Thursday, April 1, 2010

Defining a tunneling time

The question of how long it takes a quantum particle to tunnel through a potential barrier has attracted considerable interest and controversy since the early days of quantum mechanics.
It is possible to define four different time scales (Larmor, Buttiker-Landauer, Bohm-Wigner, and Pollak-Miller) in terms of different derivatives of the transmission amplitude and phase.
The four different timescales are based on four different physical interpretations, and
were all derived in a unified manner by Yamada in a PRL (which also contains some background references).

The Pollak-Miller tunneling time is defined as the derivative of the transmission amplitude with respect to energy and also equals the period of the solution to the imaginary time version of the classical equations of motion, which I discussed in an earlier post about quantum reaction rate theory.
This time can also be viewed as the lifetime of the instanton associated with tunneling.

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