Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: From the time-independent to the time-dependent quantum mechanical formulation

Laser Physics

Volumn 17, Issue 4, 2007, Pages 424-437

  Faria, C F M ^a   Fring, A ^a  

^a CITY UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; ELECTRIC FIELD EFFECTS; HAMILTONIANS; HARMONIC ANALYSIS;

HARMONIC OSCILLATORS; NON-HERMITIAN HAMILTONIANS; QUANTUM MECHANICAL FORMULATIONS;

QUANTUM THEORY;

EID: 34247247729     PISSN: 1054660X     EISSN: 15556611     Source Type: Journal    
DOI: 10.1134/S1054660X07040196     Document Type: Review

References (56)

1. H. Friedrich and D. Wintgen, Phys. Rev. A 32, 3231 (1985).
2. H. Geyer, D. Heiss, and M. Znojil (guest editors), Special Issue Dedicated to the Physics of Non-Hermitian Operators (PHHQP IV) (Univ. of Stellenbosch, South Africa, 2005), J. Phys. A 39, 9965 (2006).
3. C. Figueira de Morisson Faria and A. Fring, J. Phys. A 39, 9269 (2006).
4. C. M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998).
5. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (MacGraw-Hill, New York, 1978).
6. A. Mostafazadeh, J. Phys. A 38, 3213-3234 (2005).
7. H. F. Jones and J. Mateo, Czech. J. Phys. 55, 1117 (2005).
8. H. F. Jones and J. Mateo, Phys. Rev. D 73, 085002(4) (2006).
9. J. A. C. Weideman, J. Phys. A 39, 10229 (2006).
10. C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. Lett. 89, 270401(4) (2002).
11. P. Dorey, C. Dunning, and R. Tateo, J. Phys. A 34, 5679 (2001).
12. K. C. Shin, J. Phys. A 38, 6147 (2005).
13. E. Wigner, J. Math. Phys. 1, 409 (1960).
14. S. Weigert, J. Opt. B: Quantum Semiclass. Opt. 5, S416 (2003).
15. S. Weigert, J. Phys. A 39, 10239 (2006).
16. Z. Ahmed, Phys. Lett. A 290, 19 (2001).
17. A. Mostafazadeh, J. Math. Phys. 43, 2814 (2002).
18. F. G. Scholtz, H. B. Geyer, and F. Hahne, Ann. Phys. 213, 74 (1992).
19. W. Heisenberg, Rev. Mod. Phys. 29, 269 (1957).
20. A. Mostafazadeh, J. Math. Phys. 43, 205 (2002).
21. A. Mostafazadeh, J. Math. Phys. 43, 3944 (2002).
22. A. Mostafazadeh, J. Phys. A 36, 7081 (2003).
23. A. Mostafazadeh, J. Math. Phys. 44, 974 (2003).
24. S. Weigert, Phys. Rev. A 68, 062111(4) (2003).
25. I. Rotter and A. F. Sadreev, Phys. Rev. E 71, 0362271(14) (2005).
26. E. Persson, T. Gorin, and I. Rotter, Phys. Rev. E 54, 3339 (1996).
27. M. Leone, A. Paoletti, and N. Robotti, Phys. Perspect. 6, 271 (2004).
28. H. Silverstone and C.N. Nicolaides (Ed.) (Plenum Press, New York, 1990), pp. 295.
29. A. Fring, V. Kostrykin, and R. Schrader, J. Phys. B 29, 5651 (1996).
30. C. Figueira de Morisson Faria, A. Fring, and R. Schrader, Laser Phys. 9, 379 (1999).
31. C. Figueira de Morisson Faria, A. Fring, and R. Schrader, J. Phys. B 33, 1675 (2000).
32. M. Born and V. Fock, Z. Phys. 51, 165 (1928).
33. A. Fleischer and N. Moiseyev, Phys. Rev. A 72, 032103(11) (2005).
34. M. Lewenstein, P. Salieres, A. L'Huillier, and P. Antoine, Adv. At. Mol. Opt. Phys. 41, 83 (1999).
35. W. Becker, F. Grasbon, R. Kopold, et al., Adv. At. Mol. Opt. Phys. 48, 35 (2002).
36. C. Joachain, M. Dörr, and N. Kylstra, Adv. At. Mol. Opt. Phys. 42, 225 (2000).
37. C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. D 70, 025001(19) (2004).
38. A. Mostafazadeh, J. Phys. A 38, 6557 (2005).
39. C. Figueira de Morisson Faria and A. Fring, Czech. J. Phys. 56, 899 (2006).
40. E. Caliceti, F. Cannata, and S. Graffi, J. Phys. A 39, 10019 (2006).
41. F. G. Scholtz and H. B. Geyer, Phys. Lett. B 634, 84 (2006).
42. F. G. Scholtz and H. B. Geyer, J. Phys. A 39, 10189 (2006).
43. D. B. Fairlie, J. Chaos, Solitons Fractals 10, 365 (1999).
44. A. Mostafazadeh, J. Math. Phys. 47, 072103(11) (2006).
45. C. M. Bender, D. C. Brody, J.-H. Chen, et al., Phys. Rev. D 74, 025016(10) (2006).
46. M. S. Swanson, J. Math. Phys. 45, 585 (2004).
47. H. Jones, J. Phys. A 38, 1741 (2005).
48. E. Witten, Nucl. Phys. B 202, 253 (1982).
49. F. Cooper, A. Khare, and U. Sukhatme, Phys. Rep. 251, 267 (1995).
50. M. Znojil, Phys. Lett. A 259, 220 (1999).
51. C. Figueira de Morisson Faria, A. Fring, and H. Jones (unpublished notes).
52. C. M. Bender, J.-H. Chen, and K. A. Milton, J. Phys. A 39, 1657 (2006).
53. C. M. Bender, D. C. Brody, H. F. Jones, and B. K. Meister, quanth-ph/0609032 (2006).
54. K. A. Milton, Czech. J. Phys. 54, 85 (2004).
55. C. M. Bender, I. Cavero-Pelaez, K. A. Milton, and K. V. Shajesh, Phys. Lett. B 613, 97 (2005).
56. C. Figueira de Morisson Faria and A. Fring (in preparation).