Singularities of Berry connections inhibit the accuracy of the adiabatic approximation

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 370, Issue 1, 2007, Pages 17-21

  Liu, Jie ^a   Fu, Li Bin ^a  

^a INSTITUTE OF APPLIED PHYSICS AND COMPUTATIONAL MATHEMATICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ADIABATIC APPROXIMATIONS; POWER-LAW; QUANTUM EVOLUTION; SINGULARITY INDICES; SLOWLY VARYING PARAMETER; TWO-LEVEL MODELS;

FRUITS;

EID: 34748848044     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2007.05.021     Document Type: Article

References (38)

1. Ehrenfest P. Ann. Phys. (Berlin) 51 (1916) 327
2. Born M., and Fock V. Z. Phys. 51 (1928) 165
3. Landau L.D. Zeitschrift 2 (1932) 46
4. Zener C. Proc. R. Soc. A 137 (1932) 696
5. Schwinger J. Phys. Rev. 51 (1937) 648
6. Kato T. J. Phys. Soc. Jpn. 5 (1950) 435
7. Gell-Mann M., and Low F. Phys. Rev. 84 (1951) 350
8. Berry M.V. Proc. R. Soc. A 392 (1984) 45
9. Farhi E., et al. Science 292 (2001) 472
10. Jansen S., Ruskai M.B., and Seiler R. quant-ph/060317 and references therein
11. B. ReiChardt, in: Proc. 36th STOC, 2004, p. 502
12. Jaksic V. J. Math. Phys. 43 (1993) 2807
13. Martinez A. J. Math. Phys. 35 (1994) 3889
14. Liu J., Wu B., and Niu Q. Phys. Rev. Lett. 90 (2003) 170404
15. Anderson M.H. Science 269 (1995) 198
16. Davis K.B., et al. Phys. Rev. Lett. 75 (1995) 3969
17. Bradley C.C., et al. Phys. Rev. Lett. 75 (1995) 1687
18. Nielsen M.A., and Chuang I.L. Quantum Computation and Quantum Information (2000), Cambridge Univ. Press, Cambridge
19. Childs A.M., et al. Phys. Rev. A 65 (2002) 012322
20. Fu L.-B. Phys. Rev. Lett. 92 (2004) 130404
21. Sarandy M.S., and Lidar D.A. Phys. Rev. Lett. 95 (2005) 250503
22. Marzlin K., and Sanders B.C. Phys. Rev. Lett. 93 (2004) 160408
23. Tong D.M., Singh K., Kwek L.C., and Oh C.H. Phys. Rev. Lett. 95 (2005) 110407
24. Roland J., and Cerf N.J. Phys. Rev. A 65 (2002) 042308
25. Shi Y., and Wu Y.-S. Phys. Rev. A 69 (2004) 024301
26. Berry M.V. Proc. R. Soc. London A 392 (1984) 45-57
27. Berry M.V. In: Shapere A., and Wilczek F. (Eds). Geometric Phase in Physics (1989), World Scientific, Singapore
28. Recent progress on Berry phase refer to. Liu J., Hu B., and Li B. Phys. Rev. Lett. 81 (1998) 1749
29. Wu B., Liu J., and Niu Q. Phys. Rev. Lett. 94 (2005) 140402 and references therein
30. Manini N., and Pistolesi F. Phys. Rev. Lett. 85 (2000) 3067
31. Hasegawa Y., Loidl R., Baron M., Badurek G., and Rauch H. Phys. Rev. Lett. 87 (2001) 070401
32. Filipp S., and Sjöqvist E. Phys. Rev. Lett. 90 (2003) 050403
33. Wong H.M., Cheng K.M., and Chu M.-C. Phys. Rev. Lett. 94 (2005) 070406
34. Landau L.D., and Lifshitz E.M. Mechanics. third ed. (1976), Pergamon Press p. 160
35. The celebrated Landau-Zener model is of this exponential type tunnelling probability, see. Liu J., et al. Phys. Rev. A 66 (2002) 023404 and references therein
36. Garanin D.A., and Schilling R. Phys. Rev. B 66 (2002) 174438
37. Hanns A., et al. Phys. Rev. B 62 (2000) 13880
38. For example see. Bergmann K., Theuer H., and Shore B.W. Rev. Mod. Phys. 70 (1998) 1003