Long-lived resonances supported by a contact interaction in crossed magnetic and electric fields

Annals of Physics

Volumn 323, Issue 11, 2008, Pages 2639-2653

  Krajewska, K ^a   Kaminski J Z ^a   Potvliege, R M ^b  

^a UNIVERSITY OF WARSAW   (Poland)

^b DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Crossed fields; Landau levels; Point interaction; Quantum Hall effect; Resonances; Zero range potential

Indexed keywords

EID: 52749092910     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2008.02.006     Document Type: Article

References (46)

1. Prange R.E. Phys. Rev. B 23 (1981) 4802
2. Fernando Perez J., and Coutinho F.A.B. Am. J. Phys. 59 (1991) 52
3. Cavalcanti R.M., and de Carvalho C.A.A. J. Phys. A 31 (1998) 2391
4. Krajewska K., and Kamiński J.Z. Phys. Lett. A 301 (2002) 369
5. For the theory of resonances, see, e.g.,. Faisal F.H.M. Theory of Multiphoton Processes (1987), Plenum Press, New York
6. Kukulin V.I., Krasnopol'sky V.M., and Horáček J. Theory of Resonances, Principles and Applications (1989), Kluwer Academic Publishers, Prague
7. Kleber M. Phys. Rep. 236 (1994) 331
8. Moiseyev N. Phys. Rep. 302 (1998) 211
9. Gyger S., and Martin P.A. J. Math. Phys. 40 (1999) 3275
10. Ferrari C., and Kovaři{dotless}́k H. J. Phys. A 37 (2004) 7671
11. Hauge E.H., and van Leeuwen J.M.J. Phys. A 268 (1999) 525
12. Wódkiewicz K. Phys. Rev. A 43 (1991) 68
13. Krajewska K., and Kamiński J.Z. J. Math. Phys. 43 (2002) 3937
14. Berglund N., Hansen A., Hauge E.H., and Piasecki J. Phys. Rev. Lett. 77 (1996) 2149
15. Krajewska K., and Kamiński J.Z. Phys. Rev. B 68 (2003) 064418
16. Glasser M.L., Jaskólski W., Garci{dotless}́a-Moliner F., and Velasco V.R. Phys. Rev. B 42 (1990) 7630
17. Bylicki M., and Jaskólski W. Phys. Rev. B 60 (1999) 15924
18. Gersten J.I., and Mittleman M.H. J. Phys. B 9 (1976) 2561
19. Gavrila M., and Kamiński J.Z. Phys. Rev. Lett. 52 (1984) 613
20. Fedorov M.V., and Movsesian A.M. J. Phys. B 21 (1988) L155
21. Kamiński J.Z. Phys. Rev. A 52 (1995) 4976
22. Gavrila M. J. Phys. B 35 (2002) R147
23. For the method of contact potential, see, e.g.,. Demkov Yu.N., and Ostrovsky N.V. Zero-range Potentials and their Applications in Atomic Physics (1988), Plenum, New York
24. Albeverio S., Gesztesy F., Høegh-Krohn R., and Holden H. Solvable Models in Quantum Mechanics (1988), Springer, New York
25. Becker W., Long S., and McIver J.K. Phys. Rev. A 50 (1994) 1540
26. Milosěvić D.B., and Becker W. Phys. Rev. A 66 (2002) 063417
27. Berson I.J. J. Phys. B 8 (1975) 3078
28. Filipowicz P., Faisal F.H.M., and Rza̧żewski K. Phys. Rev. A 44 (1991) 2210
29. Potvliege R.M. Phys. Rev. A 62 (2000) 013403
30. Manakov N.L., Frolov M.V., Starace A.F., and Fabrikant I.I. J. Phys. B 33 (2000) R141
31. Manakov N.L., Frolov M.V., Borca B., and Starace A.F. J. Phys. B 36 (2003) R49
32. Rylyuk V.M., and Ortner J. Phys. Rev. A 67 (2003) 013414
33. Paulus G.G., Grasbon F., Walther H., Kopold R., and Becker W. Phys. Rev. A 64 (2001) 021401R
34. Borca B., Frolov M.V., Manakov N.L., and Starace A.F. Phys. Rev. Lett. 88 (2002) 193001
35. Borca B., Starace A.F., Flegel A.V., Frolov M.V., and Manakov N.L. Phys. Rev. A 65 (2002) 051402R
36. This is also the case in one and two dimensions-see, e.g., Ref. [9].
37. The same conclusion can be reached using another regularization procedure-see Ref. [10].
38. Busch T., Englert B.-G., Rza̧żewski K., and Wilkens M. Found. Phys. 28 (1998) 549
39. Mitra I., DasGupta A., and Dutta-Roy B. Am. J. Phys. 66 (1998) 1101
40. Sokolov A.A., Ternov I.M., and Zhukovskii V.Ch. Quantum Mechanics (1979), Nauka, Moscow (in Russian)
41. Ballentine L.E. Quantum Mechanics (1990), Prentice Hall, Englewood Cliffs
42. Białynicki-Birula I., Cieplak M., and Kamiński J. Theory of Quanta (1992), Oxford University Press, New York
43. Schiff L.I. Quantum Mechanics (1968), McGraw-Hill, New York
44. Korn G.A., and Korn T.M. Mathematical Handbook for Scientists and Engineers (1968), McGraw-Hill, New York
45. Gradshteyn I.S., and Ryzhik I.M. Tables of Integrals, Series, and Products (1980), Academic Press, San Diego (The notation used by Gradshteyn and Ryzhik for the generalized Laguerre polynomials is the same as that used by Schiff [39] for the associated Laguerre polynomials)
46. Bunkin F.V., and Prokhorov A.M. Zh. Eksp. Teor. Fiz. 46 (1964) 1090 (Sov. Phys.-JETP 19 (1964) 739)