Spectral singularities in PT-symmetric periodic finite-gap systems

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 86, Issue 8, 2012, Pages

  Correa, Francisco ^a   Plyushchay, Mikhail S ^b  

^a CENTRO DE ESTUDIOS CIENTÍFICOS CECS   (Chile)

^b UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84867763119     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.86.085028     Document Type: Article

References (80)

1. C.M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998). PRLTAO 0031-9007 10.1103/PhysRevLett.80.5243
2. For reviews, see: C.M. Bender, Rep. Prog. Phys. 70, 947 (2007); RPPHAG 0034-4885 10.1088/0034-4885/70/6/R03
3. A. Mostafazadeh, Int. J. Geom. Methods Mod. Phys. 07, 1191 (2010). 0219-8878 10.1142/S0219887810004816
4. A. Guo, G.J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G.A. Siviloglou, and D.N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009); PRLTAO 0031-9007 10.1103/PhysRevLett.103.093902
5. C.E. Ruter, K.G. Makris, R. El-Ganainy, D.N. Christodoulides, M. Segev, and D. Kip, Nature Phys. 6, 192 (2010). NPAHAX 1745-2473 10.1038/nphys1515
6. C.M. Bender, K.A. Milton, and V.M. Savage, Phys. Rev. D 62, 085001 (2000); PRVDAQ 0556-2821 10.1103/PhysRevD.62.085001
7. C.W. Bernard and V.M. Savage, Phys. Rev. D 64, 085010 (2001); PRVDAQ 0556-2821 10.1103/PhysRevD.64.085010 (Pubitemid 33794914)
8. C.M. Bender, D.C. Brody, and H.F. Jones, Phys. Rev. Lett. 93, 251601 (2004); PRLTAO 0031-9007 10.1103/PhysRevLett.93.251601 (Pubitemid 40121223)
9. C.M. Bender D.C. Brody H.F. Jones Phys. Rev. D 70, 025001 (2004); PRVDAQ 1550-7998 10.1103/PhysRevD.70.025001 (Pubitemid 44947243)
10. C.M. Bender D.C. Brody H.F. Jones Phys. Rev. D 71, 049901(E) (2005). PRVDAQ 1550-7998 10.1103/PhysRevD.71.049901
11. P.D. Mannheim, Found. Phys. 42, 388 (2012); FNDPA4 0015-9018 10.1007/s10701-011-9608-6
12. P.D. Mannheim arXiv:1205.5717.
13. J. Smejkal, V. Jakubsky, and M. Znojil, J. Phys. Stud. 11, 45 (2007); ZEDOFY 1027-4642
14. C.M. Bender and P.D. Mannheim, Phys. Rev. D 84, 105038 (2011). PRVDAQ 1550-7998 10.1103/PhysRevD.84.105038
15. T. Kato, Perturbation Theory for Linear Operators (Springer, New York, 1966).
16. M.A. Naimark, Transl.-Am. Math. Soc. 16, 103 (1960). 0065-9290
17. M.V. Berry, J. Mod. Opt. 50, 63 (2003); JMOPEW 0950-0340 10.1080/09500340308234532
18. M.V. Berry Czech. J. Phys. 54, 1039 (2004). CZLIA6 0011-4626 10.1023/B:CJOP.0000044002.05657.04 (Pubitemid 39363765)
19. W.D. Heiss, J. Phys. A 37, 2455 (2004). JPHAC5 0305-4470 10.1088/0305-4470/37/6/034
20. C. Dembowski, H.-D. Gräf, H.L. Harney, A. Heine, W.D. Heiss, H. Rehfeld, and A. Richter, Phys. Rev. Lett. 86, 787 (2001); PRLTAO 0031-9007 10.1103/PhysRevLett.86.787 (Pubitemid 32159790)
21. W.D. Heiss, M. Muller, and I. Rotter, Phys. Rev. E 58, 2894 (1998); PLEEE8 1063-651X 10.1103/PhysRevE.58.2894
22. W.D. Heiss M. Muller I. Rotter arXiv:quant-ph/9805038;
23. C. Dembowski, B. Dietz, H.-D. Gräf, H.L. Harney, A. Heine, W.D. Heiss, and A. Richter, Phys. Rev. E 69, 056216 (2004); PLEEE8 1539-3755 10.1103/PhysRevE.69.056216
