59. Burchnall J.L., and Chaundy T.W. Proc. Lond. Math. Soc. 21 (1923) 420
60. Ince E.L. Ordinary Differential Equations (1956), Dover
61. Correa F., Nieto L.M., and Plyushchay M.S. Phys. Lett. B 659 (2008) 746 [arXiv:0707.1393 [hep-th]]
62. Correa F., Jakubský V., Nieto L.M., and Plyushchay M.S. Phys. Rev. Lett. 101 (2008) 030403 [arXiv:0801.1671 [hep-th]]
63. Correa F., Jakubský V., and Plyushchay M.S. J. Phys. A 41 (2008) 485303 [arXiv:0806.1614 [hep-th]]
64. Lawden D.F. Elliptic Functions and Applications (1980), Springer Verlag, New York
65. Whittaker E.T., and Watson G.N. A Course of Modern Analysis (1980), Cambridge University Press, Cambridge
66. Correa F., Jakubský V., and Plyushchay M.S. Ann. Phys. 324 (2009) 1078 [arXiv:0809.2854 [hep-th]]
67. Fernandez D.J., Mielnik B., Rosas-Ortiz O., and Samsonov B.F. Phys. Lett. A 294 (2002) 168 [arXiv:quant-ph/0302204]
68. Shei S.S. Phys. Rev. D 14 (1976) 535
69. Dunne G.V., and Shifman M. Ann. Phys. 299 (2002) 143 [arXiv:hep-th/0204224]
70. Faux M., and Spector D. J. Phys. A 37 (2004) 10397 [arXiv:quant-ph/0401163]
71. Enolskii V.Z. Phys. Lett. A 96 (1983) 327
72. Buchstaber V.M., Enolskii V.Z., and Leikin D.V. Am. Math. Soc. Trans. Ser. 2 179 (1997) 1 solv-int/9603005
73. Eilbeck J.C., Enolskii V.Z., and Previato E. Sigma 3 (2007) 045 [arXiv:math-ph/0703038]
74. Babich M.V., Bobenko A.I., and Matveev V.B. Math. USSR Izv. 26 (1986) 479
75. Boehmer C., Thies M., and Urlichs K. Phys. Rev. D 75 (2007) 105017 [arXiv:hep-th/0702201]
76. Boehmer C., Karbstein F., and Thies M. Phys. Rev. D 77 (2008) 125031 [arXiv:0803.1369 [hep-th]]
77. Bringoltz B. JHEP 0703 (2007) 016 [arXiv:hep-lat/0612010]
78. [arXiv:0901.4035 [hep-lat]].
79. Nickel D., and Buballa M. Phys. Rev. D 79 (2009) 054009 [arXiv:0811.2400 [hep-ph]]
80. D. Nickel. [arXiv:0902.1778 [hep-ph]].
81. E. Antonyan, J.A. Harvey, S. Jensen, D. Kutasov. [arXiv:hep-th/0604017].
82. Antonyan E., Harvey J.A., and Kutasov D. Nucl. Phys. B 776 (2007) 93 [arXiv:hep-th/0608149]
83. Parnachev A., and Sahakyan D.A. Phys. Rev. Lett. 97 (2006) 111601 [arXiv:hep-th/0604173]
84. Basu A., and Maharana A. Phys. Rev. D 75 (2007) 065005 [arXiv:hep-th/0610087]
85. Davis J.L., Gutperle M., Kraus P., and Sachs I. JHEP 0710 (2007) 049 [arXiv:0708.0589 [hep-th]]
86. For details and proof see Ref. [31].
87. For its applications see Refs. [3,4,46] and references therein.
88. Hidden nonlinear supersymmetry of the reflectionless Pöschl-Teller system can be explained in terms of the Aharonov-Bohm effect for non-relativisitc particle on AdS(2), see Ref. [55].
89. ′ [4 π].