No abstract

No abstract

We demonstrate that the quantum corrections to the classical arrival time for a quantum object in a potential free region of space, as computed in Phys. Rev. A 80, 030102(R) (2009), can be eliminated up to a given order of by choosing an appropriate position-dependent phase for the object's wave-function This then implies that we can make the quantum arrival time of the object as close as possible to its corresponding classical arrival time, allowing us to synchronize a classical and quantum clock which tells time using the classical and quantum arrival time of the object, respectively . We provide an example for synchronizing such a clock by making use of a quantum object with a position-dependent phase imprinted on the object's initial wave-function with the use of an impulsive potential.

No abstract

The tunneling time problem earlier studied in Phys. Rev. Lett. 108, 170402 (2012) using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous implying that the wavepacket becomes superluminal below the barrier. The non-relativistic treatment raises the question whether the superluminal behavior is a mere non-relativistic phenomenon or an an inherent quantum effect in all energy scales. Here we extend the analysis by constructing a relativistic TOA-operator for spin-0 particles across a square potential barrier by quantizing the corresponding classical quantity, and imposing that the barrier height Vo is less than the rest mass energy. We show that only the above barrier energy components of the incident wavepacket's momentum distribution contribute to the barrier traversal time while the below barrier components are transmitted instantaneously.