24. T. Stehmann, W.D. Heiss, and F.G. Scholtz, J. Phys. A 37, 7813 (2004). JPHAC5 0305-4470 10.1088/0305-4470/37/31/012 (Pubitemid 39057697)
25. A.A. Mailybaev, O.N. Kirillov, and A.P. Seyranian, Phys. Rev. A 72, 014104 (2005). PLRAAN 1050-2947 10.1103/PhysRevA.72.014104 (Pubitemid 41492576)
26. B. Dietz, H.L. Harney, O.N. Kirillov, M. Miski-Oglu, A. Richter, and F. Schafer, Phys. Rev. Lett. 106, 150403 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.150403
27. H. Ramezani, T. Kottos, V. Kovanis, and D. Christodoulides, Phys. Rev. A 85, 013818 (2012). PLRAAN 1050-2947 10.1103/PhysRevA.85.013818
28. B. Bagchi, C. Quesne, and R. Roychoudhury, J. Phys. A 41, 022001 (2008). JPAMB5 1751-8113 10.1088/1751-8113/41/2/022001
29. B.F. Samsonov, J. Phys. A 38, L397 (2005). JPHAC5 0305-4470 10.1088/0305-4470/38/21/L04 (Pubitemid 40669837)
30. A. Mostafazadeh and H. Mehri-Dehnavi, J. Phys. A 42, 125303 (2009). JPAMB5 1751-8113 10.1088/1751-8113/42/12/125303
31. S. Longhi, Phys. Rev. A 81, 022102 (2010). PLRAAN 1050-2947 10.1103/PhysRevA.81.022102
32. A. Mostafazadeh, Phys. Rev. Lett. 102, 220402 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.220402
33. B.F. Samsonov, J. Phys. A 38, L571 (2005). JPHAC5 0305-4470 10.1088/0305-4470/38/34/L02 (Pubitemid 41168979)
34. B.F. Samsonov, J. Phys. A 43, 402006 (2010). JPAMB5 1751-8113 10.1088/1751-8113/43/40/402006
35. B.F. Samsonov, J. Phys. A 44, 392001 (2011). JPAMB5 1751-8113 10.1088/1751-8113/44/39/392001
36. B.F. Samsonov, arXiv:1207.2525.
37. A.A. Andrianov, F. Cannata, and A.V. Sokolov, J. Math. Phys. (N.Y.) 51, 052104 (2010). JMAPAQ 0022-2488 10.1063/1.3422523
38. A. Mostafazadeh, Phys. Rev. A 80, 032711 (2009); PLRAAN 1050-2947 10.1103/PhysRevA.80.032711
39. A. Mostafazadeh Phys. Rev. A 83, 045801 (2011); PLRAAN 1050-2947 10.1103/PhysRevA.83.045801
40. A. Mostafazadeh arXiv:1205.4560.
41. A. Mostafazadeh and S. Rostamzadeh, arXiv:1204.2701.
42. A. Mostafazadeh and M. Sarisaman, arXiv:1205.5472 [Proc. R. Soc. A (to be published)]. PRLAAZ 1364-5021
43. A. Mostafazadeh, arXiv:1207.2278.
44. W.D. Heiss and R.G. Nazmitdinov, Eur. Phys. J. D 63, 369 (2011). EPJDF6 1434-6060 10.1140/epjd/e2011-20174-4
45. E.D. Belokolos, Algebro-Geometric Approach to Nonlinear Integrable Equations (Springer, Berlin, 1994).
46. M.S. Plyushchay, Ann. Phys. (N.Y.) 245, 339 (1996); APNYA6 0003-4916 10.1006/aphy.1996.0012 (Pubitemid 126166737)
47. M.S. Plyushchay Int. J. Mod. Phys. A 15, 3679 (2000). IMPAEF 0217-751X 10.1142/S0217751X00001981
48. V.B. Matveev and M.A. Salle, Darboux Transformations and Solitons (Springer, Berlin, 1991).
49. F. Cannata, G. Junker, and J. Trost, Phys. Lett. A 246, 219 (1998). PYLAAG 0375-9601 10.1016/S0375-9601(98)00517-9
50. C.M. Bender, G.V. Dunne, and P.N. Meisinger, Phys. Lett. A 252, 272 (1999). PYLAAG 0375-9601 10.1016/S0375-9601(98)00960-8
51. H.F. Jones, Phys. Lett. A 262, 242 (1999). PYLAAG 0375-9601 10.1016/S0375-9601(99)00672-6
52. J.M. Cerveró, Phys. Lett. A 317, 26 (2003). PYLAAG 0375-9601 10.1016/j.physleta.2003.08.024
53. K.C. Shin, J. Phys. A 37, 8287 (2004). JPHAC5 0305-4470 10.1088/0305-4470/37/34/007 (Pubitemid 39202971)
