Time-of-arrival distributions for interaction potentials

Abstract

Several proposals for a time-of-arrival distribution of ensembles of independent quantum particles subject to an external interaction potential are compared making use of the "crossing state" concept. It is shown that only one of them has the properties expected for a classical distribution in the classical limit. The comparison is illustrated numerically with a collision of a Gaussian wave packet with an opaque square barrier.

Manufacturing time operators: Covariance, selection criteria, and examples

“…On the theory side, an open question is how to adapt the proposed framework, possibly in combination with previous investigations [18][19][20][22][23][24][25], to arrival times when a particle moves in a potential.…”

Measurement-based approach to quantum arrival times

“…In this vein, several "toy models" for arrival-time measurements have been put forward by Aharonov, Oppenheim, Reznik, Popescu and Unruh [15] (cf. also [1,16]), but these models do not incorporate the basic irreversibility inherent in any measurement process. Irreversibility has been included by Halliwell [17] in a model based on a two-level detector in which the initial excited level decays due to the presence of the particle.…”

Explicit solution for a Gaussian wave packet impinging on a square barrier

“…|ψ(p, t)| 2 as a function of momentum at t = 5 a.u., when the collision has been completed. The solid line corresponds to the exact solution, whereas the dots correspond to the reflection and transmission (structural) terms and three resonance pole terms from (21). Atomic units are used in all the calculations, and m = 1. p c = 20, d = 2.5, V 0 = 188, δ x = 100 and x c is located 50 atomic units to the left of the center of the barrier potential.…”

“…It is also used as a standard model to check the validity of approximate numerical methods [18,19], or to exemplify and test different theories for temporal quantities such as arrival, dwell, or decay times, the asymptotic behaviour at long times [20,21,22], and quantum transition state theories [23].…”