Detection Time Distribution Predicted Using Absorbing Boundary Conditions and Imaginary Potentials

TL;DR

This paper compares two theoretical methods for predicting the detection time distribution of a quantum particle, revealing effects like wave reflection and spin dependence, and contrasts these with alternative proposals.

Contribution

It provides explicit calculations of detection time distributions using absorbing boundary conditions and imaginary potentials for particles in a wave guide, highlighting their differences and similarities.

Findings

Distribution shows partial wave reflection off the detector

Spin-1/2 distribution is independent of initial spin orientation

Distribution depends on wave guide width for certain boundary conditions

Abstract

There are several inequivalent proposals in the literature for how to compute the probability distribution of the time that a detector registers for the arrival of a quantum particle. For two of these proposals, based on absorbing boundary conditions and imaginary potentials, we compute the predicted distribution for an experimental setup involving a single non-relativistic quantum particle with spin 0 or 1/2 in a wave guide along the $z$ axis with the detector waiting downstream. We find that the distribution shows signs of partial reflection of the wave function off of the detector; for a spin-1/2 wave function, it is independent of the initial spin orientation but does depend, for boundary conditions coupling to the spin, on the width of the wave guide. We also compare our predictions with the competing ones of Das and D\"urr [arXiv:1802.07141].