The Büttiker-Landauer model generalized

Abstract

Büttiker and Landauer studied scattering off an oscillating rectangular barrier in order to shed light on the time aspects of tunneling. The expression for the traversal time resulting from this study is controversial. In addition, doubts have recently been expressed on technical aspects of their work. In an attempt to clarify these issues, we investigate a generalization of their model to arbitrary oscillating barriers,V(x, t)=V 0(x)+V 1(x)cos ωt. In the process, we confirm that Büttiker and Landauer's work is technically sound. However, we show, by several examples, that no direct general relation exists between the characteristic frequency of an oscillating barrier and the duration of the tunneling process. For a wide range of realistic parameters this characteristic frequency does not even exist.

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This paper is dedicated to E. G. D. Cohen.

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Støvneng, J.A., Hauge, E.H. The Büttiker-Landauer model generalized. J Stat Phys 57, 841–863 (1989). https://doi.org/10.1007/BF01022836

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Key words

  • Tunneling
  • oscillating barriers
  • duration of tunneling
  • characteristic frequency