Non-instanton tunneling: Semiclassical and quantum interpretations

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

Volumn 84, Issue 2, 2011, Pages

  Takahashi, Kin'Ya ^a   Ikeda, Kensuke S ^b  

^a KYUSHU INSTITUTE OF TECHNOLOGY   (Japan)

^b RITSUMEIKAN UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

PERTURBATION FREQUENCY; STEP POTENTIALS; TUNNELING PROBABILITIES; TUNNELING RATES;

EID: 80051629564     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.026203     Document Type: Article

References (49)

1. Tunneling in Complex Systems, edited by S. Tomsovic (World Scientific, Singapore, 1998).
2. J. Ankerhold, Quantum Tunneling in Complex Systems, The Semiclassical Approach (Springer-Verlag, Berlin-Heidelberg, 2007).
3. S. Keshavamurthy, Int. Rev. Phys. Chem. IRPCDL 0144-235X 10.1080/01442350701462288 26, 521 (2007).
4. Dynamical Tunneling: Theory and Experiment, edited by S. Keshavamurthy and P. Schlagheck (CRC Press, Taylor & Francis Group, 2011).
5. O. Bohigas, S. Tomsovic, and D. Ullmo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65.5 65, 5 (1990);
6. O. Bohigas, S. Tomsovic, and D. Ullmo, Phys. Rep. 0370-1573 10.1016/0370-1573(93)90109-Q 223, 43 (1993).
7. S. C. Creagh and N. D. Whelan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.4084 84, 4084 (2000).
8. S. C. Creagh, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/17/4/007 17, 1261 (2004); (Pubitemid 38919693)
9. S. C. Creagh, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/18/5/011 18, 2089 (2005); (Pubitemid 41112477)
10. C. S. Drew, S. C. Creagh, and R. H. Tew, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.062501 72, 062501 (2005). (Pubitemid 41776030)
11. W. K. Hensinger, Nature NATUAS 0028-0836 10.1038/35083510 412, 52 (2001); (Pubitemid 32851504)
12. D. A. Steck, W. H. Oskay, and M. G. Raizen, Science SCIEAS 0036-8075 10.1126/science.1061569 293, 274 (2001); (Pubitemid 32694738)
13. C. Dembowski, H.-D. Gräf, A. Heine, R. Hofferbert, H. Rehfeld, and A. Richter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.867 84, 867 (2000).
14. O. Brodier, P. Schlagheck, and D. Ullmo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.064101 87, 064101 (2001);
15. O. Brodier, P. Schlagheck, and D. Ullmo, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1006/aphy.2002.6281 300, 88 (2002);
16. C. Eltschka and P. Schlagheck, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.014101 94, 014101 (2005). (Pubitemid 40629821)
17. A. Bäcker, R. Ketzmerick, S. Löck, and L. Schilling, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.104101 100, 104101 (2008); (Pubitemid 351399141)
18. A. Bäcker, R. Ketzmerick, S. Löck, M. Robnik, G. Vidmar, R. Hohmann, U. Kuhl, and H. J. Stockmann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.174103 100, 174103 (2008); (Pubitemid 351624668)
19. A. Bäcker, R. Ketzmerick, S. Löck, J. Wiersig, and M. Hentschel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.063804 79, 063804 (2009);
20. S. Löck, A. Bäcker, R. Ketzmerick, and P. Schlagheck, Rhys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.104.114101 104, 114101 (2010).
21. A. Shudo and K. S. Ikeda, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.682 74, 682 (1995);
22. A. Shudo and K. S. Ikeda, Physica D PDNPDT 0167-2789 10.1016/S0167- 2789(97)00239-X 115, 234 (1998);
23. T. Onishi, A. Shudo, K. S. Ikeda, and K. Takahashi, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.64.025201 64, 025201 (R) (2001);
24. T. Onishi, A. Shudo, K. S. Ikeda, and K. Takahashi, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.68.056211 68, 056211 (2003).
25. A. Shudo, Y. Ishii, and K. S. Ikeda, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/17/101 35, L225 (2002); (Pubitemid 37023875)
26. A. Shudo, Y. Ishii, and K. S. Ikeda, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/81/50003 81, 50003 (2008);
27. A. Shudo, Y. Ishii, and K. S. Ikeda, J. Phys. A EULEEJ 1751-8113 10.1088/1751-8113/42/26/265101 42, 265101 (2009);
28. A. Shudo, Y. Ishii, and K. S. Ikeda, J. Phys. A EULEEJ 1751-8113 10.1088/1751-8113/42/26/265102 42, 265102 (2009).
29. L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981).
30. K. Takahashi, A. Yoshimoto, and K. S. Ikeda, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(02)00155-X 297, 370 (2002);
31. K. Takahashi and K. S. Ikeda, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/29/305 36, 7953 (2003).
32. K. Takahashi and K. S. Ikeda, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2004-10538-1 71, 193 (2005); (Pubitemid 41024882)
33. K. Takahashi and K. S. Ikeda, J. Phys. A EULEEJ 1751-8113 10.1088/1751-8113/41/9/095101 41, 095101 (2008).
34. K. Takahashi and K. S. Ikeda, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.052114 79, 052114 (2009).
35. K. Takahashi and K. S. Ikeda, J. Phys. A PLRAAN 1751-8113 10.1088/1751-8113/43/19/192001 43, 192001 (2010).
36. F. Bezrukov and D. Levkov, J. Exp. Theor. Phys. JTPHES 1063-7761 10.1134/1.1757681 98, 820 (2004);
37. D. G. Levkov, A. G. Panin, and S. M. Sibiryakov, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.170407 99, 170407 (2007); (Pubitemid 350015176)
38. D. G. Levkov, A. G. Panin, and S. M. Sibiryakov, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.76.046209 76, 046209 (2007); (Pubitemid 47569152)
39. D. G. Levkov, A. G. Panin, and S. M. Sibiryakov, J. Phys. A PRLTAO 1751-8113 10.1088/1751-8113/42/20/205102 42, 205102 (2009).
40. W. H. Miller, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1674275 53, 1949 (1970);
41. W. H. Miller, Adv. Chem. Phys. JCPSA6 0065-2385 10.1002/9780470143773.ch2 25, 69 (1974).
42. E. Bedford and J. Smillie, J. Am. Math. Soc. 10.2307/2939284 4, 657 (1991).
43. M. Büttiker and R. Landauer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.49.1739 49, 1739 (1982);
44. M. Büttiker and R. Landauer, Phys. Scr. PHSTBO 0031-8949 10.1088/0031-8949/32/4/031 32, 429 (1985).
45. K. Takahashi and K. S. Ikeda, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.240403 97, 240403 (2006). (Pubitemid 44907659)
46. K. Takahashi and K. S. Ikeda, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1006/aphy.2000.6050 283, 94 (2000).
47. V. K. Melnikov, Trans. Mosc. Math. Soc. 12, 1 (1963).
48. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer-Verlag, New York, 1990).
49. L. D. Landau and E. M. Lifshitz, Quantum Mechanics Non-relativistic Theory (Butterworth Heinemann, Amsterdam, 1977).