Clocking the Quantum Sojourn Time: Spurious Scatterings and Correction to the Larmor Clock

Abstract: We revisit the notions of the quantum-mechanical sojourn time in the context of the quantum clocks to enquire whether the sojourn time be clocked without the clock affecting the dynamics of the wave motion. Upon recognizing that the positivity of conditional sojourn time is not ensured even in the case of physically co-evolving clock mechanisms, we trace its origins to the non-trivial inadvertent scattering arising from the disparity, however weak, engendered by the very clock potential. Specifically, our investigations focus on the Larmor spin rotation-based unitary clock where the alleviation of these unphysical contributions has been achieved by correcting the mathematical apparatus of extracting the sojourn times. The corrections have been obtained for both the spin precession-based and spin alignment-based scenarios. The sojourn times so obtained are found to have proper high- and low-energy limits and turn out to be positive definite for an arbitrary potential. The regimen provided here is general and appeals equivalently for unitary as well as non-unitary clocks where the clock-induced perturbations couple to the system Hamiltonian.