Tunneling times with covariant measurements

J. Kiukas*, A. Ruschhaupt, R. F. Werner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (SciVal)


We consider the time delay of massive, non-relativistic, one-dimensional particles due to a tunneling potential. In this setting the well-known Hartman effect asserts that often the sub-ensemble of particles going through the tunnel seems to cross the tunnel region instantaneously. An obstacle to the utilization of this effect for getting faster signals is the exponential damping by the tunnel, so there seems to be a trade-off between speedup and intensity. In this paper we prove that this trade-off is never in favor of faster signals: the probability for a signal to reach its destination before some deadline is always reduced by the tunnel, for arbitrary incoming states, arbitrary positive and compactly supported tunnel potentials, and arbitrary detectors. More specifically, we show this for several different ways to define "the same incoming state" and "the same detector" when comparing the settings with and without tunnel potential. The arrival time measurements are expressed in the time-covariant approach, but we also allow the detection to be a localization measurement at a later time.

Original languageEnglish
Pages (from-to)829-846
Number of pages18
JournalFoundations of Physics
Issue number7
Early online date31 Jan 2009
Publication statusPublished - 01 Jul 2009
Externally publishedYes


  • Arrival time
  • Hartman effect
  • Tunneling


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