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Dwell, Transmission, and Reflection Tunneling Times and their Relationship

Donald H. Kobe, Hisakazu IWAMOTO, Masatoshi Goto, Verissimo Manoel de Aquino, Valdir C. Aguilera-Navarro

Published Mar 1, 2000• 0 citations
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The transmission tunnelling time through a barrier is often defined as the probability that the particle is in the barrier divided by the transmission probability current density. The dwell time, the time the particle stays in the barrier, is commonly defined as the probability that the particle is in the barrier divided by the incident probability current density. We define the reflection tunnelling time in a similar way by dividing the probability that the particle is in the barrier by the reflection current density. By conservation of probability, the reciprocal of the dwell time is equal to the sum of the reciprocals of the transmission and reflection times. This relation is illustrated by calculating the different tunnelling times for a rectangular barrier.

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The transmission tunnelling time through a barrier is often defined as the probability that the particle is in the barrier divided by the transmission probability current density. The dwell time, the time the particle stays in the barrier, is commonly defined as the probability that the particle is in the barrier divided by the incident probability current density. We define the reflection tunnelling time in a similar way by dividing the probability that the particle is in the barrier by the reflection current density. By conservation of probability, the reciprocal of the dwell time is equal to the sum of the reciprocals of the transmission and reflection times. This relation is illustrated by calculating the different tunnelling times for a rectangular barrier.
As was shown in quant-ph/0405028, the state of a tunneling particle can be uniquely presented as a coherent superposition of two states to describe alternative sub-processes, transmission and reflection. In this paper, on the basis of the stationary wave functions for these sub-processes, we give new definitions of the dwell times for transmission and reflection. In the case of rectangular potential barriers the dwell times are obtained explicitly. In contrast with the well-known Büttiker's dwell-time, our dwell time for transmission increases exponentially, for the under-barrier tunneling, with increasing the barrier's width. By our approach the well-known Hartman effect is rather an artifact resulted from an improper interpretation of the wave-packet tunneling and experimental data, but not a real physical effect accompanying the tunneling phenomenon.