For the special case of freely evolving Dirac electrons in $(1+1)$ dimensions, Feynman checkerboard paths have previously been used to derive Wigner's arrival-time distribution which includes all arrivals. Here, an attempt is made to use these paths to determine the corresponding distribution of first-arrival times. Simple analytic expressions are obtained for the relevant components of the first-arrival propagator. These are used to investigate the relative importance of the first-arrival contribution to the Wigner arrival-time distribution and of the contribution arising from interference between first and later (i.e., second, third, etc.) arrivals. It is found that a distribution of (intrinsic) first-arrival times for a Dirac electron cannot in general be consistently defined using checkerboard paths, not even approximately in the nonrelativistic regime.For the special case of freely evolving Dirac electrons in $(1+1)$ dimensions, Feynman checkerboard paths have previously been used to derive Wigner's arrival-time distribution which includes all arrivals. Here, an attempt is made to use these paths to determine the corresponding distribution of first-arrival times. Simple analytic expressions are obtained for the relevant components of the first-arrival propagator. These are used to investigate the relative importance of the first-arrival contribution to the Wigner arrival-time distribution and of the contribution arising from interference between first and later (i.e., second, third, etc.) arrivals. It is found that a distribution of (intrinsic) first-arrival times for a Dirac electron cannot in general be consistently defined using checkerboard paths, not even approximately in the nonrelativistic regime.

arXiv:quant-ph/0206071Physical Review AOct 15, 20024 citations

Positive Time‚ÄìFrequency Distributions

Leon W. Cohen, Patrick J. Loughlin

Electrical engineering and applied signal processing series/The electrical engineering and applied signal processing seriesOct 29, 20021 citation

The arrival-time distribution: the extended probability approaches

Sutee Boonchui, Artit Hutem

We present a calculation of the arrival-time probability distribution based on the extended probability, as proposed by Hartle (2008 Phys. Rev. A 78 012108). We show that two cases of the arrival-time probability distribution can be used. First, we use the path decomposition expansion to discuss a fine-grained history, for which a particle has a first crossing x = 0 at time τ. The arrival-time probability, related to the probability current, is obtained. Second, we consider that the arrival-time distribution is modeled by the first photon emitted from a two-level atom (the basic atom–laser model). The partition dynamic of this system is discussed. Each history is in the form of a coarse-grained history. We confirm that the arrival-time probability distribution computed by this method agrees with that computed via the probability of no-photon detection. Crucially, the resulting arrival-time distributions can be obtained without the restriction of the consistency condition.We present a calculation of the arrival-time probability distribution based on the extended probability, as proposed by Hartle (2008 Phys. Rev. A 78 012108). We show that two cases of the arrival-time probability distribution can be used. First, we use the path decomposition expansion to discuss a fine-grained history, for which a particle has a first crossing x = 0 at time τ. The arrival-time probability, related to the probability current, is obtained. Second, we consider that the arrival-time distribution is modeled by the first photon emitted from a two-level atom (the basic atom–laser model). The partition dynamic of this system is discussed. Each history is in the form of a coarse-grained history. We confirm that the arrival-time probability distribution computed by this method agrees with that computed via the probability of no-photon detection. Crucially, the resulting arrival-time distributions can be obtained without the restriction of the consistency condition.

Journal of Physics A Mathematical and TheoreticalFeb 21, 20134 citations

Transition from discrete to continuous time-of-arrival distribution for a quantum particle

Eric A. Galapon, F.S. Delgado, Juan Gonzalo Muga +1 more

We show that the Kijowski distribution for time of arrivals in the entire real line is the limiting distribution of the time-of-arrival distribution in a confining box as its length increases to infinity. The dynamics of the confined time-of-arrival eigenfunctions is also numerically investigated and demonstrated that the eigenfunctions evolve to have point supports at the arrival point at their respective eigenvalues in the limit of arbitrarily large confining lengths, giving insight into the ideal physical content of the Kijowsky distribution.We show that the Kijowski distribution for time of arrivals in the entire real line is the limiting distribution of the time-of-arrival distribution in a confining box as its length increases to infinity. The dynamics of the confined time-of-arrival eigenfunctions is also numerically investigated and demonstrated that the eigenfunctions evolve to have point supports at the arrival point at their respective eigenvalues in the limit of arbitrarily large confining lengths, giving insight into the ideal physical content of the Kijowsky distribution.

arXiv:quant-ph/0510081Physical Review AOct 18, 200556 citations

For the special case of freely evolving Dirac electrons in

(1+1)

dimensions, Feynman checkerboard paths have previously been used to derive Wigner's arrival-time distribution which includes all arrivals. Here, an attempt is made to use these paths to determine the corresponding distribution of first-arrival times. Simple analytic expressions are obtained for the relevant components of the first-arrival propagator. These are used to investigate the relative importance of the first-arrival contribution to the Wigner arrival-time distribution and of the contribution arising from interference between first and later (i.e., second, third, etc.) arrivals. It is found that a distribution of (intrinsic) first-arrival times for a Dirac electron cannot in general be consistently defined using checkerboard paths, not even approximately in the nonrelativistic regime.