Abstract
A brief critical surveyis given of the main approaches to the tunneling time problem: when a particle has tunneled through a one-dimensional barrier, how long did it take to cross it? A new approach, based on Faddeev’s formulation of onedimensional scattering and on the evaluation of the average dwell time for an arbitrary wave packet, indicates that the problem is ill-posed. Furthermore, observations of apparent superluminal propagation do not violate causality.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. H. Hauge and J. A. Støvneng: Rev. Mod. Phys. 61, 917 (1989); R. Landauer and Th. Martin, Rev. Mod. Phys. 66, 217 (1994); R. Y. Chiao and A. M. Steinberg, in: Progress in Optics, ed. by E. Wolf (Elsevier, Amsterdam, 1997), vol. 37, p. 345.
H. M. Nussenzveig: Phys. Rev. A 62, 042107–1 (2000).
H. Lamb: Hydrodynamics, 6th edn.(Cambridge University Press, Cambridge 1953), p. 395.
Wigner, E. P., 1955 Phys. Rev. 98, 145.
T. E. Hartman: J. Appl. Phys. 33, 3427 (1962).
R. Landauer and Th. Martin: Solid State Commun. 84, 115 (1992).
R. C. T. da Costa: J. Math. Phys. 11, 2799 (1970).
A. I. Baz, Yad. Fiz. 4, 252 (1967) [Sov. J. Nucl. Phys. 4, 229 (1967)]; V. F. Rybachenko, ibid. 5, 895 (1967) [ibid. 5, 635 (1967)].
M. BĂĽttiker: Phys. Rev. B 27, 6178 (1983).
R. Landauer and Th. Martin, Rev. Mod. Phys. 66, 217 (1994).
F. T. Smith: Phys. Rev. 118, 349 (1960).
H. M. Nussenzveig: Phys. Rev. 177, 1848 (1969).
M. BĂĽttiker and R. Landauer: Phys. Rev. Lett. 49, 1739 (1982).
M. BĂĽttiker and R. Landauer: Phys. Scr. 32, 429 (1985).
Y. Aharonov, D. Z. Albert and L. Vaidman: Phys. Rev. Lett. 60, 1351 (1988).
Y. Aharonov and L. Vaidman: Phys. Rev. A 14, 11 (1990).
A. M. Steinberg: Phys. Rev. Lett. 74, 2405 (1995).
D. Sokolovski and L. M. Baskin: Phys. Rev. A 36, 4604 (1987).
H. A. Fertig: Phys. Rev. Lett. 65, 2321 (1990).
N. Yamada: Phys. Rev. Lett. 83, 3350 (1999).
C. R. Leavens and G. C. Aers, in: Scanning Tunneling Microscopy III, eds. R. Wiesendanger and H. J. GĂĽntherodt (Springer, New York, 1993), p. 105.
H. M. Nussenzveig: Phys. Rev. D 6, 1534 (1972).
M. Froissart, M. L. Goldberger and K. M. Watson: Phys. Rev. 131, (1963).
H. M. Nussenzveig: Phys. Rev. A 55, 1012 (1997).
L. D. Faddeev: Trudy Mat. Inst. Steklov 73, 314 (1964) [Am. Math. Soc. Transl. 2, 139 (1964)]; K. Chadan and P. C. Sabatier: Inverse Problems in Quantum Scattering Theory, 2nd. ed. (Springer, New York, 1989).
E. H. Hauge, J. P. Falck and T. A. Fjeldly: Phys. Rev. B 36, 4203 (1987).
G. Iannaconne, in: Tunneling and its Implications, ed. by D. Mugnai, A. Ranfagni and L. S. Schulman (World Scientific, Singapore, 1997), p. 292.
N. G. van Kampen: Phys. Rev. 91, 1267 (1953).
Y. Z. Huang and C. M. Wang: J. Phys. Condens. Matter 3, 5915 (1991).
J. Friedel: Philos. Mag. 43, 153 (1952). R. Balian and C. Bloch: Ann. Phys. (N.Y.) 85, 514 (1974).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nussenzweig, H. (2001). Time Delay and Tunneling. In: Orszag, M., Retamal, J.C. (eds) Modern Challenges in Quantum Optics. Lecture Notes in Physics, vol 575. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45409-8_15
Download citation
DOI: https://doi.org/10.1007/3-540-45409-8_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41957-0
Online ISBN: 978-3-540-45409-0
eBook Packages: Springer Book Archive