Correcting the quantum clock: Conditional sojourn times
Raman Research Institute -
C.V. Raman Avenue, Bangalore 560 080, India
Corresponding author: firstname.lastname@example.org
Accepted: 3 September 2002
Can the quantum-mechanical sojourn time be clocked without the clock affecting the sojourn time? Here we re-examine the previously proposed non-unitary clock, involving absorption/amplification by an added infinitesimal imaginary potential , and find it not to preserve, in general, the positivity of the sojourn time, conditional on eventual reflection or transmission. The sojourn time is found to be affected by the scattering concomitant with the mismatch, however small, due to the very clock potential introduced for the purpose, as also by any prompt scattering involving partial waves that have not traversed the region of interest. We propose a formal procedure whereby the sojourn time so clocked can be corrected for these spurious scattering effects. The resulting conditional sojourn times are then positive-definite for an arbitrary potential, and have the proper high- and low-energy limits. We note that such a correction also applies to the Larmor clock and identical results are obtained by applying our procedure in that case as well.
PACS: 03.65.Xp – Tunneling, traversal time, quantum Zeno dynamics / 73.23.-b – Electronic transport in mesoscopic systems
© EDP Sciences, 2002