Equivalence between the real-time Feynman histories and the quantum-shutter approaches for the "passage time" in tunneling

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 67, Issue 5, 2003, Pages 521061-521066

  García Calderón, Gastón ^a   Villavicencio, Jorge ^b   Yamada, Norifumi ^c  

^a UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^b UNIVERSIDAD AUTÓNOMA DE BAJA CALIFORNIA   (Mexico)

^c UNIVERSITY OF FUKUI   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; PROBABILITY DISTRIBUTIONS; THEOREM PROVING; WAVE EQUATIONS;

PASSAGE TIME;

QUANTUM THEORY;

EID: 0038106586     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (31)

1. L.A. MacColl, Phys. Rev. 40, 621 (1932).
2. See, for example, E.H. Hauge and J.A. Støvneng, Rev. Mod. Phys. 61, 917 (1989); R. Landauer and Th. Martin, ibid. 66, 217 (1994); Time in Quantum Mechanics, edited by J.G. Muga, R. Sala, and I.L. Egusquiza (Springer-Verlag, Berlin, 2002).
3. See, for example, E.H. Hauge and J.A. Støvneng, Rev. Mod. Phys. 61, 917 (1989); R. Landauer and Th. Martin, ibid. 66, 217 (1994); Time in Quantum Mechanics, edited by J.G. Muga, R. Sala, and I.L. Egusquiza (Springer-Verlag, Berlin, 2002).
4. See, for example, E.H. Hauge and J.A. Støvneng, Rev. Mod. Phys. 61, 917 (1989); R. Landauer and Th. Martin, ibid. 66, 217 (1994); Time in Quantum Mechanics, edited by J.G. Muga, R. Sala, and I.L. Egusquiza (Springer-Verlag, Berlin, 2002).
5. N. Yamada, Phys. Rev. A 54, 182 (1996).
6. N. Yamada, Phys. Rev. Lett. 83, 3350 (1999).
7. N. Yamada (unpublished); N. Yamada in Meeting Abstracts of the Physical Society of Japan (Physical Society of Japan, Tokyo, 2000), Vol. 55, p. 227.
8. N. Yamada (unpublished); N. Yamada in Meeting Abstracts of the Physical Society of Japan (Physical Society of Japan, Tokyo, 2000), Vol. 55, p. 227.
9. G. García-Calderón and A. Rubio, Phys. Rev. A 55, 3361 (1997).
10. G. García-Calderón and J. Villavicencio, Phys. Rev. A 64, 012107 (2001).
11. R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
12. Here we consider such a probability distribution of tunneling times that is intrinsic to the scattering event.
13. M. Büttiker and R. Landauer, Phys. Rev. Lett. 49, 1739 (1982).
14. D.G. Sokolovskii and L.M. Baskin, Zh. Tech. Fiz. 55, 1838 (1985) [Sov. Phys. Tech. Phys. 30, 1076 (1985)]; D. Sokolovshi and L.M. Baskin, Phys. Rev. A 36, 4604 (1987).
15. D.G. Sokolovskii and L.M. Baskin, Zh. Tech. Fiz. 55, 1838 (1985) [Sov. Phys. Tech. Phys. 30, 1076 (1985)]; D. Sokolovshi and L.M. Baskin, Phys. Rev. A 36, 4604 (1987).
16. L.S. Schulman and R.W. Ziolkowski, in Proceedings of Third International Conference on Path Integrals from meV to MeV, edited by V. Sa-yakanit et al. (World Scientific, Singapore, 1989), p. 253.
17. G. García-Calderón and J. Villavicencio, e-print quant-ph/0008014.
18. M. Gell-Mann and J.B. Hartle, in Proceedings of the Third International Symposium on the Foundations of Quantum Mechanics in the Light of New Technology, edited by S. Kobayashi et al (Physical Society of Japan, Tokyo, 1990), p. 321.
19. M. Gell-Mann and J.B. Hartle, in Proceedings of the 25th International Conference on High Energy Physics, edited by K.K. Phua and Y. Yamaguchi (World Scientific, Singapore, 1991), p. 1303.
20. J.B. Hartle, Phys. Rev. D 44, 3173 (1991); M. Gell-Mann and J.B. Hartle, ibid. 47, 3345 (1993).
21. J.B. Hartle, Phys. Rev. D 44, 3173 (1991); M. Gell-Mann and J.B. Hartle, ibid. 47, 3345 (1993).
22. J. Humblet and L. Rosenfeld, Nucl. Phys. 26, 529 (1961).
23. t2dt] dt] for Complex Argument, translated by D.G. Fry and B.A. Hons (Pergamon, London, 1961); Handbook of Mathematical Functions, edited by M. Abramowitz and I.A. Stegun (Dover, New York, 1965), p. 297; G.P.M. Poppe and C.M.J. Wijers, ACM Trans. Math. Softw. 16, 38 (1990); 16, 47 (1990). The above references discuss also numerical methods to evaluate the complex error function w.
24. t2dt] dt] for Complex Argument, translated by D.G. Fry and B.A. Hons (Pergamon, London, 1961); Handbook of Mathematical Functions, edited by M. Abramowitz and I.A. Stegun (Dover, New York, 1965), p. 297; G.P.M. Poppe and C.M.J. Wijers, ACM Trans. Math. Softw. 16, 38 (1990); 16, 47 (1990). The above references discuss also numerical methods to evaluate the complex error function w.
25. t2dt] dt] for Complex Argument, translated by D.G. Fry and B.A. Hons (Pergamon, London, 1961); Handbook of Mathematical Functions, edited by M. Abramowitz and I.A. Stegun (Dover, New York, 1965), p. 297; G.P.M. Poppe and C.M.J. Wijers, ACM Trans. Math. Softw. 16, 38 (1990); 16, 47 (1990). The above references discuss also numerical methods to evaluate the complex error function w.
26. t2dt] dt] for Complex Argument, translated by D.G. Fry and B.A. Hons (Pergamon, London, 1961); Handbook of Mathematical Functions, edited by M. Abramowitz and I.A. Stegun (Dover, New York, 1965), p. 297; G.P.M. Poppe and C.M.J. Wijers, ACM Trans. Math. Softw. 16, 38 (1990); 16, 47 (1990). The above references discuss also numerical methods to evaluate the complex error function w.
27. E.G. Tichmarsh, The Theory of Functions, 2nd ed. (Oxford University Press, London, 1939), p. 110.
28. G. García-Calderón (unpublished). A similar expansion in three dimensions is presented in the paper, G. García-Calderón and A. Rubio, Nucl. Phys. A 458, 560 (1986).
29. G. García-Calderón (unpublished). A similar expansion in three dimensions is presented in the paper, G. García-Calderón and A. Rubio, Nucl. Phys. A 458, 560 (1986).
30. G. García-Calderón, Solid State Commun. 62, 441 (1987).
31. D.K. Ferry and S.M. Goodnick, Transport in Nanostructures (Cambridge University Press, Cambridge, 1997), pp. 91-201.