Times of Arrival and Gauge Invariance

TL;DR

This paper critically examines two quantum arrival-time distributions, highlighting inconsistencies and gauge dependence issues, and compares their properties and limitations in different physical setups.

Contribution

It identifies a flaw in Kijowski's distribution and demonstrates the gauge dependence of the ABK distribution in magnetic fields, providing insights into their foundational differences.

Findings

Kijowski's distribution has negative arrival times.

ABK distribution is gauge-dependent in magnetic fields.

QF distribution remains gauge-invariant despite backflow issues.

Abstract

We revisit the arguments underlying two well-known arrival-time distributions in quantum mechanics, viz., the Aharonov-Bohm and Kijowski (ABK) distribution, applicable for freely moving particles, and the quantum flux (QF) distribution. An inconsistency in the original axiomatic derivation of Kijowski's result is pointed out, along with an inescapable consequence of the "negative arrival times" inherent to this proposal (and generalizations thereof). The ABK free-particle restriction is lifted in a discussion of an explicit arrival-time setup featuring a charged particle moving in a constant magnetic field. A natural generalization of the ABK distribution is in this case shown to be critically gauge-dependent. A direct comparison to the QF distribution, which does not exhibit this flaw, is drawn (its acknowledged drawback concerning the quantum backflow effect notwithstanding).