Instantons re-examined: Dynamical tunneling and resonant tunneling

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 81, Issue 4, 2010, Pages

  Le Deunff, Jérémy ^a   Mouchet, Amaury ^a  

^a UNIVERSITÉ DE TOURS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX TRAJECTORIES; DECAY RATE; DOUBLE-WELL POTENTIAL; HAMILTONIAN SYSTEMS; INSTANTONS; TIME DOMAIN; TUNNELING EFFECTS; TUNNELING SPLITTINGS;

DECAY (ORGANIC); HAMILTONIANS; RESONANT TUNNELING; ROTATION;

WIND TUNNELS;

EID: 77950940988     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.046205     Document Type: Article

References (50)

1. Instantons in gauge theories, Advanced Series in Mathematical Physics edited by, M. A. Shifman, (World Scientific, Singapore, 1994), Vol. 5.
2. S. Coleman, Aspects of Symmetry (selected Erice lectures) (Cambridge University Press, Cambridge, 1985).
3. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 4th ed., International Series of Monographs on Physics (Clarendon Press, Oxford, 2002), Vol. 113.
4. M. J. Davis and E. J. Heller, J. Chem. Phys. 75, 246 (1981). 10.1063/1.441832
5. N. T. Maitra and E. J. Heller, Phys. Rev. A 54, 4763 (1996). 10.1103/PhysRevA.54.4763
6. N. T. Maitra and E. J. Heller, Phys. Rev. Lett. 78, 3035 (1997). 10.1103/PhysRevLett.78.3035
7. K. F. Freed, J. Chem. Phys. 56, 692 (1972). 10.1063/1.1677217
8. T. F. George and W. H. Miller, J. Chem. Phys. 56, 5722 (1972). 10.1063/1.1677094
9. W. H. Miller, Adv. Chem. Phys. 25, 69 (1974). 10.1002/9780470143773.ch2
10. U. Weiss and W. Haeffner, Phys. Rev. D 27, 2916 (1983). 10.1103/PhysRevD.27.2916
11. R. D. Carlitz and D. A. Nicole, Ann. Phys. (N.Y.) 164, 411 (1985). 10.1016/0003-4916(85)90021-1
12. E. M. Ilgenfritz and H. Perlt, J. Phys. A 25, 5729 (1992). 10.1088/0305-4470/25/21/026
13. N. T. Maitra and E. J. Heller, in Classical, Semiclassical and Quantum Dynamics in Atoms, edited by, H. Friedrich, and, B. Eckhardt, (Springer-Verlag, Berlin, 1997), pp. 94-111.
14. S. C. Creagh and N. D. Whelan, Ann. Phys. (N.Y.) 272, 196 (1999). 10.1006/aphy.1998.5887
15. A. M. Ozorio de Almeida, J. Phys. Chem. 88, 6139 (1984). 10.1021/j150669a017
16. D. Farrelly and T. Uzer, J. Chem. Phys. 85, 308 (1986). 10.1063/1.451657
17. E. J. Heller, J. Phys. Chem. 99, 2625 (1995). 10.1021/j100009a021
18. S. Tomsovic, J. Phys. A 31, 9469 (1998). 10.1088/0305-4470/31/47/008
19. D. W. Mclaughlin, J. Math. Phys. 13, 1099 (1972). 10.1063/1.1666102
20. Y. Zohta, Phys. Rev. B 41, 7879 (1990). 10.1103/PhysRevB.41.7879
21. D. Bohm, Quantum Theory (Prentice Hall, Englewood Cliffs, N. J., 1951).
22. K. Takahashi and N. Saitôn, Phys. Rev. Lett. 55, 645 (1985). 10.1103/PhysRevLett.55.645
23. E. J. Heller, in Chaos et Physique Quantique-Chaos and Quantum Physics (Ref.), pp. 547-663.
24. G. Torres-Vega and J. H. Frederick, J. Chem. Phys. 93, 8862 (1990). 10.1063/1.459225
25. Chaos et Physique Quantique-Chaos and Quantum Physics, Les Houches, école d'été de physique théorique 1989, session LII, edited by, M. Giannoni, A. Voros, and, J. Zinn-Justin, (North-Holland, Amsterdam, 1991).
26. M. Wilkinson, Physica D 21, 341 (1986). 10.1016/0167-2789(86)90009-6
27. S. C. Creagh, in Tunneling in Complex Systems, Proceedings from the Institute for Nuclear Theory, edited by, S. Tomsovic, (World Scientific, Singapore, 1997), Vol. 5, pp. 35-100.
28. A. Garg, Am. J. Phys. 68, 430 (2000). 10.1119/1.19458
29. A. Mouchet, J. Phys. A 40, F663 (2007). 10.1088/1751-8113/40/29/F02
30. A. Shudo and K. S. Ikeda, Phys. Rev. Lett. 76, 4151 (1996). 10.1103/PhysRevLett.76.4151
31. A. Shudo, Y. Ishii, and K. S. Ikeda, J. Phys. A 42, 265101 (2009). 10.1088/1751-8113/42/26/265101
32. J. M. Robbins, S. C. Creagh, and R. G. Littlejohn, Phys. Rev. A 39, 2838 (1989). 10.1103/PhysRevA.39.2838
33. H. J. Korsch and Glück, Eur. J. Phys. 23, 413 (2002). 10.1088/0143-0807/23/4/305
34. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Nonrelativistic Theory), Course of Theoretical Physics, 3rd ed. (Pergamon Press, Oxford, 1977), Vol. 3.
35. E. Gildener and A. Patrascioiu, Phys. Rev. D 16, 423 (1977). 10.1103/PhysRevD.16.423
36. T. Connor, J. N. L. and Uzer, R. A. Marcus, and A. D. Smith, J. Chem. Phys. 80, 5095 (1984). 10.1063/1.446581
37. M. Abramowitz and I. A. Segun, Handbook of Mathematical Functions (Dover, New York, 1965).
38. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965).
39. D. Khuat-duy and P. LebOuf, Appl. Phys. Lett. 63, 1903 (1993). 10.1063/1.110643
40. A. Bäcker, R. Ketzmerick, S. Löck, and L. Schilling, Phys. Rev. Lett. 100, 104101 (2008). 10.1103/PhysRevLett.100.104101
41. S. Löck, A. Bäcker, R. Ketzmerick, and P. Schlagheck, Phys. Rev. Lett. 104, 114101 (2010). 10.1103/PhysRevLett.104.114101
42. R. F. Dashen, B. Hasslacher, and A. Neveu, Phys. Rev. D 10, 4114 (1974). 10.1103/PhysRevD.10.4114
43. F. Haake, Quantum Signatures of Chaos (Springer-Verlag, Berlin, 2001).
44. J. B. Keller, Ann. Phys. (N.Y.) 4, 180 (1958). 10.1016/0003-4916(58) 90032-0
45. I. C. Percival, Adv. Chem. Phys. 36, 1 (1977). 10.1002/9780470142554.ch1
46. S. C. Creagh and N. D. Whelan, Phys. Rev. Lett. 77, 4975 (1996). 10.1103/PhysRevLett.77.4975
47. S. Tomsovic and D. Ullmo, Phys. Rev. E 50, 145 (1994). 10.1103/PhysRevE.50.145
48. F. Leyvraz and D. Ullmo, J. Phys. A 29, 2529 (1996). 10.1088/0305-4470/ 29/10/030
49. Statistical approaches have also been proposed.
50. The other order lim τ →0 lim →0 corresponds to the quantization of a kicked Hamiltonian that leads to τ -dependent results as shown in.