Abstract
There is a growing interest in the investigation about the time required by particles to tunnel accross potential barriers, due both to important technological advances on the subject and to concerns of a conceptual nature. The fact that the various proposed versions of tunneling times are mutually inconsistent and give widely different outcomes, reveals that there is still much to be learned from such an apparently simple problem.
In this paper we approach the problem by using the phenomenological theory of stochastic quantum mechanics to obtain semi-quantitative information about the tunneling times. The results are in good agreement with recent numerical calculations performed within the framework of Nelson’s stochastic theory. In particular, the most important effect of an opaque barrier on the tunneling particles is shown to occur before they actually enter the barrier. Further, a very simple statistical approach is shown to give valuable information on the average time spent by all particles inside the barrier.
The stochasticity of the particle dynamics, combined with the obviously wavelike features exhibited in the tunnel effect, call for an analysis within the framework of stochastic electrodynamics. As a first entry to this program, we briefly discuss the possible role of the zeropoint field in determining the behavior of tunneling particles, with the purpose of ultimately obtaining a satisfactory understanding of this intriguing quantum phenomenon.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
H. Rauch, W. Treimer and U. Bonse, Phys. Lett. A 47, 369 (1974).
See, e.g., J.S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987). F. Selleri, Quantum Paradoxes and Physical Reality (Kluwer Academic, Dordrecht, 1990). T.W. Marshall and E. Santos, Phys. Rev. A 39, 6271 (1989).
F. Capasso, K. Mohammed and A.Y. Cho, IEEE J. Quantum Electron. QE-22, 1853 (1986).
E.H. Hauge and J.A. Støvneng, Rev. Mod. Phys. 61, 917 (1989).
V.S. Olkhovsky and E. Recami, Phys. Rep. 214, 339 (1992).
R. Landauer and Th. Martin, Rev. Mod. Phys. 66, 217 (1994).
Th. E. Hartman, J. Applied Phys. 33, 3427 (1962).
F.T. Smith, Phys. Rev. 118, 349 (1960).
M. Büttiker, Phys. Rev. B 27, 6178 (1983).
A.I. Baz’, Yad. Fiz. 4, 252 (1966).
V.F. Rybachenko, Yad. Fiz. 5, 895 (1967).
J.R. Fletcher, J. Phys. C 18, L55 (1985).
M. Büttiker and R. Landauer, J. Phys. C 21, 6207 (1988).
K. Imafukii, I. Ohba and Y. Yamanaka, Phys. Lett. A 204, 329 (1995).
M McClendon and H. Rabitz, Phys. Rev. A 37, 3479 (1988).
E. Nelson, Phys. Rev. 150, 1079 (1966), Quantum Fluctuations (Princeton University Press, Princeton, New Jersey, 1985), and references therein. L. de la Peña, J. Math. Phys. 10, 1620 (1969). L. de la Peña and A.M. Cetto, Found. Phys. 12, 1017 (1982), reprinted in: Quantum, Space and Time: The Quest Continues, A.O. Barut, A. van der Merwe, and J.-P. Vigier, eds. (Cambridge University Press, Cambridge, 1984). F. Guerra, Phys. Rep. 77, 263 (1981).
L. de la Peña and A.M. Cetto, The Quantum Dice. An introduction to stochastic electrodynamics (Kluwer Academic, Dordrecht, 1966), and references therein.
G. García-Calderón and A. Rubio, “Transient effects and delay time in the dynamics of resonant tunneling,” preprint SC96-10, IFUNAM, 1996.
R. Landauer, IBM J.Res.Dev. 32, 306 (1988); A.D. Stone and A. Szafer, IBM J.Res.Dev. 32, 384 (1988).
See, e.g., H. van Houten and C. Beenakker, Phys. Today, July 1996, p. 22, and references therein.
A.M. Cetto and L. de la Peña, in Fundamental Problems in Quantum Physics, M. Ferrero and A. van der Merwe, eds. (Kluwer Academic, Dordrecht, 1995), p. 47; in Chaos—The Interplay Between Stochastic and Deterministic Behaviour, P. Garbaczewski, M. Wolf and A. Weron, eds. (Springer, Berlin, 1996), p. 51.
L. de la Peña and A.M. Cetto, “Dynamical effect of de Broglie waves on quantum particles,” under preparation.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Cetto, A.M., de la Peña, L. (1997). Stochastic Approach to the Tunnel Effect. In: Ferrero, M., van der Merwe, A. (eds) New Developments on Fundamental Problems in Quantum Physics. Fundamental Theories of Physics, vol 81. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5886-2_12
Download citation
DOI: https://doi.org/10.1007/978-94-011-5886-2_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6487-3
Online ISBN: 978-94-011-5886-2
eBook Packages: Springer Book Archive