54. B.F. Samsonov and P. Roy, J. Phys. A 38, L249 (2005). JPHAC5 0305-4470 10.1088/0305-4470/38/15/L02 (Pubitemid 41236941)
55. B.F. Samsonov, Phys. Lett. A 358, 105 (2006). PYLAAG 0375-9601 10.1016/j.physleta.2006.04.109 (Pubitemid 44176226)
56. A. Khare and B.P. Mandal, Pramana J. Phys. 73, 387 (2009). PRAMCI 0304-4289 10.1007/s12043-009-0130-8
57. S. Longhi, J. Phys. A 44, 485302 (2011). JPAMB5 1751-8113 10.1088/1751-8113/44/48/485302
58. G.V. Dunne and J. Feinberg, Phys. Rev. D 57, 1271 (1998). PRVDAQ 0556-2821 10.1103/PhysRevD.57.1271
59. F. Correa and M.S. Plyushchay, Ann. Phys. (N.Y.) 322, 2493 (2007). APNYA6 0003-4916 10.1016/j.aop.2006.12.002
60. F. Correa and M.S. Plyushchay, Ann. Phys. (N.Y.) 327, 1761 (2012). APNYA6 0003-4916 10.1016/j.aop.2012.03.004
61. W. Magnus and S. Winkler, Hill's Equation (Wiley, New York, 1966).
62. E.T. Whittaker and G.N. Watson, Course of Modern Analysis (Cambridge University Press, Cambridge, England, 1980).
63. F. Correa, V. Jakubsky, and M.S. Plyushchay, J. Phys. A 41, 485303 (2008). JPAMB5 1751-8113 10.1088/1751-8113/41/48/485303
64. A.P. Veselov, Lett. Math. Phys. 96, 209 (2011). LMPHDY 0377-9017 10.1007/s11005-010-0420-6
65. B. Bagchi and C. Quesne, Phys. Lett. A 273, 285 (2000); PYLAAG 0375-9601 10.1016/S0375-9601(00)00512-0
66. B. Bagchi C. Quesne J. Phys. A 43, 305301 (2010). JPAMB5 1751-8113 10.1088/1751-8113/43/30/305301
67. A. Khare and U. Sukhatme, Phys. Lett. A 324, 406 (2004); PYLAAG 0375-9601 10.1016/j.physleta.2004.03.006
68. A. Khare Uday Sukhatme J. Math. Phys. (N.Y.) 46, 082106 (2005); JMAPAQ 0022-2488 10.1063/1.2000207 (Pubitemid 41247104)
69. A. Khare Uday Sukhatme J. Math. Phys. (N.Y.) 47, 062103 (2006). JMAPAQ 0022-2488 10.1063/1.2204810 (Pubitemid 44000485)
70. F. Correa, V. Jakubsky, L.-M. Nieto, and M.S. Plyushchay, Phys. Rev. Lett. 101, 030403 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.030403
71. P.D. Lax, Commun. Pure Appl. Math. 21, 467 (1968). CPMAMV 0010-3640 10.1002/cpa.3160210503
72. M.S. Plyushchay and L.-M. Nieto, Phys. Rev. D 82, 065022 (2010); PRVDAQ 1550-7998 10.1103/PhysRevD.82.065022
73. M.S. Plyushchay, A. Arancibia, and L.-M. Nieto, Phys. Rev. D 83, 065025 (2011). PRVDAQ 1550-7998 10.1103/PhysRevD.83.065025
74. F. Correa, M.A. del Olmo, and M.S. Plyushchay, Phys. Lett. B 628, 157 (2005). PYLBAJ 0370-2693 10.1016/j.physletb.2005.09.046 (Pubitemid 41416779)
75. F. Correa and M.S. Plyushchay, J. Phys. A 40, 14403 (2007). JPAMB5 1751-8113 10.1088/1751-8113/40/48/007
76. F. Correa, V. Jakubsky, and M.S. Plyushchay (unpublished).
77. F. Correa, G.V. Dunne, and M.S. Plyushchay, Ann. Phys. (N.Y.) 324, 2522 (2009). APNYA6 0003-4916 10.1016/j.aop.2009.06.005
78. G. Basar and G.V. Dunne, Phys. Rev. Lett. 100, 200404 (2008); PRLTAO 0031-9007 10.1103/PhysRevLett.100.200404 (Pubitemid 351718013)
79. G. Basar G.V. Dunne Phys. Rev. D 78, 065022 (2008). PRVDAQ 1550-7998 10.1103/PhysRevD.78.065022
80. V. Jakubsky and M.S. Plyushchay, Phys. Rev. D 85, 045035 (2012). PRVDAQ 1550-7998 10.1103/PhysRevD.85.045035